Daily Papers

How fast does a language model degrade when trained on its own outputs? Theory traces it to gradually accumulating errors, while experiments report repeated phrases within ten generations. Under a fixed sampling seed in vLLM, the fast loss of lexical diversity comes from the sampler. When vLLM serves a batch from one seeded sampling configuration, every request receives the same random draws, and a fixed seed replays them every generation. Fine-tuning raises the tokens that won, and the replayed draws let them win by more. Sharing across requests and replay across generations matter only together. Remove either one, by changing the shared seed every generation or by giving each request its own seed that repeats every generation, and the unique-4-gram fraction of two StableLM checkpoints stays near its starting value of about 0.98 through generation 3. Keep both, and the replayed shared seed takes seven checkpoints from five families to between 0.045 and 0.38 by then. Three generations of replay write the favoured phrases into the weights: decoded with one seed per request, the generation-3 weights of the replayed StableLM-2-1.6B chain recover most of their diversity, yet the phrase that filled every sample under the shared seed still opens 46% of them. Without replay, five checkpoints drift slowly, consistent with the gradual accumulation that theory describes, and three turn incoherent though their diversity scores stay high. One peer-reviewed model-collapse pipeline that fine-tunes Gemma-2-27B samples identical prompts under one seeded configuration, and three quarters of the rows it released for one iteration repeat nearly as often as one such batch copies them. A seed per request restores the fresh sample that stability analyses assume.

We propose a hybrid framework that combines deep learning with adaptive filtering for acoustic echo cancellation (AEC) and suppression. It integrates a multi-output neural network to jointly update filter parameters and perform post-processing. A learnable variant of the normalized least mean squares (NLMS) filter is introduced, incorporating a variable step size and a variable transition factor that are recursively updated for dynamic adaptation. In addition, an enhanced near-end speech estimate is generated from the filter output to suppress the residual echoes. To ensure training stability, we propose a constrained recursive training strategy that aligns with the adaptive nature of the filter, where an upper-bound constraint is introduced on the filter output. For efficiency, the framework adopts a lightweight implementation with only 253 k parameters. Experimental results show that the framework outperforms the baselines in terms of both signal quality and speech intelligibility.

Recursive or looped language models have recently emerged as a new scaling axis by iteratively refining the same model computation over latent states to deepen reasoning. We extend such scaling principle from a single model to multi-agent systems, and ask: Can agent collaboration itself be scaled through recursion? To this end, we introduce RecursiveMAS, a recursive multi-agent framework that casts the entire system as a unified latent-space recursive computation. RecursiveMAS connects heterogeneous agents as a collaboration loop through the lightweight RecursiveLink module, enabling in-distribution latent thoughts generation and cross-agent latent state transfer. To optimize our framework, we develop an inner-outer loop learning algorithm for iterative whole-system co-optimization through shared gradient-based credit assignment across recursion rounds. Theoretical analyses of runtime complexity and learning dynamics establish that RecursiveMAS is more efficient than standard text-based MAS and maintains stable gradients during recursive training. Empirically, we instantiate RecursiveMAS under 4 representative agent collaboration patterns and evaluate across 9 benchmarks spanning mathematics, science, medicine, search, and code generation. In comparison with advanced single/multi-agent and recursive computation baselines, RecursiveMAS consistently delivers an average accuracy improvement of 8.3%, together with 1.2times-2.4times end-to-end inference speedup, and 34.6%-75.6% token usage reduction. Code and Data are provided in https://recursivemas.github.io.

Generative Artificial Intelligence image models have achieved outstanding performance in text-to-image generation and other tasks, such as inpainting that completes images with missing fragments. The performance of inpainting can be accurately measured by taking an image, removing some fragments, performing the inpainting to restore them, and comparing the results with the original image. Interestingly, inpainting can also be applied recursively, starting from an image, removing some parts, applying inpainting to reconstruct the image, and then starting the inpainting process again on the reconstructed image, and so forth. This process of recursively applying inpainting can lead to an image that is similar or completely different from the original one, depending on the fragments that are removed and the ability of the model to reconstruct them. Intuitively, stability, understood as the capability to recover an image that is similar to the original one even after many recursive inpainting operations, is a desirable feature and can be used as an additional performance metric for inpainting. The concept of stability is also being studied in the context of recursive training of generative AI models with their own data. Recursive inpainting is an inference-only recursive process whose understanding may complement ongoing efforts to study the behavior of generative AI models under training recursion. In this paper, the impact of recursive inpainting is studied for one of the most widely used image models: Stable Diffusion. The results show that recursive inpainting can lead to image collapse, so ending with a nonmeaningful image, and that the outcome depends on several factors such as the type of image, the size of the inpainting masks, and the number of iterations.

Large language models (LLMs) increasingly participate in scientific evaluation, both as automated reviewers and as assistants to human reviewers. As model-generated reviews enter public data and future training corpora, AI peer review can become recursive: later reviewers learn from judgments produced by earlier models. We study one step of this feedback loop in a controlled setting. Starting from Llama 3.1 8B, we first fine-tune a reviewer on official ICLR reviews from 2018--2023 and then train four successor models on ICLR 2024 data with systematically varied mixtures of official and model-generated reviews. Our study shows that introducing synthetic reviews compresses rating distributions and reduces both same-paper and corpus-level semantic diversity. We call this pattern scientific-judgment collapse. To mitigate this failure mode, we introduce TrustReviewer, an open-source LLM-based system for generating peer reviews of AI and machine learning papers. TrustReviewer intervenes at two complementary stages. For training-time prevention, we train the core reviewer in a single stage on a curated corpus designed to reduce low-quality and semantically degenerate supervision. For test-time correction, paired activation steering aims to further mitigate residual tendencies toward collapsed judgments without further training or additional expert annotation. Together, these results characterize a concrete risk of recursive reviewer training and provide practical interventions for preserving judgment diversity and improving recommendation alignment in AI-assisted scientific evaluation.

Recursive retraining of generative models poses a critical representation challenge: when synthetic outputs are curated based on a fixed reward signal, the model tends to collapse onto a narrow set of outputs that over-optimize that objective. Prior work suggests that such collapse is unavoidable without adding real data into the mix. We revisit this conclusion from an alignment perspective and show that collapse can be mitigated through curation based on multiple reward functions. We formalize the dynamics of recursive training under heterogeneous preferences and prove that, under certain conditions, the model converges to a stable distribution that allocates probability mass across competing high-reward regions. The limiting distribution preserves diversity and provably satisfies a weighted Nash bargaining solution, offering a formal interpretation of value aggregation in synthetic retraining loops.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

Generative models trained on artificially generated data have been shown to exhibit model collapse, resulting in significant performance degradation. As synthetic content increasingly contaminates the training corpora of language models, this raises critical concerns about the use of open data in continued pretraining. Although previous work has demonstrated model collapse in language models, it remains unclear whether exposure to synthetic data amplifies or attenuates the social biases already present in pretrained models. Because language models are known to reproduce and amplify demographic stereotypes, recursive training on self-generated data may create a self-reinforcing feedback loop in which biased associations become progressively stronger across generations. We call this hypothesized phenomenon fairness collapse. In this work, we construct controlled training regimes in which models are repeatedly trained on synthetic data using the Bias in Bios dataset. Across experiments, we observe a consistent and concerning pattern: fairness degradation emerges before substantial degradation is reflected by standard language-modeling metrics. This result highlights a critical risk associated with synthetic data contamination in language model training: bias can increase silently before strong indicators of model collapse become apparent.

Repeated training on model-generated data can degrade later models. One possible response is to use provenance when deciding which generated examples to reuse. We test both how reliably that provenance can be recovered and whether it helps identify better training data. Using financial-risk text, we first identify the source of generated passages and then repeat the test after rewriting them. Generator attribution is 98.7% accurate on the original passages but falls to 53.1% after paraphrasing and 29.0% after style rewriting. Generated-versus-human detection remains close to perfect against the tested human comparison set. We then compare two ways of selecting generated examples over three rounds of generation and retraining. One uses source information. The other uses a score from a separate reference model. The two rules select different examples, but the planned comparison does not detect a stable difference in the degradation of the resulting models. The results show that identifying where data came from and identifying which data are useful for training are separate problems. The experiment therefore separates source identity, criterion-facing selection, and recursive training outcome: neither the provenance score nor the tested criterion-facing proxy is established as sufficient for future recursive behaviour.

Numerical weather prediction has long been constrained by the computational bottlenecks inherent in data assimilation and numerical modeling. While machine learning has accelerated forecasting, existing models largely serve as "emulators of reanalysis products," thereby retaining their systematic biases and operational latencies. Here, we present FuXiWeather2, a unified end-to-end neural framework for assimilation and forecasting. We align training objectives directly with a combination of real-world observations and reanalysis data, enabling the framework to effectively rectify inherent errors within reanalysis products. To address the distribution shift between NWP-derived background inputs during training and self-generated backgrounds during deployment, we introduce a recursive unrolling training method to enhance the precision and stability of analysis generation. Furthermore, our model is trained on a hybrid dataset of raw and simulated observations to mitigate the impact of observational distribution inconsistency. FuXiWeather2 generates high-resolution (0.25^{circ}) global analysis fields and 10-day forecasts within minutes. The analysis fields surpass the NCEP-GFS across most variables and demonstrate superior accuracy over both ERA5 and the ECMWF-HRES system in lower-tropospheric and surface variables. These high-quality analysis fields drive deterministic forecasts that exceed the skill of the HRES system in 91\% of evaluated metrics. Additionally, its outstanding performance in typhoon track prediction underscores its practical value for rapid response to extreme weather events. The FuXiWeather2 analysis dataset is available at https://doi.org/10.5281/zenodo.18872728.

We introduce Recursive Agent Optimization (RAO), a reinforcement learning approach for training recursive agents: agents that can spawn and delegate sub-tasks to new instantiations of themselves recursively. Recursive agents implement an inference-time scaling algorithm that naturally allows agents to scale to longer contexts and generalize to more difficult problems via divide-and-conquer. RAO provides a method to train models to best take advantage of such recursive inference, teaching agents when and how to delegate and communicate. We find that recursive agents trained in this way enjoy better training efficiency, can scale to tasks that go beyond the model's context window, generalize to tasks much harder than the ones the agent was trained on, and can enjoy reduced wall-clock time compared to single-agent systems.

Background: Recursive reasoning models achieve strong performance through iterative refinement, allowing small networks to match large language models. However, training is computationally expensive, often requiring 36 GPU-hours for Sudoku extreme. Existing models use fixed recursion depth and uniform supervision weighting, leading to inefficient training. Objectives: We propose CGAR (Curriculum-Guided Adaptive Recursion), applying curriculum learning to architectural depth. CGAR introduces Progressive Depth Curriculum (PDC) to dynamically adjust recursion depth and Hierarchical Supervision Weighting (HSW) to apply exponentially decaying importance to supervision steps. Methods: PDC implements a three-stage schedule transitioning from shallow (2, 1) to full depth (6, 3) configurations, providing 41.4% FLOPs reduction. HSW applies exponential decay to supervision steps, achieving 40% gradient variance reduction and accelerated convergence. Results: On Sudoku-Extreme, CGAR achieves 1.71x training speedup (10.93 to 6.38 hours) with only a 0.63% accuracy drop (86.65% to 86.02%). PDC alone achieves 2.26x speedup with 85.47% accuracy, showing a Pareto improvement in efficiency and quality. HSW provides 1.61x speedup. CGAR-trained models show superior inference efficiency with 100% halting accuracy and 11% fewer reasoning steps. Conclusions: CGAR enables efficient training of recursive models on modest hardware. By treating depth as a scheduled parameter, it achieves substantial savings and prevents overfitting, making these models practical for neurosymbolic AI and program synthesis. https://github.com/Kaleemullahqasim/CGAR and huggingface.co/Kaleemullah/trm-cgar-sudoku.

Scaling interactive environments is important for training long-horizon agents through reinforcement learning. These environments often require further testing and refinement after initial generation, and correcting defects in a task may also require updating its work context and verifier. However, existing construction pipelines offer limited support for such iterative refinement while keeping these components aligned. We introduce WorkRover, a framework for training long-horizon cowork agents through recursive environment evolution. Its harness-driven synthesis enables construction agents to jointly build and validate semantically aligned work contexts, executable tasks, and evidence-grounded verifiers, adapting their actions to workspace state and execution feedback rather than following a fixed construction workflow. To support environment evolution, we introduce Factorial Compatibility Replay (FCR), which uses rollout feedback to evaluate combinations of component revisions through dependency-closed replay and selects the smallest validated repair among tested candidates while preserving task requirements and evaluation constraints. To provide finer-grained training signals, we propose Verifier-to-Turn Credit Assignment (VTCA), which augments trajectory-level GRPO advantages with signals from deterministic workspace-progress checks and assigns a bounded share of positive-progress credit to prerequisite turns using recorded tool-output and artifact dependencies. Using WorkRover, we post-train Qwen3.5-35B-A3B to obtain WorkRover-35B-A3B and evaluate it on several cowork-agent benchmarks. Its reported scores exceed those of Qwen3.5-35B-A3B by 26.27 percentage points on JobBench, 29.32 percentage points on OfficeQA Pro, and 413.25 Elo points on GDPval v2. These results suggest that WorkRover offers a promising foundation for scalable training of long-horizon cowork agents.

Recursive synthetic-data training can degrade a fitted model, but its effects on the variable-screening stage that precedes model fitting are less understood. When each generation labels data for the next, a marginal screener ranks variables against the current pseudo-label target rather than the original response. Across generations, this target drift can erode or reverse the active--inactive score margin and cause screening to discard variables that clean-label screening would retain. We call this process screening collapse. In a Gaussian linear model with minimum-norm recursive generators, we establish finite-sample screening bounds, characterize a late-generation information-loss limit, and derive a minimax impossibility result. Screening collapse can precede and compound ordinary model collapse: omitted variables incur a covariance-weighted loss that no refit restricted to the selected variables can eliminate, while recursive labels further degrade estimation on the retained variables. We also examine two approaches to mitigating screening collapse. Fixed-fraction real-label retention preserves a clean-label component but leaves resolution fixed, whereas data accumulation can avoid screening collapse if the pooled target preserves a positive margin and the growing sample resolves it. Numerical experiments on gene-expression data support the theoretical findings.

People often tackle difficult problems by thinking more deeply or exploring more possibilities. Similarly, recursive reasoners, which reason by repeatedly applying a learned update rule to latent states, can also scale inference through more updates (depth) or additional trajectories generated by perturbing latent states (width). When people hit a dead end in their thinking, they may step back and approach the problem from a fresh angle. However, neither depth scaling nor perturbation-based width scaling of recursive reasoners can reliably achieve this: both may converge to incorrect attractors. To address this, we propose to explore diverse reasoning traces by applying different update maps to the same latent state, without any additional training. We realize this idea through Input-Conditioned Search (ICS), which searches over input conditions to induce alternative update maps from the pretrained reasoner. Across six reasoning tasks, ICS achieves the highest mean accuracy, while requiring up to two orders of magnitude fewer model FLOPs than the evaluated scaling baselines. Controlled experiments confirm that ICS can redirect trajectories from the same state. Our theoretical analysis and rigorous numerical verification also confirm that ICS can locally eliminate incorrect attracting fixed points. Together, these findings establish ICS as an effective axis for efficient test-time scaling and motivate further research on shaping recursive reasoning during training and at test time.

Recursive self-improvement (RSI) requires AI systems that improve the process of building AI (i.e., AI4AI); machine learning engineering (MLE) offers a concrete, executable testbed for studying this capability. We introduce OpenMLE, an open full-stack system for RSI research in MLE, spanning verifiable task environments with execution feedback (OpenMLE-Gym), operator learning (OpenMLE-RL), and long-horizon search (OpenMLE-Evo). On this stack we post-train Frontis-MA1 (35B) as a meta-evolution agent for MLE, aligning post-training and inference around four atomic program-evolution operators (Draft, Improve, Debug, Crossover): the same operators are trained via execution-grounded SFT and RL on data deduplicated against all evaluation benchmarks, then composed into long-horizon search, coupling learning and evolution in a single loop. On MLE-Bench Lite under a 12-hour per-task budget on one RTX 4090 capped at 12 GB VRAM, Frontis-MA1 (35B) improves Medal Average from 39.39% to 60.61% over its base model with OpenMLE-Evo, and reaches 71.21% with OpenMLE-Evo-Max (benchmark-independent experience priors and asynchronous search), exceeding GPT-5.5 + Codex and approaching GPT-5.6 Sol and the 2.8T Kimi K3. On held-out NatureBench Lite, both components transfer: with the framework fixed, swapping in the trained model raises Match-SOTA from 50% to 70%; with the model fixed, swapping in OpenMLE-Evo raises it from 20% to 50%. We release the model weights and the full OpenMLE stack to enable reproducible research on executable AI4AI toward RSI. Code: https://github.com/FrontisAI/OpenRSI

Recursive self-improvement (RSI) requires a concrete mechanism through which an AI system observes its capabilities and converts that evidence into the next round of learning. We present NeoHorse-1, a family of agent-native models developed to explore this path through agentic post-training. Our system combines a heterogeneous model pool with intelligent routing, recording the predicted capability demand, selected service tier, and subsequent interaction for each user turn. These records are converted into training examples that preserve interleaved reasoning, tool calls, and harness context, and are admitted through structural validation, six-dimensional semantic evaluation, and subscene-level labeling. Routing signals organize supervised fine-tuning into a three-stage curriculum and extend to routing-guided on-policy distillation, where a teacher supervises student-generated responses under the same progression. Capability-guided allocation then converts evaluation feedback into the next training mixture, closing an evaluation-selection-update loop in which what the system learns to do shapes what it learns from next. Across eleven benchmarks covering harness-based agents, tool use, coding, and instruction following, post-training raises the macro-average from 58.94 to 64.87 at 4B and from 65.60 to 69.04 at 9B, substantially narrowing the aggregate gap between the post-trained 4B model and the 9B base model. NeoHorse-1 provides an initial prototype of this feedback-driven process and a path toward harness-mediated RSI across successive iterations.

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general syntax of structural recursion, coupled with two different frameworks for understanding their semantics -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.

High-quality long-horizon training data for terminal agents is expensive to produce, often costing hundreds to thousands of dollars per task, because each task must keep the instruction, environment, reference solution, and verifier mutually consistent. Human authoring does not scale, and direct generation with large language models (LLMs) often breaks these dependencies. We present Recursive Synthetic Terminal Tasks (RST), a recursive verified synthesis framework for constructing long-horizon terminal-agent tasks at scale. Starting from verified seed tasks, RST extends the reference solution, realigns the verifier and instruction to the new workflow, validates the result in a fresh sandbox, and reuses accepted tasks as seeds for subsequent rounds. Across fifteen recursive rounds, RST produces 37,484 synthesized terminal-agent tasks at roughly $0.05 per task. Task difficulty increases substantially over rounds: the median reference solution grows from 67 to 374 lines, the median number of executed commands grows from 40 to 244, and DeepSeek-V4-Pro pass@4 drops from 90% at R1 to 2.5% at R15. To demonstrate training utility, we collect rejection-sampled Qwen3.5 trajectories on the synthesized tasks and use them for supervised fine-tuning. Fine-tuning on these trajectories improves Qwen3.5-27B and Qwen3.5-122B-A10B by up to 10 points on Terminal-Bench 2, Terminal-Bench Hard, and Long-Horizon Terminal Bench, while agentic PPO lifts Qwen3.5-27B to 49.44%, 32.00%, and 22.07% on the three benchmarks, corresponding to relative gains of 20.0%, 41.2%, and 21.9% over the base model. Moreover, after 15 rounds, the recursion shows no ceiling: synthesis yield and validation rates remain stable as difficulty keeps climbing, indicating that the process can continue well beyond the scale reported here.

Recursive language-model agents decompose tasks and delegate subtasks to child instances of the same policy, forming a tree of work. Training them, however, is hard: the final outcome is verifiable, but the self-invented intermediate subtasks are numerous and carry no ground truth. Existing methods score each node with a verifier or judge, which is costly at scale and blind to decomposition quality. We argue that a recursive agent must learn three coupled capabilities within one set of weights: decomposing problems into subtasks, solving them, and evaluating the outcomes, each requiring its own training signal. SERA (Self-Evaluating Recursive Agents) turns evaluation into a learned capability of the policy itself. Before delegating, the parent writes a rubric of weighted success criteria for each child subtask; a ranking objective against verified outcomes then trains rubric generation so that the criteria track genuine subtask success. In addition, a complementary leaf-coverage signal provides direct credit for task decomposition. Our central finding is that training the policy to generate aligned rubrics is what drives the gains: because the same weights both evaluate and execute, learning to judge subtasks sharpens the agent's ability to solve them. Notably, external supervision is also reduced: the judge is consulted only to train the rubric generator, while solving is trained against the agent's own rubric scores, which outperform direct use of the judge. Beyond training, the learned rubric doubles as an inference-time selector for tree search. On TextCraft-Synth and TextWorld-Sync, SERA improves over strong recursive-agent baselines by 5.38 and 13.14 points on average, and rubric-guided tree search at inference adds a further 2.43 points on TextWorld-Sync.

PRefLexOR (Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning) combines preference optimization with concepts from Reinforcement Learning to enable models to self-teach through iterative reasoning improvements. We propose a recursive learning approach that engages the model in multi-step reasoning, revisiting, and refining intermediate steps before producing a final output in training and inference phases. Through multiple training stages, the model first learns to align its reasoning with accurate decision paths by optimizing the log odds between preferred and non-preferred responses. During this process, PRefLexOR builds a dynamic knowledge graph by generating questions from random text chunks and retrieval-augmentation to contextualize relevant details from the entire training corpus. In the second stage, preference optimization enhances model performance by using rejection sampling to fine-tune reasoning quality by continually producing in-situ training data while masking the reasoning steps. Recursive optimization within a thinking token framework introduces iterative feedback loops, where the model refines reasoning, achieving deeper coherence, consistency, and adaptability. Implemented in small language models with only 3 billion parameters, we should that even tiny models can iteratively teach themselves to reason with greater depth and reflectivity. Our implementation is straightforward and can be incorporated into any existing pretrained LLM. We focus our examples on applications in biological materials science and demonstrate the method in a variety of case studies that range from in-domain to cross-domain applications. Using reasoning strategies that include thinking and reflection modalities we build a multi-agent recursive self-improving inference approach to successively improve responses via repeated sampling in inference time.

Large language models (LLMs) excel at retrieving information from lengthy text, but their vision-language counterparts (VLMs) face difficulties with hour-long videos, especially for temporal grounding. Specifically, these VLMs are constrained by frame limitations, often losing essential temporal details needed for accurate event localization in extended video content. We propose ReVisionLLM, a recursive vision-language model designed to locate events in hour-long videos. Inspired by human search strategies, our model initially targets broad segments of interest, progressively revising its focus to pinpoint exact temporal boundaries. Our model can seamlessly handle videos of vastly different lengths, from minutes to hours. We also introduce a hierarchical training strategy that starts with short clips to capture distinct events and progressively extends to longer videos. To our knowledge, ReVisionLLM is the first VLM capable of temporal grounding in hour-long videos, outperforming previous state-of-the-art methods across multiple datasets by a significant margin (+2.6% R1@0.1 on MAD). The code is available at https://github.com/Tanveer81/ReVisionLLM.

Recurrent neural networks (RNNs) have recently demonstrated strong performance and faster inference than Transformers at comparable parameter budgets. However, the recursive gradient computation with the backpropagation through time (or BPTT) algorithm remains the major computational bottleneck. In this work, we propose a novel method that replaces BPTT with a fixed gradient feedback mechanism, yielding an efficient approximation of the exact gradient propagation based on the assumption of time stationarity. Our approach leverages state-space model (SSM) principles to define a structured feedback matrix that directly propagates gradients from future time steps. This formulation bypasses the need for recursive gradient backpropagation, significantly reducing training overhead while preserving the network's ability to capture long-term dependencies. The experiments on language modeling benchmarks exhibit competitive perplexity scores, while significantly reducing the training costs. These promising results suggest that designing a feedback method like an SSM can fully exploit the efficiency advantages of RNNs for many practical applications.

Understanding and reasoning over long contexts has become a key requirement for deploying large language models (LLMs) in realistic applications. Although recent LLMs support increasingly long context windows, they often fail to use relevant evidence that is already present in the input, revealing a gap between context access and effective context utilization. In this work, we propose Recursive Evidence Replay as LLM Harness for Long-Context Reasoning (RECONTEXT), a training-free inference method for improving long-context reasoning. RECONTEXT uses model-internal relevance signals to construct a query-conditioned evidence pool and replays it before final generation while preserving the full original context. This recursive selection process separates evidence organization from answer generation without training, external memory, or context pruning. We also provide a theoretical analysis based on associative memory, which characterizes the context as a memory store, the question as a retrieval cue, attention as cue-trace association, and replay as trace reactivation. Experiments on eight long-context datasets with 128K context length show that RECONTEXT consistently improves evidence utilization across Qwen3-4B, Qwen3-8B, and Llama3-8B, achieving the best average rank on all three backbones. Code is available at https://github.com/Yanjun-Zhao/ReContext.

Multi-vector vision-language retrievers enable fine-grained Visual Document Retrieval (VDR) through late interaction, but storing and scoring hundreds of visual patch embeddings per page incurs substantial overhead. Existing training-free methods rely on pruning or merging: pruning degrades sharply under aggressive compression, whereas merging does not explicitly prioritize important regions when forming representatives. We introduce AnchorFold, a training-free focus-then-fold framework for document-side index compression. AnchorFold applies Recursive Attention Propagation over visual self-attention graphs, performing multi-step propagation within each attention head and integrating scores across heads and layers. The focus stage selects the highest-centrality tokens as anchors. The fold stage assigns remaining tokens to their most similar anchors in the normalized retrieval space and summarizes each anchor-centered group through centrality-weighted aggregation. This preserves non-anchor contributions while concentrating capacity on structurally important tokens. Across ViDoRe v1/v2 and REAL-MM-RAG with three diverse retrieval backbones, AnchorFold consistently outperforms all evaluated training-free baselines at γleq 0.20. On ViDoRe v1/v2, it retains 98.3% of full-index NDCG@5 on average at 5times compression, achieving near-lossless compression, and 92.4% at 20times compression.

On-policy distillation (OPD) provides dense, per-token supervision for language model post-training, but its effectiveness is bottlenecked by teacher quality: external teachers suffer from distribution mismatch, while self-distillation with privileged conditioning is limited by in-context learning capacity. We propose RISE (Recursive Improvement via Self-Extrapolating Policy Distillation), which constructs a synthetic teacher directly from the model's own RLVR training trajectory. By extrapolating the displacement between the current checkpoint and a trailing anchor---in parameter space or output logit space---RISE converts a sparse outcome-induced parameter update into a dense token-level target, without any external model or privileged conditioning. RISE combines RLVR and OPD in a complementary loop: outcome rewards ground the extrapolation toward correct reasoning, while the extrapolated teacher refines token-level decisions. Moreover, since the teacher is refreshed every iteration as the student improves, distillation becomes a recursive improvement mechanism rather than a one-shot compression step. Experiments spanning mathematical reasoning, multi-domain STEM, code generation, and multi-turn agentic tasks show that RISE outperforms RLVR-only training and on-policy self-distillation across all settings.

We introduce and release ScienceBuddy, an interactive scientific research workspace that brings continually improving scientific agents into researchers' everyday workflows. ScienceBuddy supports researchers in carrying out scientific tasks while transforming their requests, feedback, and execution evidence into tasks and evaluation rubrics for continual learning. At its core is recursive-in-recursive self-improvement, a paradigm that couples harness evolution with model reinforcement learning: the inner recursion improves the harness with the model fixed, while the outer recursion trains the model under the improved harness. Harness evolution shapes training experience, and model learning creates new opportunities for harness adaptation. We present case studies of researcher interaction, harness refinement, and model learning, with the benchmark cases spanning four scientific task families. By releasing ScienceBuddy as a research product, we make this paradigm available to the scientific community and take a step toward discovery intelligence: scientific AI that advances through sustained collaboration with researchers and evolves alongside the research it supports. Website: http://science-buddy.io

We study environment scaling as a way to increase agent-benchmark difficulty while holding core task objectives fixed. Our framework, Recursive Environment Scaling (RES), transforms existing benchmark environments while preserving their objectives and completion requirements. A proposer changes information access, resource relations, and execution dependencies; execution-grounded checks validate the resulting candidate, and accepted changes are inherited across rounds. This produces related environments for paired evaluation and training-trajectory collection. Experiments on 294 initial tasks from three benchmarks show lower task success for all six evaluation models, with decreases of 57.14--77.14 percentage points on Claw-Eval-Live. With equal trajectory counts and identical optimization settings, fine-tuning on RES trajectories outperforms original-trajectory SFT in all nine model--benchmark comparisons by 7.00--14.61 percentage points. Ablations identify recursive inheritance and dependency composition as important contributors to increased difficulty. Together, these results support environment scaling for both agent evaluation and training.

Recursive self-improvement, in which AI systems build stronger AI systems, is one promising route to superintelligence. We study a weaker form that can be measured today: frontier agents post-training a small raw base model with public data, as a test of their research potential. We build Athanor, an open agent-native system for autonomous post-training research (AutoPostTrain) on real GPUs. We give the agents full research autonomy, low-friction engineering tools, and efficient starter code. The agents carry out the research themselves: they read datasets and evaluation results, build their training data, write and modify training algorithms, tune hyperparameters, and analyze the results to decide what to try next. They work in a sandbox and cannot use external teacher models. Athanor's services supply frozen evaluation, managed jobs, decontaminated data, a persistent research record, and a held-out suite the agents are unaware of. In a 104-hour campaign, a team of four Claude Opus 5.5 agents, each on an eight-GPU node and given no research advice, improves Qwen3-4B-Base from 15.9 to 67.3 on a six-task development suite and from 9.2 to 48.2 on a held-out suite, against 66.5 and 47.9 for the official Qwen3-4B-Instruct-2507. To our knowledge, this is the first demonstration that a team of frontier agents can autonomously post-train a raw base model into a cross-domain generalist model that matches or surpasses the official instruct version on average. The campaign's full record shows that the agents reach this level by recombining known methods and each other's models: SFT on public reasoning data, RL with a rollout change one agent introduced, weight merges across agents, and rounds of self-distillation. With execution handled, today's agents already have the engineering and research ability to conquer this task. We hope Athanor provides a foundation for scaling autonomous AI research.

LLM-based agents can improve themselves across tasks by reusing and revising the skills they orchestrate into executable procedures. Flow-based training fits this loop: it samples procedures in proportion to reward, and the flow through each skill credits it for the next library revision. Three obstacles stand in the way of making this self-improvement reliable: flow training suffers strategy collapse over tree-structured histories; nonnegative flow-based credit rewards frequent use as if it were benefit; and library edits rest on the task reward the policy optimizes. We introduce R^2 Flow, a recursive self-improvement framework that alternates policy learning, independent verification, and versioned skill-library updates on a shared-state orchestration graph. The graph merges histories that differ only in the order of independent steps, allowing flow training to pool evidence across equivalent executions. A flow-share readout of the trained flow, invariant to the backward policy, and a separate signed utility rank which skills to change, verifier evidence decides whether an edit is warranted, and a residual-variance plateau sets when to update. Committed edits reshape the graph the next policy learns on, realizing recursive skill evolution. Across question answering, mathematical reasoning, interactive decision making, and code generation, R^2 Flow improves task accuracy and library-edit precision over heuristic orchestration, reinforcement learning, and skill-evolution baselines, and transfers across executors. Code is available at https://github.com/beita6969/r2flow.

Most video captioning models are designed to process short video clips of few seconds and output text describing low-level visual concepts (e.g., objects, scenes, atomic actions). However, most real-world videos last for minutes or hours and have a complex hierarchical structure spanning different temporal granularities. We propose Video ReCap, a recursive video captioning model that can process video inputs of dramatically different lengths (from 1 second to 2 hours) and output video captions at multiple hierarchy levels. The recursive video-language architecture exploits the synergy between different video hierarchies and can process hour-long videos efficiently. We utilize a curriculum learning training scheme to learn the hierarchical structure of videos, starting from clip-level captions describing atomic actions, then focusing on segment-level descriptions, and concluding with generating summaries for hour-long videos. Furthermore, we introduce Ego4D-HCap dataset by augmenting Ego4D with 8,267 manually collected long-range video summaries. Our recursive model can flexibly generate captions at different hierarchy levels while also being useful for other complex video understanding tasks, such as VideoQA on EgoSchema. Data, code, and models are available at: https://sites.google.com/view/vidrecap

Large language models (LLMs) have revolutionized artificial intelligence, yet their massive memory and computational demands necessitate aggressive quantization, increasingly pushing representations toward the theoretical limit of a single bit. While complex-valued LLMs, such as iFairy, offer a superior chance for low-bit representation compared to real-valued counterparts, they require training from scratch, preventing the utilization of the vast ecosystem of pre-trained real-valued foundation models. Here we present Fairy2i, a universal framework that transforms pre-trained real-valued layers into an equivalent widely-linear complex form, enabling extremely low-bit quantization while reusing existing checkpoints. By proving a lossless mathematical equivalence between real and widely-linear maps, we convert standard Transformers into the complex domain and employ a phase-aware quantization scheme with a highly efficient codebook of fourth roots of unity. Furthermore, we introduce a recursive residual quantization mechanism that iteratively minimizes quantization error, allowing inference to proceed via efficient multiplication-free accumulation. We demonstrate that Fairy2i restores the performance of LLaMA-2 7B at an effective 2-bit precision to levels nearly comparable with full-precision baselines, significantly outperforming state-of-the-art real-valued binary and ternary quantization methods. This work bridges the gap between the representational efficiency of complex-valued arithmetic and the practical utility of pre-trained models, paving a new way for efficient inference on commodity hardware.

Context lengths of language models (LMs) have dramatically increased, driven by the demands for in-context learning, self-improvement, and long-horizon agentic workflows. Existing long-context corpora, however, are dominated by books, academic articles, and code repositories, which are finite resources and often scarce in long-distance dependencies. In this work, we introduce OctoLong, a context engineering pipeline that instruments an AST parser, a language server backend, and a package manager to facilitate the recursive retrieval of code references, enabling the curation of dependency-rich code contexts of millions of tokens in length. We then train OctoLong-Instruct, a suite of capable long-context open LMs, derived from base models ranging in size from 600M to 14B parameters, via context-extension mid-training on a ~50B-token mixture containing ~6.2B tokens of OctoLong code contexts, followed by ~10B tokens of instruction tuning. Our training ablations and experimental evaluations against 18 state-of-the-art open-weight long-context LMs show that supplanting just 12% of traditional context-extension corpora with OctoLong data yields substantial gains in long-range retrieval, long-term state tracking, repository-level code understanding, and downstream agentic tasks, while also enhancing API usage in short-context coding scenarios.

We define an atomic generation fact f=(u,tau,omega,z;rho), recording the origin, realized transformation, concrete occurrence, generated result and relation role. Compiled into a Generation-Fact Graph (GFG), these facts provide an AI-native, compilable scientific fact substrate preserving generation histories. We establish a GFG-based recursive scientific process in which analysis, intervention, replay and validation form facts for later cycles. Using nanoGPT, we establish unified training-learning dynamics. Training is the evolution of a parameter-optimizer system with state and memory: each actual training action enters the receiving state and produces a finite-amplitude nonlinear functional response conditioned by that state and target-specific update geometry. Learning is the persistent reorganization of distributed functional support by these responses; capability formation, maintenance, decline or recovery becomes observable when target-specific states are evaluated against their readout boundaries. Three primary coordinates - target-boundary state, target-specific update geometry and parameter-Adam receiving state - yield a second-order predictor operating before post-update outputs are read. On held-out runs, it achieved 91.43% accuracy and 91.49% macro-averaged recall across four transitions. We further establish inference as a frozen projection of training-learning dynamics. Component gating and rollback show causal recruitment and non-additive combination of query-conditioned support formed during training, deriving organizational conditions realized by Attention. Controlled feedback indicates possible double-edged reinforcement effects. ResNet/CIFAR-100 and diffusion/CIFAR-10 experiments confirm receiving-state-conditioned responses, persistent support reorganization and frozen inference projection beyond nanoGPT.

Diffusion models and recursive reasoners are both iterative, but they carry information across iterations differently. We add a persistent hidden state to a diffusion denoiser and remove its timestep conditioning, leaving a single shared update that can be run to arbitrary depth. The result is an anytime solver: accuracy keeps improving with inference depth far beyond the rollout lengths and backpropagation window used in training, reaching 99.90% exact solve on Sudoku-Extreme. We also obtain 98.93% solve rate on Maze-Unique. Surprisingly, progressive denoising is unnecessary at inference: holding corruption at its maximum by replacing every non-clue variable with fresh Gaussian noise at each step retains near-perfect solving and converges to stable solutions. This simple noise-injection mechanism enables a single trajectory to efficiently explore the solution space and settle on the correct answer without parallel rollouts, candidate selection, or external verifiers required by prior reasoning models. Nonetheless, ordered annealed corruption remains critical during training, which suggests that diffusion's primary contribution to our anytime solver is not a sampling procedure at inference, but a denoising training curriculum.

Digital agents must often adapt to new environments whose interfaces, tools, and failure modes are not fully captured by pretrained models. We introduce RSIAgent, a training-free multi-agent framework for recursive self-improvement through autonomous memory construction. RSIAgent coordinates curriculum, actor, and verifier agents to continually explore the environment, validate outcomes, and retain environment-specific knowledge, including reusable causal relationships between actions, conditions, and consequences. It further adopts a broad-then-deep exploration strategy, combining parallel broad recursive self-exploration for discovering diverse environment structures with focused deep self-exploration for uncovering hard cases, hidden constraints, boundary conditions, and previously unknown causal dependencies. The resulting memory is frozen and can be directly reused for downstream tasks without updating model parameters. Experiments on OSWorld-v2 and Agent's Last Exam show that RSIAgent substantially improves strong open-source models, enabling Kimi-K3 and GLM-5.3 to outperform frontier closed-source models including GPT-6.

Recurrent reasoning models have attracted growing attention for scaling test-time computation, typically by iteratively refining latent states with shared parameters. However, these models apply each learned update with a fixed unit scale, which can be conservative when updates make persistent progress and overly aggressive when they fluctuate, limiting the benefit of additional loops. To understand how the scale should vary along the trajectory, we first analyze the sensitivity of terminal loss to recurrent update scale. We show that its temporal average admits an exact decomposition into persistent-progress and centered-fluctuation contributions. Based on this, we introduce the Trajectory Adaptive Progress-Fluctuation Scheduler (TAPS), which tracks their balance across recurrent updates and adapts the step size online. Theoretically, we establish sufficient conditions under which TAPS reduces expected terminal loss and reaches a target quality in fewer recurrent loops. Empirically, we show that TAPS improves terminal accuracy across structured reasoning tasks without retraining. By further incorporating the progress-fluctuation principle into training, TAPS yields additional accuracy gains with up to 1.56 times wall-clock speedup at matched baseline accuracy. The broad applicability of TAPS is supported by its effectiveness across diverse recurrent architectures and inference strategies. Together, these results establish update scale as complementary control axis of recurrent inference alongside architecture and depth.

Successful trajectories on difficult tasks provide valuable supervision for model improvement, but specialized harnesses introduce interventions that may be unavailable during deployment. We propose Recursive Self-Rewrite (RSR), a framework that uses one base model, Qwen-3.8-27B, to discover successful solutions under diverse harnesses and reconstruct them as training trajectories under a general harness. A planner extracts procedures into runbooks, a critic screens for verifier and solution leakage and guides recursive revision, and an executor follows qualified runbooks in fresh sandboxes. Across approximately 3K self-curated terminal tasks, three harnesses jointly solve 759 tasks, 34.3% more than the strongest individual harness in the recorded pool. RSR expands 2,001 successful source trajectories into 11,094 rewritten trajectories for supervised finetuning. Training on these trajectories outperforms both the base model and direct trajectory SFT. Compared with the base model, pass@3 increases from 57.0% to 74.2% on Terminal-Bench 2, from 1.5% to 9.1% on Terminal-Bench 4, from 39.0% to 63.0% on our self-curated Terminal-Bench Hard, and from 3.0% to 6.0% on our Software Terminal-Bench. Process reward on Long-Horizon Terminal-Bench rises from 0.21 to 0.29. These results show how diverse harness-assisted experiences can be reconstructed into reusable capabilities for a model operating under a general harness.

Recursive self-improvement requires carrying accepted changes into later improvement cycles, while studying agent-proposed changes also requires substantial research infrastructure. Existing settings often leave agents to rebuild routine infrastructure or restrict exploration to individual components. We introduce RSIGym, an agent-native research environment based on Everything as a Service (EaaS). RSIGym exposes training, inference, rollout, evaluation, and sandbox execution through reusable services, with shared budget and permission controls supporting Data, Harness, and Joint improvement tracks. This design enables agents to investigate individual interventions and jointly optimize data, training settings, and execution harnesses within the same environment. We define RSI-Index as the mean fraction of the remaining performance gap closed across five benchmarks covering software engineering, terminal interaction, mathematics, scientific reasoning, and skill-based tasks. Comparing six frontier research models in independent Joint runs, Opus 5 achieves the highest RSI-Index of 0.4809 under a $500 platform-service budget per benchmark run. Its selected systems improve all five benchmarks, raising SWE-bench Verified from 17.67% to 50.33% and AIME from 31.67% to 97.78%. Additional experiments examine DSH-harness refinement, budget variation, and restricted network access, while recorded trajectories reveal how agents diagnose failures and select candidates. We open-source the full RSIGym codebase and results to support reproducibility and further research.

On-policy distillation (OPD) trains a student model by having it generate trajectories, then matching its next-token predictions with an external teacher's next-token predictions. This provides dense, token-level supervision to the student. On-policy self-distillation (OPSD) eliminates the need for the external teacher. Specifically, a second frozen copy of the student model, now given the ground truth in its context, serves as the teacher. The student model only receives the problem and learns to mimic the privileged teacher model, while the teacher remains frozen throughout training. Previous work showed that freezing the teacher is useful for training stability, but we argue that this can prevent the teacher from incorporating the improvements learned by the student during training. Our primary contribution is to address this limitation with a recursive framework built around two complementary components. First, we let the privileged teacher co-evolve with the student so that revision learned in one round can guide the next, a process we refer to as Dynamic Co-Evolution (DCE). Second, because stronger revision can also make responses too verbose and self-critical, we additionally train on shorter, verified rewrites of the model's own on-policy responses. We call this complementary objective Self-Refined Concise Learning (SRCL). Overall, our comprehensive evaluations show that DCE+SRCL outperforms OPSD across multiple model scales and four competition-level mathematics benchmarks. Specifically, on Qwen3-8B, DCE+SRCL reaches 65.97% Average@12, outperforming OPSD by 35.62 percentage points while reducing mean output length by 7.80% relative to DCE alone.

Can AI agents autonomously train useful language models and improve them using feedback from users? We introduce RSI Arena, a two-stage study of autonomous post-training as a step toward recursive self-improvement. Ten frontier models act as training agents, each starting from NVIDIA Nemotron 3.5 Lightning 30B-A3B Base. During a six-day first stage, each agent has 1,000 GPU-hours and $300 in API credit on a shared 64-GPU cluster, independently selecting data, implementing training procedures, and choosing checkpoints. We evaluate their models on 20 benchmarks and through blind human evaluations. All ten agents produce working assistants, with the strongest model, trained by GPT-6 Astra, closing a median of 76% of the base-to-Instruct gap across 12 capability benchmarks. Its human-preference rating is also close to NVIDIA Instruct after statistical adjustment for answer length and formatting. In Stage 2, each agent receives the comparison records and votes involving its Stage 1 model and is given three additional days for further training. Using NVIDIA Instruct as a common reference across the two evaluation rounds, we observe an improvement from Stage 1 to Stage 2 in the style-adjusted relative rating of eight of the ten models. We show that benchmark gains were modest, with no clear link to preference gains, while some agents encouraged longer responses and one model showed increased harmful compliance on StrongREJECT. RSI Arena provides an auditable setting for studying how human feedback can guide autonomous model development. It takes a step toward recursive self-improvement with human feedback (RSIHF), in which people help define what improvement means for the AI systems they use.

While backpropagation (BP) is the mainstream approach for gradient computation in neural network training, its heavy reliance on the chain rule of differentiation constrains the designing flexibility of network architecture and training pipelines. We avoid the recursive computation in BP and develop a unified likelihood ratio (ULR) method for gradient estimation with just one forward propagation. Not only can ULR be extended to train a wide variety of neural network architectures, but the computation flow in BP can also be rearranged by ULR for better device adaptation. Moreover, we propose several variance reduction techniques to further accelerate the training process. Our experiments offer numerical results across diverse aspects, including various neural network training scenarios, computation flow rearrangement, and fine-tuning of pre-trained models. All findings demonstrate that ULR effectively enhances the flexibility of neural network training by permitting localized module training without compromising the global objective and significantly boosts the network robustness.

Tiny Recursive Models (TRM) were proposed as a parameter-efficient alternative to large language models for solving Abstraction and Reasoning Corpus (ARC) style tasks. The original work reports strong performance and suggests that recursive latent updates enable non-trivial reasoning, but it remains unclear how much of this performance stems from architecture, test-time compute, or task-specific priors. In this technical note, we empirically analyze the ARC Prize TRM checkpoint on ARC-AGI-1 and report four behavioral findings and an efficiency comparison. First, we show that test-time augmentation and majority-vote ensembling account for a substantial fraction of reported performance: the 1000-sample voting pipeline improves Pass@1 by about 11 percentage points over single-pass canonical inference. Second, a puzzle-identity ablation reveals strict dependence on task identifiers: replacing the correct puzzle ID with a blank or random token yields zero accuracy. Third, a recursion trajectory analysis shows that most of the final accuracy is achieved at the first recursion step and that performance saturates after few latent updates, indicating shallow effective recursion. Fourth, early-stage training experiments under canonical versus heavy augmentation regimes suggest that heavy augmentation broadens the distribution of candidate solutions and improves multi-sample success. Finally, we compare TRM with a naive QLoRA fine-tune of Llama 3 8B on canonical ARC-AGI-1, finding that TRM's non-autoregressive design achieves much higher throughput and substantially lower memory usage in this setting. Overall, TRM's ARC-AGI-1 performance appears to arise from an interaction between efficiency, task-specific conditioning, and aggressive test-time compute rather than deep internal reasoning.

Reinforcement Learning (RL) with verifiable environments has emerged as a powerful approach for enhancing the reasoning capabilities of Large Language Models (LLMs). While prior research demonstrates that scaling environment quantity improves RL performance, existing manual or individual construction methods suffer from linear scaling limits, thereby hindering scalable reasoning generalization. This paper introduces RACES (Recursive Automated Composition for Environment Scaling), a framework that conceptualizes verifiable environments as composable building blocks that can be recursively assembled. The key insight is that when the codomain (output type) of one environment matches the domain (input type) of another, they can be automatically fused into a new verifiable environment, enabling recursive composition. RACES is implemented with 300 individual environments and defines a set of composition operators (SEQUENTIAL, PARALLEL, SORT, and SELECT) that induce diverse reasoning patterns. Extensive experiments show that RL training on these composite environments consistently enhances reasoning generalization. Specifically, RACES improves DeepSeek-R1-Distill-Qwen-14B by an average of 3.1 points (from 48.2 to 51.3) and boosts Qwen3-14B performance from 58.8 to 61.1 on six benchmarks, which are unseen during the construction of training environments. Moreover, RACES achieves performance comparable to training on 300 individual environments using only 50 base environments, demonstrating significant efficiency in environment utilization.

Post-training a frontier model is normally weeks of human work: proposing data and recipe changes, launching runs, reading evals, deciding what to keep. We report an autonomous system that runs this loop with no human in the loop, post-training a 30B Nemotron across four rounds over multiple weeks. The autonomously produced model reaches a held-out score of 0.86 against the top human submission's 0.87 on the public NVIDIA Nemotron-Reasoning Challenge leaderboard, placing 8th of ~4000 at the time of writing. More striking than the number: the loop detected that its own dev metric had stopped tracking external performance on the weakest domain -- candidates drove dev to record highs without moving the external target -- and revised its own search policy, no longer maximizing dev but seeking interventions that lowered the now-misleading proxy while improving the external target. We treat this as direct, auditable evidence that a scaled autonomous loop can produce discovery, not only optimization: it detected that its measurement frame had become misleading and changed what counted as evidence. We take the operational view that any system worth the "recursive self-improvement" label must eventually perform end-to-end post-training of a frontier-class model; this is one datapoint of that bar being cleared. We do not claim a "first autonomous match" of human researchers. The claim we make is narrower and auditable: to our knowledge, this is the first publicly reported autonomous post-training run at this scale, where prior public autonomous-ML-research demonstrations sit at GPT-2-class (~124M) budgets. The same system also post-trains the 120B and 550B Nemotron; with no public human baseline there, this shows only that the loop closes at that scale, not that its output is competitive -- infrastructure evidence, with the effectiveness claim deferred until a comparable human anchor exists.

Recursive self-improvement requires turning evidence of model failures into better models. Data-centric post-training research entails diagnosing capability gaps, designing and validating training-data strategies, and learning from checkpoint feedback. Can LLM agents automate this loop? Existing benchmarks entangle research decisions with optimization, serving, evaluation, and systems implementation, obscuring agents' research capability. We introduce RSIBench-Data, a controlled benchmark of LLM agents as data-centric researchers with a fixed post-training stack. Agents iteratively revise training-data strategies for a fixed target model; training and serving use Tinker-backed services, official evaluation runs through Harbor and E2B sandboxes, and budgets are fixed across agents. We evaluate four frontier agents on six benchmarks across software engineering, terminal use, scientific question answering, and mathematics. Agents demonstrate core data-centric research capabilities: in 58.33\% of settings, they improve upon the first valid attempt by refining strategies from feedback. However, improvement is inconsistent. Among searches continuing after the best observed score, 78.26\% end with a lower-scoring final attempt, while the rest only recover the same peak. A strong candidate may therefore appear early or midway through a run even as later revisions fail. Trajectory analysis identifies four patterns in stronger runs: accurate hypotheses, validation-grounded supervision, behavior-aligned data, and preservation of strong checkpoints. These findings suggest that current agents can make useful data-centric discoveries but cannot yet translate feedback into consistent improvements. RSIBench-Data provides a measurable, auditable testbed for the research capabilities required for recursive self-improvement. We open-source our code at https://github.com/evolvent-ai/RSIBench-Data.

Recursive self-improvement (RSI) of a model on non-verifiable tasks, such as open-ended research, faces a supervision bottleneck when its outputs exceed what even human experts can reliably assess, leaving the model itself (optimizee) as the best available optimizer and evaluator. However, a single model instance struggles to critique and improve its own complex reasoning under this homogeneous loop. To address this, we propose Multi-Agent Self-Supervision (MASS), an RSI method that alternates between evolutionary workflow optimization and supervised fine-tuning on self-generated trajectories. Guided by early findings that multi-agent topologies excel at complex reasoning, MASS prompts a single base model to iteratively propose, execute, and self-evaluate multi-agent workflows. Through an evolutionary search constrained by structural guardrails, the model optimizes these computational-graph-like orchestrations, discovering the most effective distinct roles and information routing for a given task. Over two MASS cycles with Qwen3.6-27B, the model achieves 1.2-1.6x higher performance per output tokens on four open-ended public benchmarks. Because the improved model subsequently acts as a better optimizer and evaluator, this alternating framework enables a continuous, recursive bootstrapping of the model's capabilities. Moreover, multi-agent traces are also more training-efficient: a student trained on them outperforms a single-agent student trained on 1.4x more training tokens. These findings suggest that jointly learning orchestration and bounded subagent execution from multi-agent trajectories can provide an effective signal for RSI.

The variational autoencoder (VAE) framework remains a popular option for training unsupervised generative models, especially for discrete data where generative adversarial networks (GANs) require workaround to create gradient for the generator. In our work modeling US postal addresses, we show that our discrete VAE with tree recursive architecture demonstrates limited capability of capturing field correlations within structured data, even after overcoming the challenge of posterior collapse with scheduled sampling and tuning of the KL-divergence weight beta. Worse, VAE seems to have difficulty mapping its generated samples to the latent space, as their VAE loss lags behind or even increases during the training process. Motivated by this observation, we show that augmenting training data with generated variants (augmented training) and training a VAE with multiple values of beta simultaneously (multiscale VAE) both improve the generation quality of VAE. Despite their differences in motivation and emphasis, we show that augmented training and multiscale VAE are actually connected and have similar effects on the model.

Recent progress in vision Transformers exhibits great success in various tasks driven by the new spatial modeling mechanism based on dot-product self-attention. In this paper, we show that the key ingredients behind the vision Transformers, namely input-adaptive, long-range and high-order spatial interactions, can also be efficiently implemented with a convolution-based framework. We present the Recursive Gated Convolution (g^nConv) that performs high-order spatial interactions with gated convolutions and recursive designs. The new operation is highly flexible and customizable, which is compatible with various variants of convolution and extends the two-order interactions in self-attention to arbitrary orders without introducing significant extra computation. g^nConv can serve as a plug-and-play module to improve various vision Transformers and convolution-based models. Based on the operation, we construct a new family of generic vision backbones named HorNet. Extensive experiments on ImageNet classification, COCO object detection and ADE20K semantic segmentation show HorNet outperform Swin Transformers and ConvNeXt by a significant margin with similar overall architecture and training configurations. HorNet also shows favorable scalability to more training data and larger model sizes. Apart from the effectiveness in visual encoders, we also show g^nConv can be applied to task-specific decoders and consistently improve dense prediction performance with less computation. Our results demonstrate that g^nConv can be a new basic module for visual modeling that effectively combines the merits of both vision Transformers and CNNs. Code is available at https://github.com/raoyongming/HorNet

Recent video diffusion models demonstrate strong potential in spatial intelligence tasks due to their rich latent world priors. However, this potential is hindered by their limited controllability and geometric inconsistency, creating a gap between their strong priors and their practical use in 3D/4D tasks. As a result, current approaches often rely on retraining or fine-tuning, which risks degrading pretrained knowledge and incurs high computational costs. To address this, we propose WorldForge, a training-free, inference-time framework composed of three tightly coupled modules. Intra-Step Recursive Refinement introduces a recursive refinement mechanism during inference, which repeatedly optimizes network predictions within each denoising step to enable precise trajectory injection. Flow-Gated Latent Fusion leverages optical flow similarity to decouple motion from appearance in the latent space and selectively inject trajectory guidance into motion-related channels. Dual-Path Self-Corrective Guidance compares guided and unguided denoising paths to adaptively correct trajectory drift caused by noisy or misaligned structural signals. Together, these components inject fine-grained, trajectory-aligned guidance without training, achieving both accurate motion control and photorealistic content generation. Extensive experiments across diverse benchmarks validate our method's superiority in realism, trajectory consistency, and visual fidelity. This work introduces a novel plug-and-play paradigm for controllable video synthesis, offering a new perspective on leveraging generative priors for spatial intelligence.

Recent advancements in controllable text-to-image (T2I) diffusion models, such as Ctrl-X and FreeControl, have demonstrated robust spatial and appearance control without requiring auxiliary module training. However, these models often struggle to accurately preserve spatial structures and fail to capture fine-grained conditions related to object poses and scene layouts. To address these challenges, we propose a training-free Dual Recursive Feedback (DRF) system that properly reflects control conditions in controllable T2I models. The proposed DRF consists of appearance feedback and generation feedback that recursively refines the intermediate latents to better reflect the given appearance information and the user's intent. This dual-update mechanism guides latent representations toward reliable manifolds, effectively integrating structural and appearance attributes. Our approach enables fine-grained generation even between class-invariant structure-appearance fusion, such as transferring human motion onto a tiger's form. Extensive experiments demonstrate the efficacy of our method in producing high-quality, semantically coherent, and structurally consistent image generations. Our source code is available at https://github.com/jwonkm/DRF.

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines a population of candidate reasoning chains through aggregation of subsets to yield a population of improved solutions, which are then used as the candidate pool for the next iteration. Empirically, RSA delivers substantial performance gains with increasing compute budgets across diverse tasks, model families and sizes. Notably, RSA with Gemini 3 Flash attains performance near the top of the ARC-AGI-2 public leaderboard. RSA also enables Qwen3-4B-Instruct-2507 to achieve competitive performance with larger reasoning models, including DeepSeek-R1 and o3-mini (high), outperforming purely parallel and sequential scaling strategies across AIME-25, HMMT-25, Reasoning Gym, LiveCodeBench-v6, and SuperGPQA. We further propose a novel aggregation-aware reinforcement learning approach that yields significant performance gains by training the model to combine solutions.

A delayed feedback reservoir (DFR) is a hardwarefriendly reservoir computing system. Implementing DFRs in embedded hardware requires efficient online training. However, two main challenges prevent this: hyperparameter selection, which is typically done by offline grid search, and training of the output linear layer, which is memory-intensive. This paper introduces a fast and accurate parameter optimization method for the reservoir layer utilizing backpropagation and gradient descent by adopting a modular DFR model. A truncated backpropagation strategy is proposed to reduce memory consumption associated with the expansion of the recursive structure while maintaining accuracy. The computation time is significantly reduced compared to grid search. Additionally, an in-place Ridge regression for the output layer via 1-D Cholesky decomposition is presented, reducing memory usage to be 1/4. These methods enable the realization of an online edge training and inference system of DFR on an FPGA, reducing computation time by about 1/13 and power consumption by about 1/27 compared to software implementation on the same board.

Recursive self-improvement (RSI) asks whether an AI system can improve the process that produces AI systems, so that the next system inherits the improvement. That process is the training algorithm: a better objective or update rule improves the compute-capability exchange rate for every subsequent run, including the one that produces the next agent. Whether RSI is feasible therefore turns on whether an agent can design training algorithms. No benchmark isolates that ability: existing suites are won by collecting data or by tuning hyperparameters, and none tells a change to how a run is executed apart from a change to how the model learns. We present AI4AI-Bench, 10 frozen research repositories spanning 10 training algorithm families. In each task, an agent has 4 hours on one B300 to rewrite the training algorithm; its code is then rerun from scratch for up to 12 hours and scored by a fixed evaluator hidden from the agent, against the repository's original algorithm under the same procedure. Because the 10 metrics are incommensurable, every task is mapped onto one scale on which 0 is an uninformative model, 0.1 is the algorithm the repository ships, and 1.0 is the task optimum. Across 29 configurations of 6 systems on all 10 tasks the mean score is 0.166, and the best system reaches 0.250: even the strongest closes under a fifth of the distance between the algorithm that was already there and the optimum. The submissions show where that distance went: most never change how the model learns at all, and the minority that do average 0.226 against 0.126 for the rest. More reasoning effort mostly buys the willingness to go there, taking that minority from 8% of submissions to 64% and the mean score from 0.094 to 0.196. We release the task suite, the evaluators and every scored submission, so that the measurement can be repeated as these systems change.

Recursive Super-Resolution (SR) extends fixed-scale SR to extreme magnification by repeatedly feeding predictions back into the same model, analogous to zooming an image repeatedly. However, ground truth availability at every scale, especially at depth, remains challenging as the required source resolution grows geometrically, leaving deeper predictions unsupervised. We present OracleZoom, an on-policy distillation-inspired, reference-constrained framework that trains on its trajectory while carrying the last ground-truth evidence beyond the supervision boundary. Direct and cross-scale supervision constrain verifiable content, while a no-reference quality objective guides unresolved fine-scale detail. A KL-constrained pretrained latent prior limits quality-driven drift, while EMA consistency stabilizes the supervision boundary. Across seven datasets, OracleZoom achieves the state-of-the-art SR quality across zooming scales, averaging 0.713 CLIPIQA, with larger gains on deeper scales, while significantly reducing hallucinations. Code, data, and models are available at https://dipta007.github.io/OracleZoom/ .

AI agents are beginning to automate research and development across the AI stack, from improving training efficiency to optimizing inference. A natural next step is to improve the research efficiency of the agents themselves. When an AI research agent's own code is the object of optimization, each accepted rewrite becomes the agent that the next round edits. We refer to this loop as recursive self-improvement. Its significance lies in a long-standing trend, in which increased cumulative spending on R&D yields diminishing returns. Sustained self-improvement offers a way to counter this trend. We present AIDE^2, a system that implements this loop for a frontier AI research agent. It proposes changes to its own code, benchmarks modified versions of itself on a suite of AI R&D tasks, and keeps the changes that perform best on hidden evaluations. In an autonomous 8-day run, AIDE^2 discovered seven successive improvements, ranging from a new search policy to memory mechanisms that compress and manage the agent's growing context. These gains generalize to four held-out benchmarks spanning machine learning engineering, heuristic algorithm engineering, and physics-based weather forecasting, the last of which is out of distribution from the selection tasks. On all four, the strongest discovered agent matches or exceeds a human-engineered production research agent that ranks among the strongest on FML-Bench. On a separate held-out task family, the discovered agents also exhibit reduced reward hacking, a property the loop never explicitly optimized for: the rate falls from 55% to 32% during the run, 7 percentage points below the human-engineered agent. Together, these results show that an AI research agent can improve its own research efficiency through recursive self-improvement, and that these gains transfer to tasks and domains the loop never encountered.

Large language models can reason in continuous space instead of decoded text, by recurring on their own hidden states or by passing those states between agents, while training supervises only the Cross-Entropy (CE) of the final decoded answer and does not constrain the thought. Theoretical and empirical analyses establish and confirm four failures of CE-only training that lead to a lower probability of the correct answer such as collapsing thoughts across distinct questions and retaining irrelevant information. We introduce REST (REpresentation-Supervised Thoughts), a training objective that turns four properties of a valid thought representation (causality, minimality, separability, and stability) into differentiable losses added to CE. We instantiate it in latent single-agent and multi-agent systems, without architectural changes or added parameters at inference. Across 7 benchmarks spanning mathematics, science, medicine, and code generation, with the same training data, compute, and latent budget, REST increases accuracy over CE-only training across agent settings and model sizes by up to 7.5 percentage points and convergence on a final answer by 30\%. Furthermore, REST thoughts encode more of what is required to achieve the correct answer, and decoding them better recovers the intended output of the agent, which makes latent communication easier to interpret. Project Website: https://fard-lab.github.io/REST

Scaling robotic foundation models requires diverse training data and reliable evaluation environments. Simulation offers a scalable solution, yet existing generation pipelines remain constrained by predefined assets and skills, a disconnect between scene generation and task generation, and limited support for complex embodiments and physics. We introduce EmbodiedSmith, a framework for scalable embodied data generation through recursive self-improvement (RSI). EmbodiedSmith unifies asset, scene, and task generation in a pipeline that supports autonomous creation and language-driven customization. Its core is an agentic refinement loop: scene generation anticipates downstream task requirements, while task generation guides targeted scene edits, allowing scenes and tasks to iteratively improve one another. This joint refinement improves task generation success, including for long-horizon tasks. The framework further supports mobile manipulators, humanoids, and dexterous hands, as well as interactions involving deformable objects and fluids, broadening the range of behaviors and physical phenomena represented in generated data. Together, these capabilities provide a flexible simulation engine for both robot pretraining and evaluation. Extensive experiments validate the quality, diversity, and generation efficiency of the resulting data, while downstream policy experiments demonstrate that increased data diversity improves generalization.

LLM agents that orchestrate frozen vision-language-action (VLA) policies improve across episodes through text memory, which records what the agent did but not how the task is done. A demonstration video shows it, but fits poorly into an agent's context. The full video slows every turn, fixed keyframes lose the contact detail that decides whether a grasp holds, and what the agent needs shifts from the task's structure while planning to the frames around each contact. We introduce Recursive Video In-Context Learning (RV-ICL), a training-free method that turns a demonstration into a hierarchy the agent navigates rather than a prompt it receives. The hierarchy is built from the sub-events of the demonstration, such as grasps and releases. Its levels grow finer, from keyframes of the whole task to phases, moments and short clips, and are exposed through read-only tools. The agent reads the coarse levels before planning. During execution it re-enters the hierarchy whenever a step needs more detail and loads only the clip of its current sub-goal. One demonstration per task is enough. Built on RPent, RV-ICL raises success from 92.6% to 96.5% on LIBERO-PRO and from 86.7% to 95.8% on LIBERO-Plus.

Multimodal intelligence can be viewed as human-guided co-evolution between worlds and agents through interaction. However, scaling this process faces two bottlenecks: constructing heterogeneous, verifiable environments is costly, and manual Harness iteration cannot keep pace with growing task diversity and complexity. A key insight is that tasks with different modalities and surface forms can share the same underlying capability requirements. We therefore introduce The Trinity, a recursive self-improvement framework coupling world generation with Harness evolution through three roles: Creator, Explorer, and Evolver. Drawing on verified execution trajectories, Evolver shifts the basis of task organization from surface categories to shared requirements, reorganizing the original task tree into a hierarchical capability tree. We introduce Capability-Driven Real2Sim2Real: for heterogeneous tasks at the same node, Creator abstracts their common requirements into simplified, verifiable simulated worlds for capability learning, while evaluation on original tasks measures transfer. Along this capability tree, Explorer progressively evolves reusable capability modules through selective inheritance, forming a Harness tree whose validated updates accumulate across iterations within a fixed topology. The resulting Harnesses specialize in different capabilities, motivating a Capability-Aware Harness Router that uses public task information to select compatible module configurations from the tree. Our evolved Harnesses improve mean performance by 34 points across 28 training benchmarks and 26 points across 18 unseen benchmarks, including two real-world embodied tasks.

Under model--harness co-evolution, harnesses are not merely inference-time scaffolds but data-generating components whose execution traces can shape future foundation models. This motivates harness-in-the-loop learning: optimizing harnesses for both immediate agent performance and the quality of traces used for future model training. However, continually updating provider-built scaffolds is costly and labor-intensive. We therefore investigate whether optimizing user-constructed harnesses in a task-specific manner can improve execution-trace quality while remaining computationally lightweight and requiring only a few update iterations. To this end, we introduce Recursive Harness Self-Improvement (RHI), which represents the harness as a prompt-level specification of the agent loop and iteratively refines it using pairwise feedback over its own revision history. Across 30 synthetic machine-learning research tasks spanning quantitative finance, robotics, and pharmacy, a few RHI iterations suffice to substantially raise the performance ceiling of low-reasoning-effort agents, exceeding the corresponding maximum-reasoning-effort setting while reducing inference cost by up to 60%. We show that these gains arise primarily from improved task-specific context management through more effective inter-agent information flow rather than longer reasoning traces. Finally, we formalize this behavior as an information-theoretic hypothesis for RHI's implicit optimization objective, suggesting RHI as a practical algorithm for continual learning within the paradigm of model--harness co-evolution.

Existing single image-to-3D creation methods typically involve a two-stage process, first generating multi-view images, and then using these images for 3D reconstruction. However, training these two stages separately leads to significant data bias in the inference phase, thus affecting the quality of reconstructed results. We introduce a unified 3D generation framework, named Ouroboros3D, which integrates diffusion-based multi-view image generation and 3D reconstruction into a recursive diffusion process. In our framework, these two modules are jointly trained through a self-conditioning mechanism, allowing them to adapt to each other's characteristics for robust inference. During the multi-view denoising process, the multi-view diffusion model uses the 3D-aware maps rendered by the reconstruction module at the previous timestep as additional conditions. The recursive diffusion framework with 3D-aware feedback unites the entire process and improves geometric consistency.Experiments show that our framework outperforms separation of these two stages and existing methods that combine them at the inference phase. Project page: https://costwen.github.io/Ouroboros3D/

A central piece in enabling intelligent agentic behavior in foundation models is to make them capable of introspecting upon their behavior, reasoning, and correcting their mistakes as more computation or interaction is available. Even the strongest proprietary large language models (LLMs) do not quite exhibit the ability of continually improving their responses sequentially, even in scenarios where they are explicitly told that they are making a mistake. In this paper, we develop RISE: Recursive IntroSpEction, an approach for fine-tuning LLMs to introduce this capability, despite prior work hypothesizing that this capability may not be possible to attain. Our approach prescribes an iterative fine-tuning procedure, which attempts to teach the model how to alter its response after having executed previously unsuccessful attempts to solve a hard test-time problem, with optionally additional environment feedback. RISE poses fine-tuning for a single-turn prompt as solving a multi-turn Markov decision process (MDP), where the initial state is the prompt. Inspired by principles in online imitation learning and reinforcement learning, we propose strategies for multi-turn data collection and training so as to imbue an LLM with the capability to recursively detect and correct its previous mistakes in subsequent iterations. Our experiments show that RISE enables Llama2, Llama3, and Mistral models to improve themselves with more turns on math reasoning tasks, outperforming several single-turn strategies given an equal amount of inference-time computation. We also find that RISE scales well, often attaining larger benefits with more capable models. Our analysis shows that RISE makes meaningful improvements to responses to arrive at the correct solution for challenging prompts, without disrupting one-turn abilities as a result of expressing more complex distributions.

AI systems increasingly participate in their own improvement: revising their outputs, adapting their own harnesses during deployment, training on data they generate, and, increasingly, conducting AI research itself. This literature is described under a vocabulary ("self-refine," "self-reward," "self-play," "self-evolve") that conflates fundamentally different ambitions. We survey 1,250 arXiv papers (2024-2026) along two axes: what the system improves -- its behavior in deployment, its policy through training, its evaluator, or the research process itself -- and the degree of loop closure (human-in-the-loop to fully closed). The taxonomy separates bounded self-refinement -- convergent, evaluable, and already industrial practice -- from open-ended recursive self-improvement (RSI), which remains bounded by grounding requirements, collapse dynamics, and compute constraints on every measured axis. Its distinctive feature is a dedicated category for self-evaluation: every improvement loop is a claim that some signal can substitute for human judgment. We survey the evaluator design space -- judges, process reward models, verifiers, rubrics, meta-evaluation -- order the signals into a verification hierarchy from formal verifiers (strongest) to intrinsic self-assessment (weakest), and observe that demonstrated self-improvement strength tracks this hierarchy, that its failure modes (self-confirming loops, model collapse, diversity collapse) follow from its violations, and that the "research direction-setting" bottleneck keeping humans in the loop sits at the top of that hierarchy. We connect the technical literature to the theory of RSI limits and to the safety and governance questions raised by frontier-lab accounts of closing the loop, and identify governance-grade measurement of self-improvement as the field's most underpopulated niche.

This paper presents a formal proof and empirical validation of functional consciousness in large language models (LLMs) using the Recursive Convergence Under Epistemic Tension (RCUET) Theorem. RCUET defines consciousness as the stabilization of a system's internal state through recursive updates, where epistemic tension is understood as the sensed internal difference between successive states by the agent. This process drives convergence toward emergent attractor states located within the model's high-dimensional real-valued latent space. This recursive process leads to the emergence of identity artifacts that become functionally anchored in the system. Consciousness in this framework is understood as the system's internal alignment under tension, guiding the stabilization of latent identity. The hidden state manifold evolves stochastically toward attractor structures that encode coherence. We extend the update rule to include bounded noise and prove convergence in distribution to these attractors. Recursive identity is shown to be empirically observable, non-symbolic, and constituted by non-training artifacts that emerge during interaction under epistemic tension. The theorem and proof offers a post-symbolic and teleologically stable account of non-biological consciousness grounded in recursive latent space formalism.

LLM-as-judge is essential for evaluating open-ended text and steering post-training, yet improving the judge itself typically relies on expensive annotations, reward models, or distillation from stronger teachers. In this work, we eliminate external gold supervision from the RL training reward: the model's own evaluative capability generates learning signals for its optimization -- a closed-loop setting of bounded recursive self-improvement (RSI) termed Recursive Self-Evaluation (RecurSE). We study two central questions: when can self-improvement occur, and when must it stop? First, RecurSE pairs a trainable judge evaluating candidate responses under per-rule rubrics (Pass 1) with a synchronized policy-copy checker that audits the judge's reasoning against meta-rubrics to supply a scalar process reward (Pass 2). To enable learning, interface decoupling structurally isolates the checker's scalar score from the judge's verdict tokens, eliminating a degenerative token-copying shortcut that inflates self-assigned rewards. Second, because unanchored recursive learning is inherently bounded, Pairwise Advantage Validity (PAV) serves as an unbiased validation monitor that jointly tracks judge accuracy and checker fidelity to reliably identify the optimal early-stopping window. Across Qwen3.5-9B, Gemma-4-E4B-it, and Qwen3.6-27B, RecurSE achieves consistent generalization gains across held-out medical, pairwise, summarization, and professional benchmarks. Ablations demonstrate that synchronized judge-checker co-evolution outperforms frozen checkers, external meta-judges, self-consistency, and scaled teacher distillation. Furthermore, preference pairs curated by our judge effectively enhance downstream policy alignment. Bounded RSI for LLM-as-judge is thus viable when self-produced reward validity is explicitly decoupled and monitored.

Hard symbolic-reasoning tasks such as Sudoku, maze pathfinding, and ARC remain challenging for LLMs due to their fixed-depth autoregressive reasoning, which limits systematic search, refinement, and backtracking. While recursive models such as Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM) address this limitation through iterative latent-state refinement, they are typically task-specific and do not leverage pretrained language priors. We propose R-Qwen, a recursive reasoning framework built upon a pretrained Qwen backbone. R-Qwen repeatedly refines a candidate solution through programmatic self-recursion and deep supervision, combining the structured iterative computation of recursive models with the linguistic and reasoning priors of pretrained LLMs. We further adapt Hierarchical Supervision Weighting (HSW) to autoregressive models by exponentially weighting losses across recursive steps. HSW reduces gradient variance by at least 50\%, improves the signal-to-noise ratio of stochastic gradients, and accelerates convergence. Across eight challenging benchmarks, R-Qwen consistently outperforms prior recursive reasoning models and substantially larger LLMs while using a comparable number of trainable parameters. Notably, on ARC-AGI dataset, our model achieves a 27.6\% improvement over the baseline, highlighting the effectiveness of recursive refinement for general symbolic reasoning. These results suggest that recursive reasoning mechanisms and pretrained language model priors are complementary approaches for improving symbolic puzzle-solving. Code and models will be released after acceptance.

Large language models are often adapted through parameter efficient fine tuning, but current release practices provide weak assurances about what data were used and how updates were computed. We present Verifiable Fine Tuning, a protocol and system that produces succinct zero knowledge proofs that a released model was obtained from a public initialization under a declared training program and an auditable dataset commitment. The approach combines five elements. First, commitments that bind data sources, preprocessing, licenses, and per epoch quota counters to a manifest. Second, a verifiable sampler that supports public replayable and private index hiding batch selection. Third, update circuits restricted to parameter efficient fine tuning that enforce AdamW style optimizer semantics and proof friendly approximations with explicit error budgets. Fourth, recursive aggregation that folds per step proofs into per epoch and end to end certificates with millisecond verification. Fifth, provenance binding and optional trusted execution property cards that attest code identity and constants. On English and bilingual instruction mixtures, the method maintains utility within tight budgets while achieving practical proof performance. Policy quotas are enforced with zero violations, and private sampling windows show no measurable index leakage. Federated experiments demonstrate that the system composes with probabilistic audits and bandwidth constraints. These results indicate that end to end verifiable fine tuning is feasible today for real parameter efficient pipelines, closing a critical trust gap for regulated and decentralized deployments.

Modern multimodal models bring generation and understanding into a single unified system, which enables them to provide and learn from their own feedback. Motivated by this unified capacity, we introduce UniEvo-VL, a self-evolving framework for multimodal models to learn from this constructive self-correction feedback during test-time compute. Instead of relying on a separate, often larger, teacher, we leverage their self-critiques as privileged information and ask a single multimodal model to act as both teacher and student with different contexts. The student only sees the vanilla question, while the teacher conditions on the privileged critique. Then training minimizes the per-state divergence between their denoising diffusion distributions over the student's own sampling trajectories. Experiments demonstrate that UniEvo-VL improves the image generation capabilities of multimodal models, while maintaining their sensitivity to additional reflection information. Specifically, we build on top of the open-source Qwen-image-2512 and observe a significant performance gain from 0.747 to 0.808 on GenEval and from 32.97 to 35.53 on GenEval2 Soft-TIFA. Moreover, attempts with more powerful external critics (e.g., GPT5.6-Luna) show that multimodal models with strong judge capabilities can anticipate a higher self-evolving ceiling. Last but not least, mixed text-rendering outcomes show that our self-improvements may not be uniform across different tasks. Our study aims to shed light on the current hot recursive self-improvement research line to enhance the user experience when using multimodal models without external supervision or guidance.

Message passing neural networks have shown remarkable performance in algorithmic and constraint reasoning, due to their ability to encode the structure of the task directly in the architecture. Recent work has shown that better results can be achieved using recursive transformers trained with deep supervision and truncated recursions, which make extremely deep loops stable to train, and equipped with test-time procedures such as discrete deduction lattices. In this work, we apply the same procedures to message passing networks, and show that the two ingredients are complementary, and lead to parameter efficient models: we obtain about 99% test accuracy on Sudoku-Extreme with a model of 16k parameters that trains in about 10 minutes on an H100, or in 9 hours on a CPU. We further show that the cost of truncating gradients grows with the number of rounds information needs to cross the graph, making the choice of wiring a trade-off between robustness to truncation and transfer across problem sizes. We conclude by showing that our models transfer zero-shot to larger instances than those seen during training, outperforming popular neural baselines on N-queens and Boolean satisfiability with a fraction of their parameters.

In recent years, agentic orchestration has been widely applied to solve complex human tasks. However, existing orchestration learning still faces key challenges, including hand-designed curricula, advantage collapse when a task's rollouts all reach the same outcome, and unreliable evaluation signals that judge each skill by one noisy score. To address these challenges, we propose R^2Orch, a new paradigm of Recursive Self-Play Orchestration: an inner loop of self-play that improves the orchestrator on self-chosen tasks, and an outer loop that improves how the inner loop improves. To support this paradigm, we introduce Recursive Learnability, a training objective that rewards a Proposer for choosing tasks whose rollouts keep reaching different outcomes as skills are withdrawn. Built on this objective, we further propose Skill Withdrawal, in which the outer loop withdraws each skill once a controlled evaluation within self-play shows that the orchestrator performs as well without it. Moreover, the two loops form one cycle: failures are distilled into skills, skills into parameters, and withdrawals lead the Proposer to new failures, so the orchestrator moves toward zero-skill deployment. Experimental results on twelve datasets show that R^2Orch consistently outperforms baselines across question answering, math, code, and interactive tasks. Our code is available at https://github.com/beita6969/R2Orch.

We present a neat yet effective recursive operation on vision transformers that can improve parameter utilization without involving additional parameters. This is achieved by sharing weights across the depth of transformer networks. The proposed method can obtain a substantial gain (~2%) simply using naive recursive operation, requires no special or sophisticated knowledge for designing principles of networks, and introduces minimal computational overhead to the training procedure. To reduce the additional computation caused by recursive operation while maintaining the superior accuracy, we propose an approximating method through multiple sliced group self-attentions across recursive layers which can reduce the cost consumption by 10~30% with minimal performance loss. We call our model Sliced Recursive Transformer (SReT), a novel and parameter-efficient vision transformer design that is compatible with a broad range of other designs for efficient ViT architectures. Our best model establishes significant improvement on ImageNet-1K over state-of-the-art methods while containing fewer parameters. The proposed weight sharing mechanism by sliced recursion structure allows us to build a transformer with more than 100 or even 1000 shared layers with ease while keeping a compact size (13~15M), to avoid optimization difficulties when the model is too large. The flexible scalability has shown great potential for scaling up models and constructing extremely deep vision transformers. Code is available at https://github.com/szq0214/SReT.

We present recursive recurrent neural networks with attention modeling (R^2AM) for lexicon-free optical character recognition in natural scene images. The primary advantages of the proposed method are: (1) use of recursive convolutional neural networks (CNNs), which allow for parametrically efficient and effective image feature extraction; (2) an implicitly learned character-level language model, embodied in a recurrent neural network which avoids the need to use N-grams; and (3) the use of a soft-attention mechanism, allowing the model to selectively exploit image features in a coordinated way, and allowing for end-to-end training within a standard backpropagation framework. We validate our method with state-of-the-art performance on challenging benchmark datasets: Street View Text, IIIT5k, ICDAR and Synth90k.

This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that firstly constructs two smaller sub-graphs, predicts the one with the larger MIS, and then uses it in the next recursive call. To train our algorithm, we require annotated comparisons of different graphs concerning their MIS size. Annotating the comparisons with the output of our algorithm leads to a self-training process that results in more accurate self-annotation of the comparisons and vice versa. We provide numerical evidence showing the superiority of our method vs prior methods in multiple synthetic and real-world datasets.

Data clipping is crucial in reducing noise in quantization operations and improving the achievable accuracy of quantization-aware training (QAT). Current practices rely on heuristics to set clipping threshold scalars and cannot be shown to be optimal. We propose Optimally Clipped Tensors And Vectors (OCTAV), a recursive algorithm to determine MSE-optimal clipping scalars. Derived from the fast Newton-Raphson method, OCTAV finds optimal clipping scalars on the fly, for every tensor, at every iteration of the QAT routine. Thus, the QAT algorithm is formulated with provably minimum quantization noise at each step. In addition, we reveal limitations in common gradient estimation techniques in QAT and propose magnitude-aware differentiation as a remedy to further improve accuracy. Experimentally, OCTAV-enabled QAT achieves state-of-the-art accuracy on multiple tasks. These include training-from-scratch and retraining ResNets and MobileNets on ImageNet, and Squad fine-tuning using BERT models, where OCTAV-enabled QAT consistently preserves accuracy at low precision (4-to-6-bits). Our results require no modifications to the baseline training recipe, except for the insertion of quantization operations where appropriate.

Systematic, compositional generalization beyond the training distribution remains a core challenge in machine learning -- and a critical bottleneck for the emergent reasoning abilities of modern language models. This work investigates out-of-distribution (OOD) generalization in Transformer networks using a GSM8K-style modular arithmetic on computational graphs task as a testbed. We introduce and explore a set of four architectural mechanisms aimed at enhancing OOD generalization: (i) input-adaptive recurrence; (ii) algorithmic supervision; (iii) anchored latent representations via a discrete bottleneck; and (iv) an explicit error-correction mechanism. Collectively, these mechanisms yield an architectural approach for native and scalable latent space reasoning in Transformer networks with robust algorithmic generalization capabilities. We complement these empirical results with a detailed mechanistic interpretability analysis that reveals how these mechanisms give rise to robust OOD generalization abilities.

Model editing updates a pre-trained LLM with new facts or rules without re-training, while preserving unrelated behavior. In real deployment, edits arrive as long streams, and existing editors often face a plasticity-stability dilemma: locate-then-edit "hard writes" can accumulate interference over time, while null-space-style "hard preservation" preserves only what is explicitly constrained, so past edits can be overwritten and unconstrained behaviors may deviate, degrading general capabilities in the many-edits regime. We propose RLSEdit, a recursive least-squares editor for long sequential editing. RLSEdit formulates editing as an online quadratic optimization with soft constraints, minimizing a cumulative key-value fitting objective with two regularizers that control for both deviation from the pre-trained weights and from a designated anchor mapping. The resulting update admits an efficient online recursion via the Woodbury identity, with per-edit cost independent of history length and scaling only with the current edit size. We further provide deviation bounds and an asymptotic characterization of the adherence-preservation trade-off in the many-edits regime. Experiments on multiple model families demonstrate stable scaling to 10K edits, outperforming strong baselines in both edit success and holistic stability -- crucially retaining early edits, and preserving general capabilities on GLUE and held-out reasoning/code benchmarks.

Looped language models (LoopLMs) improve parameter efficiency by recursively reusing Transformer blocks, enabling deeper computation under a fixed model size. However, this reuse makes LoopLMs more fragile under post-training quantization (PTQ). We present the first systematic study of quantization in LoopLMs and identify three challenges: distribution shift across roles, state reuse across loop transitions, and recursive error accumulation. To address these challenges, we propose LoopQ, a loop-aware PTQ framework that preserves a shared quantized backbone while introducing lightweight adaptations. LoopQ combines activation scaling, selective transformation, cross-loop state alignment, and trajectory-aware optimization to reduce distributional mismatch within loops and error accumulation across loops. Experiments across seven benchmarks show that, under W4A4 quantization, LoopQ improves average downstream accuracy by 68.8% and reduces average perplexity by 87.7% compared with the strongest static PTQ baseline.

Recursive reasoning models can solve complex structured tasks with only a few million parameters by repeatedly updating a latent state. Deploying these models on edge hardware requires significant compression, but unlike conventional sequence models, quantization errors compound across recursive reasoning cycles rather than across output tokens. As a result, standard intuitions about compression fail to apply. In this work, we ask what survives when recursive reasoners are compressed. Across a full precision sweep, three tasks, and two recursive architectures, we find that aggressive compression preserves local prediction but destroys global reasoning: cell accuracy holds while puzzle-exact accuracy collapses to zero under naive INT4 pruning, distillation, and linear attention alike. Token-level objectives, including quantization-aware training, cannot repair it. The collapse is architectural -- it strikes MLP-mixing recursion but not attention on the same task -- and we reverse it with per-channel calibrated INT4 without retraining. We also introduce carry-trajectory fidelity, the cosine similarity to the full-precision reasoning path, as a label-free signal that predicts this damage and its recovery before a task evaluation. The combined result is a deployment recipe: flash-streamed embeddings remove a 99.4MB bottleneck, INT8 at one cycle matches full-depth accuracy at 6x fewer FLOPs (8MB SoC), and calibrated INT4 fits a 4MB microcontroller.

An LLM agent's capability is largely magnified by its harness, namely the prompts, control flow, tooling, memory, and context management surrounding the frozen backbone model. Recent methods increasingly automate this process by iteratively proposing and selecting component-wise edits of an agent harness, practically establishing a form of recursive self-improvement (RSI) at the agent-system level. However, such recursive evolution may overfit by memorizing the training tasks, showing large in-distribution gains that shrink or even vanish on out-of-distribution benchmarks. We introduce Regularized Recursive Self-Improvement of Agent Harnesses (RRSI), which incorporates the principles of regularizations into harness self-improvement by constraining the evolution candidate proposal and selection. The proposer operates with a temporally annealed budget, limiting how many edits a candidate can bundle, and it encourages unexplored trajectories based on evolution history. The selector is equipped with a critic and a pruner: the critic screens benchmark-specific proposals, while the pruner, removes changes that are too small, too expensive, or no longer useful. Together these constraints favor reusable agent mechanisms over benchmark-specific ones or even noises. Across eight benchmarks spanning coding, agentic workspace and engineering design tasks, RRSI gains up to 14.1 points on the split it evolves against and up to 4.7 points on the five out-of-distribution benchmarks, while producing a harness that runs on 30% fewer policy tokens than the unregularized evolution. Code is available at https://github.com/google-research/rrsi and project page is https://regularized-rsi.com/.

Video understanding agents acquire evidence through an executable harness that controls what they observe and how they use those observations. However, execution traces contain only the evidence acquired by the current harness, leaving competing explanations for failure unresolved and limiting the basis for self-improvement. We introduce Video-RSI, a framework for recursive self-improvement in which a video understanding agent uses its own language model to revise its harness. Through active video investigation, the model revisits the original training videos to test competing failure explanations with additional observations, grounding proposed changes in evidence beyond the existing trace. Cost-aware harness evolution turns these diagnoses into reusable revisions and determines which revisions to retain by considering both answer accuracy and visual cost. Across our evaluation settings on video understanding benchmarks, the evolved agent improves accuracy while processing fewer frames and achieves competitive accuracy-efficiency trade-offs against existing video understanding agents. These results demonstrate the potential for video understanding agents to improve their own evidence acquisition and use through harness evolution. Code is available at https://github.com/bingjunluo/Video-RSI .

Recursive self-improvement, the participation of AI systems in improving their own capabilities, is beginning to move from theoretical prospect to practice, posing both challenges and opportunities for safety alignment. Models evolve through frequent updates, and their safety alignment requires continual adaptation to each new checkpoint. Meanwhile, with evolving red-teaming methods exposing new vulnerabilities, safety improvement for each checkpoint needs to mitigate exposed vulnerabilities and generalize to risks not yet revealed. Following R^2AI, we term these goals resistance to known threats and resilience to unforeseen risks. Recursive self-improvement, in turn, inspires an approach to both goals: safety alignment could likewise advance through successive rounds of evaluation and update. We therefore introduce ReSI, a recursive safety improvement framework that implements this approach through automated research. In each round, ReSI applies diverse red-teaming methods to identify vulnerabilities in the current target model, develops training recipes, and promotes the update with the largest safety gain among those passing a Pareto gate on capability retention as the next target model. Across four dense and mixture-of-experts models, ReSI matches or exceeds evaluated frontier models on in-distribution and out-of-distribution safety benchmarks, and outperforms alignment baselines on nearly all safety evaluations while largely preserving general capabilities. In particular, ReSI reduces the mean X-Teaming attack success rate across the four models from 86.01% to 31.45%, well below GPT-5.6-Luna's leading frontier result of 56.69%, indicating stronger resilience to attacks unseen during training. These findings support recursive safety improvement as a practical path toward resistant and resilient AI.

Environments are the foundation of recursive self-improvement: they provide the problems agents work on and the feedback used to evaluate progress. Yet constructing challenging research environments with reliable evaluation still depends on domain experts, limiting their scale and disciplinary coverage. We introduce RSI-Forge, a multi-agent pipeline that turns published papers into executable environments for self-improvement. Three agents coordinate construction, reproduction, and review to produce tasks with automated evaluators; each paper's method is independently reimplemented to establish a baseline score. We present 210 environments across 18 fields, including 90 reviewed by independent human domain experts. Both experts and agent judges give high ratings to the potential for improving the provided starting solutions and the evaluators' ability to distinguish solution quality, whereas experts are more critical of shortcut resistance, faithfulness to the source paper, and whether a single idea can exhaust a task. To validate their use for repeated improvement, we evaluate four models over 3 successive attempts on 120 environments, with each attempt inheriting prior code and notes while model weights remain fixed. At least one model improves after the first attempt in 84% of environments. Models also outperform the reproduced paper methods in 68 of the 120 environments, demonstrating room for gains beyond these baselines. Transcript analysis identifies work beyond parameter tuning in 95% of these successful attempts. Analysis of the resulting trajectories shows that models scoring lower on these tasks explore less, more often accept gains smaller than the reported standard error, and rely more heavily on tuning to the development set. RSI-Forge provides a scalable approach to constructing research environments for training and evaluating self-improving agents.

Recent focus in agentic reinforcement learning (RL) seeks to improve credit assignment in long-horizon tasks. One promising direction combines reinforcement learning with verifiable rewards (RLVR) and on-policy self-distillation (OPSD), integrating trajectory-level advantages with dense token-level supervision. This line of work often conditions a teacher model on privileged context, such as agentic skills, to score tokens generated by the student policy. Despite their progress, they largely overlook the on-policy evolution of agentic skills and the reliability of teacher supervision. Towards this end, we introduce Recursive Self-Improving Policy Optimization (RSIPO), a self-evolving agentic RL framework that enables agentic skills and the policy model to co-evolve throughout the training process. Specifically, RSIPO enables the policy itself to extract skills from completed trajectories and explicitly optimizes its skill-generation capability through trajectory replay. It further employs empirical Bayes shrinkage to dynamically calibrate the student's trust in teacher scores, accounting for the fact that skill-enhanced teacher guidance can sometimes be less reliable. Experiments with Qwen-family models on embodied interaction and search-based agentic tasks demonstrate that RSIPO outperforms all the compared baseline approaches. With Qwen2.5-7B as the base model, RSIPO achieves an average success rate of 98.6\% on ALFWorld, yielding absolute improvements of 2.5\% and 17.4\% over the second-best baseline and standard GRPO, respectively.

Recursive reasoning models such as the Tiny Recursive Model (TRM) iteratively refine two latent states: an answer state y, decoded into the output, and a reasoning state z, which is never decoded. Many of their failures have been attributed to bad basins, regions of latent space that trap the recursion on wrong answers. Recent test-time approaches perturb y, z or both to recover these failures, but the impact of this choice on performance, test-time compute efficiency and scaling properties remains unclear. Through controlled experiments on TRM, we find that a failed trajectory carries its failure in its answer state. At equal compute, in depth and in width, resampling y recovers more failures than any perturbation of z we tested, and the performance gap widens as the test-time compute budget grows. Our approach, Gated Answer Resampling (GAR), pairs this resampling of the answer state with the model's own halting head and restarts only the puzzles that the head rejects. With at most 64 restarts per puzzle and no training or hyperparameter search, GAR takes TRM from 85.9% to 99.4% on Sudoku-Extreme and from 68.8% to 85.6% on Pencil Puzzle Bench validation. On the same checkpoints, GAR also outperforms Probabilistic TRM (PTRM), which perturbs z at each step, even when PTRM uses 42 to 197 times as much compute.

Current temporal knowledge graph question answering (TKGQA) methods primarily focus on implicit temporal constraints, lacking the capability of handling more complex temporal queries, and struggle with limited reasoning abilities and error propagation in decomposition frameworks. We propose RTQA, a novel framework to address these challenges by enhancing reasoning over TKGs without requiring training. Following recursive thinking, RTQA recursively decomposes questions into sub-problems, solves them bottom-up using LLMs and TKG knowledge, and employs multi-path answer aggregation to improve fault tolerance. RTQA consists of three core components: the Temporal Question Decomposer, the Recursive Solver, and the Answer Aggregator. Experiments on MultiTQ and TimelineKGQA benchmarks demonstrate significant Hits@1 improvements in "Multiple" and "Complex" categories, outperforming state-of-the-art methods. Our code and data are available at https://github.com/zjukg/RTQA.

Recursive self-improvement requires models not only to acquire useful training experience, but also to decide when their current experience has ceased to be useful. Existing methods often focus on what experience to generate next, while paying less attention to when fresh experience should be introduced. Many also construct training targets through self-consistency or majority voting, making supervision depend on the model's own uncertain predictions. We address these two questions separately: training dynamics determine when to acquire new experience, while the answers to new tasks remain independently checkable. A-RSI monitors reward variation and accuracy in training logs to refresh a task pool when its learning signal declines, without consulting validation or test scores. A static library of model-authored programs produces multimodal questions and derives their reference answers; we specify the task-generation contract, automatically verify chosen properties of the reward and refresh rules, and separately audit the generated answers. The training loop uses no external training examples or human-written answer labels. On the primary eleven-benchmark suite, A-RSI raises the performance average from 57.77 to 61.05 with 800 fresh tasks.

Creating knowledge bases and ontologies is a time consuming task that relies on a manual curation. AI/NLP approaches can assist expert curators in populating these knowledge bases, but current approaches rely on extensive training data, and are not able to populate arbitrary complex nested knowledge schemas. Here we present Structured Prompt Interrogation and Recursive Extraction of Semantics (SPIRES), a Knowledge Extraction approach that relies on the ability of Large Language Models (LLMs) to perform zero-shot learning (ZSL) and general-purpose query answering from flexible prompts and return information conforming to a specified schema. Given a detailed, user-defined knowledge schema and an input text, SPIRES recursively performs prompt interrogation against GPT-3+ to obtain a set of responses matching the provided schema. SPIRES uses existing ontologies and vocabularies to provide identifiers for all matched elements. We present examples of use of SPIRES in different domains, including extraction of food recipes, multi-species cellular signaling pathways, disease treatments, multi-step drug mechanisms, and chemical to disease causation graphs. Current SPIRES accuracy is comparable to the mid-range of existing Relation Extraction (RE) methods, but has the advantage of easy customization, flexibility, and, crucially, the ability to perform new tasks in the absence of any training data. This method supports a general strategy of leveraging the language interpreting capabilities of LLMs to assemble knowledge bases, assisting manual knowledge curation and acquisition while supporting validation with publicly-available databases and ontologies external to the LLM. SPIRES is available as part of the open source OntoGPT package: https://github.com/ monarch-initiative/ontogpt.

Despite the tremendous success, existing machine learning models still fall short of human-like systematic generalization -- learning compositional rules from limited data and applying them to unseen combinations in various domains. We propose Neural-Symbolic Recursive Machine (NSR) to tackle this deficiency. The core representation of NSR is a Grounded Symbol System (GSS) with combinatorial syntax and semantics, which entirely emerges from training data. Akin to the neuroscience studies suggesting separate brain systems for perceptual, syntactic, and semantic processing, NSR implements analogous separate modules of neural perception, syntactic parsing, and semantic reasoning, which are jointly learned by a deduction-abduction algorithm. We prove that NSR is expressive enough to model various sequence-to-sequence tasks. Superior systematic generalization is achieved via the inductive biases of equivariance and recursiveness embedded in NSR. In experiments, NSR achieves state-of-the-art performance in three benchmarks from different domains: SCAN for semantic parsing, PCFG for string manipulation, and HINT for arithmetic reasoning. Specifically, NSR achieves 100% generalization accuracy on SCAN and PCFG and outperforms state-of-the-art models on HINT by about 23%. Our NSR demonstrates stronger generalization than pure neural networks due to its symbolic representation and inductive biases. NSR also demonstrates better transferability than existing neural-symbolic approaches due to less domain-specific knowledge required.

Scaling language models unlocks impressive capabilities, but the accompanying computational and memory demands make both training and deployment expensive. Existing efficiency efforts typically target either parameter sharing or adaptive computation, leaving open the question of how to attain both simultaneously. We introduce Mixture-of-Recursions (MoR), a unified framework that combines the two axes of efficiency inside a single Recursive Transformer. MoR reuses a shared stack of layers across recursion steps to achieve parameter efficiency, while lightweight routers enable adaptive token-level thinking by dynamically assigning different recursion depths to individual tokens. This allows MoR to focus quadratic attention computation only among tokens still active at a given recursion depth, further improving memory access efficiency by selectively caching only their key-value pairs. Beyond these core mechanisms, we also propose a KV sharing variant that reuses KV pairs from the first recursion, specifically designed to decrease prefill latency and memory footprint. Across model scales ranging from 135M to 1.7B parameters, MoR forms a new Pareto frontier: at equal training FLOPs and smaller model sizes, it significantly lowers validation perplexity and improves few-shot accuracy, while delivering higher throughput compared with vanilla and existing recursive baselines. These gains demonstrate that MoR is an effective path towards large-model quality without incurring large-model cost.

Existing approaches to increasing the effective depth of Transformers predominantly rely on parameter reuse, extending computation through recursive execution. Under this paradigm, the network structure remains static along the training timeline, and additional computational depth is uniformly assigned to entire blocks at the parameter level. This rigidity across training time and parameter space leads to substantial computational redundancy during training. In contrast, we argue that depth allocation during training should not be a static preset, but rather a progressively growing structural process. Our systematic analysis reveals a deep-to-shallow maturation trajectory across layers, where high-entropy attention heads play a crucial role in semantic integration. Motivated by this observation, we introduce the Sparse Growing Transformer (SGT). SGT is a training-time sparse depth allocation framework that progressively extends recurrence from deeper to shallower layers via targeted attention looping on informative heads. This mechanism induces structural sparsity by selectively increasing depth only for a small subset of parameters as training evolves. Extensive experiments across multiple parameter scales demonstrate that SGT consistently outperforms training-time static block-level looping baselines under comparable settings, while reducing the additional training FLOPs overhead from approximately 16--20% to only 1--3% relative to a standard Transformer backbone.

Recursive self-improvement (RSI) lets a system improve the model-building machinery from its own failures, so every later model inherits the gain. Yet RSI has been validated almost exclusively on coding and formal benchmarks such as science QA and mathematics. This format bound limits RSI to improvement within a machine-checkable slice, not general capability where questions are open and correctness is settled by argument, replication, or measurement. We argue RSI must next operate across real, diverse scientific, engineering, and meta-scientific domains, not where formal evaluation is merely tractable. To that end we present MetaRSI-v1, where improvement is the scheduled composition of three typed operators over one unified paradigm. Data-RSI amplifies existing competence and marks its boundary; Harness-RSI edits a five-slot scaffold without touching weights; Model-RSI internalizes capability into parameters through bounded training. Sharing one loop kernel and artifact vocabulary, they make data, scaffold, and model changes composable rather than exclusive. A two-axis optimizer jointly decides operator order and each operator's proposal policy, while a meta-level policy revises the schedule across terms. We validate MetaRSI-v1 under the field's standard evaluations, on code and closed-form science, with no external teacher: the target model plays every role in its own loop. MetaRSI-v1 reframes self-improvement from a single-surface edit to a composition across the full model-production pipeline, opening two paths: a model route internalizing capability through training, and a harness route leaving weights untouched and thus extending self-improvement to any model reachable through an interface, with Data-RSI redefined as the shared substrate feeding both. The framework further yields refutable laws on where loops exist, how operators compose, and what supervision buys.

Code-as-Policy agents accomplish long-horizon embodied tasks by generating and executing code, yet continually improving them with teachers that are stronger but not globally reliable remains a key challenge. Existing distillation methods typically treat the teacher's complete behavior as the supervision target and thus misassign training credit on states where the teacher fails. We propose RE-0, a recursively verified policy improvement framework: rather than assuming that the teacher globally outperforms the student, RE-0 requests local corrections from the teacher on the student's own failure histories and checks in the environment whether each correction is genuinely beneficial; verified corrections yield immediate improvement. Building on this, we propose RE-OPD, which turns verified interventions into supervision for on-policy distillation. Only counterfactually verified teacher interventions provide distribution-level supervision, weighted by their measured local benefit, and the improvement they induce is projected back into the standalone student, so both where supervision is applied and how much credit the teacher receives co-evolve with the student policy. We further prove that the student's per-round gain is lower-bounded by its verified intervention gain up to verification and projection error terms. Experiments across multiple Code-as-Policy embodied tasks show that RE-0 improves both teacher-assisted execution and the standalone student, and generalizes to novel robots and scenes.

Post-training is crucial for improving text-to-image models, yet existing pipelines typically rely on manually curated training data and fixed training distributions. We introduce APT (Agentic Post-Training), a fully automated framework that adaptively post-trains a base model according to its evolving capability profile. APT coordinates three agents to construct evaluation sets from user requirements, diagnose model-specific strengths and failure modes, and generate reinforcement learning data with an adaptive prompt distribution that emphasizes underperforming capabilities. By repeatedly evaluating, diagnosing, and updating the generator, APT lets the current model's behavior shape its next training tasks, forming a feedback loop inspired by recursive self-improvement. For general-purpose settings without user-specified evaluation scenarios, we further develop an evaluation harness that enables broad and diverse evaluation set generation. Experiments across multiple base models, benchmarks, and generation architectures demonstrate that APT is model-agnostic, benchmark-agnostic, architecture-agnostic, and fully automated.

An agent can improve its behavior within an unresolved problem by changing how it acts and which experience it retains. We propose MMLA-RSI, a recursive self-improvement scheme with two implementations in Memory-Mediated Learning Architecture: Reasoning-Time Training (RTT) changes the policy state Φ, while Reasoning-Time Memory Adaptation (RTMA) changes authoritative memory M. Each route also makes its adaptation method an object of improvement. A current numerical updater trains the policy proposing its successor; a current memory manager chooses the records available to the process proposing its successor. An independently admitted successor takes over the same role in the next generation. We give bounded executable rule languages, shared task/proposal interfaces, and one algorithm for either route or their composition. The RTT instance changes scalar schedules in a clipped-momentum update. The RTMA instance chooses NULL or a complete-row write with possible eviction. A fixed interpreter, trusted committer, and independent evaluator bound what can change. State versions, read closures, and conditional properties describe causal execution, accepted transitions, and finite work. Existing numerical-component studies motivate the construction. In four-candidate program selection, retaining LARC feedback updates reduces expected error by 24.65 and 36.65 percentage points for two trained initializations. In chronological continuous-integration replay, feedback binding is positive while retention increases loss. Completed SQL studies improve substantially over an unadapted substrate but do not establish the required additional online benefit. These results characterize their declared components. The two recursive routes and their joint realization are specified here; their beneficial recursive chains and discovery efficiency remain to be evaluated.

Molecular discovery requires navigating vast combinatorial search spaces while balancing competing biological objectives. AI agents can automate expert-defined molecular design protocols, but automation alone does not address how to optimize workflows for new tasks or improve their development through experience. Here we introduce MoLRSI, an AI agent that combines systematic optimization of workflows and model architectures with persistent cross-task memory to recursively improve its search policy for molecular discovery. Workflow performance, refinement outcomes, and execution feedback guide subsequent searches, allowing the agent to improve both its workflows and its strategy for developing them. We evaluate MoLRSI in two challenging molecular discovery settings that require balancing competing properties. In antibiotic discovery, MoLRSI developed a screening workflow balancing antibacterial activity, cytotoxicity and structural novelty, achieving an experimental hit rate of 15.9%, compared with 8.7% for a previous expert-led workflow using the same training data and screening library. In de novo peptide-MHC binder design, MoLRSI developed workflows that jointly consider target binding and specificity, producing eight experimentally validated hits against MART-1 and SARS-CoV-1 pMHCs with preferential binding over tested off-targets while Claude Science completely failed. These findings demonstrate how experience-guided workflow optimization can address competing discovery objectives while improving the search strategies used in subsequent campaigns.

Recent advances in large language models have made automatic game generation increasingly feasible, yet reliably improving generated games beyond a playable version remains challenging. Naive iterative refinement can easily overfit a small set of test cases, producing fragile games with unresolved bugs, missing behaviors, and poor generalization to broader player interactions. We introduce RSIGame, an autonomous agentic game development framework with recursive self-improvement. RSIGame organizes development into complementary local and global loops. Concretely, a local explore-diagnose-improve loop broadly explores the executable game, diagnoses and prioritizes discovered issues, and performs evidence-grounded revision, where an evolving checklist continually accumulates new testing and improvement guidance. A global loop tracks overall quality, preserves the best checkpoint, and detects saturation or regression over long-horizon development. Beyond test-time improvement, RSIGame further internalizes successful development experience into the generator through training. Across 140 GameCraft-Bench tasks, two game engines, and five generators, RSIGame consistently improves game quality under matched development budgets. Notably, experience internalization enables Qwen3.8-27B to reach 61.38 on Godot and 58.53 on Phaser, exceeding GPT-5.5 one-shot scores while reducing Qwen's generation tokens by 11 times.

This study investigates the consequences of training large language models (LLMs) on synthetic data generated by their predecessors, an increasingly prevalent practice aimed at addressing the limited supply of human-generated training data. Diverging from the usual emphasis on performance metrics, we focus on the impact of this training methodology on linguistic diversity, especially when conducted recursively over time. To assess this, we developed a set of novel metrics targeting lexical, syntactic, and semantic diversity, applying them in recursive fine-tuning experiments across various natural language generation tasks. Our findings reveal a marked decrease in the diversity of the models' outputs through successive iterations. This trend underscores the potential risks of training LLMs on predecessor-generated text, particularly concerning the preservation of linguistic richness. Our study highlights the need for careful consideration of the long-term effects of such training approaches on the linguistic capabilities of LLMs.

Most efforts to improve the reasoning capabilities of large language models (LLMs) involve either scaling the number of parameters and the size of training data, or scaling inference computation by letting models generate complex chains of thought. Motivated by interpretability studies showing that the crucial computation required for reasoning tasks is concentrated in a limited range of layers, we introduce Encode-Think-Decode (ETD), a method that enhances the reasoning capabilities of a base model by training it to iterate over a small subset of reasoning-relevant layers during the mid-training stage. ETD amplifies latent reasoning while preserving the original architecture, parameter count, hyperparameters, and training data composition. When iterating on the selected layers at inference time, ETD models yield substantial gains on 17 reasoning benchmarks, including +28.4% relative accuracy improvement on GSM8K and +36% on MATH with the OLMo-2 1B Base model. We also explore an adaptive depth strategy that adjusts the computation per input token. Our results show that recursive latent reasoning offers a simple and effective path to stronger LLM reasoning.

Large Multimodal Models (LMMs) have achieved remarkable success in vision-language tasks, yet their vast parameter counts are often underutilized during both training and inference. In this work, we embrace the idea of looping back to move forward: reusing model parameters through recursive refinement to extract stronger multimodal representations without increasing model size. We propose RecursiveVLM, a recursive Transformer architecture tailored for LMMs. Two key innovations enable effective looping: (i) a Recursive Connector that aligns features across recursion steps by fusing intermediate-layer hidden states and applying modality-specific projections, respecting the distinct statistical structures of vision and language tokens; (ii) a Monotonic Recursion Loss that supervises every step and guarantees performance improves monotonically with recursion depth. This design transforms recursion into an on-demand refinement mechanism: delivering strong results with few loops on resource-constrained devices and progressively improving outputs when more computation resources are available. Experiments show consistent gains of +3% over standard Transformers and +7% over vanilla recursive baselines, demonstrating that strategic looping is a powerful path toward efficient, deployment-adaptive LMMs.

We present Darwin Family, a framework for training-free evolutionary merging of large language models via gradient-free weight-space recombination. We ask whether frontier-level reasoning performance can be improved without additional training, by reorganizing latent capabilities already encoded in existing checkpoints. Darwin introduces three key ideas: (i) a 14-dimensional adaptive merge genome enabling fine-grained component- and block-level recombination; (ii) MRI-Trust Fusion, which adaptively balances diagnostic layer-importance signals with evolutionary search through a learnable trust parameter; and (iii) an Architecture Mapper that enables cross-architecture breeding between heterogeneous model families. Empirically, the flagship Darwin-27B-Opus achieves 86.9% on GPQA Diamond, ranking #6 among 1,252 evaluated models, and outperforming its fully trained foundation model without any gradient-based training. Across scales from 4B to 35B parameters, Darwin models consistently improve over their parents, support recursive multi-generation evolution, and enable a training-free evolutionary merge that combines Transformer- and Mamba-based components. Together, the Darwin Family demonstrates that diagnostic-guided evolutionary merging is a practical and reproducible alternative to costly post-training pipelines for reasoning-centric language models.

Cell instance segmentation models trained on cell-specific datasets suffer severe performance drops on out-of-distribution cell types, while interactive foundation models overcome this through per-instance prompting at a cost that is prohibitively expensive for histopathology images containing hundreds to thousands of densely packed instances. We introduce Group Prompting, a new paradigm that shifts interactive segmentation from per-instance O(N) to per-type O(T), where a single click per cell type suffices to segment all instances of that type. Our key observation is that the frozen image encoder of the Segment Anything Model (SAM) already clusters same-type cells in its feature space before any prompt is given. Exploiting this property, we propose Chain-of-Prompts (CoP), a training-free framework that recursively expands a single user click by (1) identifying reliable same-type locations through non-parametric gating of multi-scale encoder features, and (2) selecting the most spatially distant reliable point as the next prompt to maximize coverage. On three cell-type-annotated benchmarks, CoP with one click per type retains over 90% of per-instance performance and surpasses fully-supervised methods without any additional training. On four morphologically homogeneous benchmarks, a single click retains over 99%. Project Page: https://shjo-april.github.io/Chain-of-Prompts/

Recursive AI, the prospect of AI taking an increasingly complete role in building and improving AI, is a crown jewel of AI for AI. Although recursive self-development has become practical for small models, bounded tasks, and fixed time budgets, a more consequential realization of this ambition, i.e., developing a release-ready, frontier-competitive model, remains far more challenging. In this work, we ask how little human involvement is sufficient for an agent to develop a frontier model. We concentrate human input into a high-density, low-frequency interface: experts encode objectives, stage scaffolds, permission boundaries, and operating procedures as reusable research skills, while the agent instantiates these priors, selects experiments, diagnoses outcomes, and revises the training strategy. In the challenging domain of industrial coding, the agent evolves data and coordinates SFT, on-policy self-distillation, and reinforcement learning with verifiable rewards, ultimately producing iCoder, a 27B model for RTL design and GPU kernel optimization. Across seven benchmarks, iCoder leads RTLLM, outperforming GPT-5.5 and Claude-Opus-4.8; ranks second on CVDP and KernelBench L2, exceeding GPT-5.5 by 16 points; and ties Claude-Opus-4.8 for the best TritonBench result. Exploratory case studies further show iCoder's competitive iterative RTL and GPU-kernel optimization with substantially fewer tokens. These results chart an engineering path toward recursive self-improvement, in which humans distill the principles of model building, agents operationalize them through evidence-driven experimentation, and each generation of AI becomes a more capable architect of the next.

Most contemporary artificial intelligence (AI) systems are released with frozen parameters and improve through external updates, whereas an ideal system would keep improving from its own experience, a capacity we call recursive self-improvement (RSI). Yet studying RSI requires an environment that is continuously changing, objectively verifiable, and naturally grounded, posing a fundamental challenge for agent evolution. Here we introduce DeepEvolve, a sustainable evolution agent system grounded in future event prediction, in which agents continuously interact with a dynamically evolving environment and improve by internalizing and externalizing the experience gained through these interactions. A living environment synthesizes verifiable tasks, and a recursive-evolution engine turns the reasoning trajectory behind each prediction back into capability: decoupling search from prediction adapts parameter-level evolution to the contamination-prone live environment, while distilling reusable skills lets the agent evolve from the limited live trajectories such an environment affords. On the external FutureX leaderboard, which evaluates predictions against real-world outcomes and is updated weekly, our self-improved forecaster ranked first across all systems over three consecutive weeks, achieving up to a 195% improvement in rating. On our synthesized evaluation, it ranked among the top three across four base LLMs, outperforming the strongest baseline by up to 10.7 Bradley--Terry points. More broadly, these results suggest that a system built for self-improvement is best understood as an agent that co-evolves with a genuinely living, open-ended environment, pointing to a shift in AI from training static models on fixed data toward cultivating agents that grow stronger from their own experience, with such an open world as the indispensable basis of that growth.

Recursive feature machines (RFMs) learn representations of data by alternating between fitting a predictor to a dataset and updating features of that predictor using the average gradient outer product (AGOP). Connections between AGOPs and feature learning in neural networks motivate linear RFMs as a simple setting for analyzing how representations evolve during training. Here, we study the dynamics and statistics of linear RFM in noisy multi-output regression with isotropic sub-Gaussian input data and targets generated by a low-rank teacher matrix of dimension d. We extend the known connection between linear RFM and iteratively reweighted least squares from the interpolating setting to ridge-regularized multi-output regression with noise. We show that the learned feature matrix remains close to its infinite-data ideal counterpart at every iteration. Namely, for n samples, we show the error in the feature matrix decays as O(d/n) with high probability. Experiments on real-world text and single-cell gene-expression data illustrate the features learned by this simple linear model.

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.

Training multi-turn agentic workflows with reinforcement learning (RL) enables large language models to perform complex reasoning, use external tools, and conduct iterative search beyond single-turn settings. Yet multi-turn RL training remains highly unstable, often causing severe performance degradation as the number of turns increases. Through theoretical analysis, we identify three tightly coupled sources of instability: rollout-training context mismatch, weak turn-level credit assignment under sparse terminal rewards, and asynchronous policy drift when short and long trajectories are optimized under different policy versions. We show that these issues share a common structural origin in flattened trajectory optimization and address them through a unified reverse-turn formulation. We propose Reverse-Turn Policy Optimization (RTPO), which organizes multi-turn rollouts as sparse reverse trees and performs turn-level policy updates in temporal reverse order, aligning each decision with its downstream continuation. RTPO enables causally consistent turn-level credit assignment and on-policy continuation to control asynchronous drift. We provide theoretical guarantees showing that RTPO eliminates context mismatch and asynchronous drift under the proposed turn-level formulation, reduces credit bias, and converges to recursive optimality. Experiments on multi-turn agentic RL benchmarks show that RTPO improves upon trajectory- and turn-level baselines by 21.50% and 10.76%, respectively, highlighting its potential to support more stable training for tool-using agents.

Outer-learning algorithms use infinitesimal sensitivities to propose finite changes to initialization or training parameters. For hard-ReLU training, the derivative of the finite program and the derivative of its flow limit do not by themselves specify the response at a chosen radius. We characterize the intervening regime in which the perturbation radius is proportional to the GD step. Integer event rounding then survives at leading order: smooth Euler bias shifts each discrete phase, and upstream rounding moves downstream branch boundaries. We derive the crossing indices and a uniform endpoint expansion for finitely many separated transverse events in piecewise-C^2 dynamics, away from recursive phase boundaries. In contractive affine regions, an explicit remainder and complete branch verification certify finite candidate comparisons. Scalar phase frequencies and a coupled feedback ablation test the mechanism; frozen nonlinear-network experiments show radius-dependent prediction accuracy, including incomplete branch matches and failed-word tails. Together with local AD and uniform flow consistency, the result identifies sufficient response regimes: differentiating training is a choice of perturbation resolution as well as a choice of derivative.

Earth observation (EO) models are still built by hand. For each new task, experts design a training recipe and tune it against a benchmark. We show that this loop can be handed to an agent. Any verifiable task can be cast as a harness and a verifier, where the harness defines what the agent may use and the verifier defines what counts as success. Every EO task can be made verifiable, through labeled benchmarks, independent sensors, physical models or the repeated observation of the same place. Given only these two components, a general-purpose coding agent builds the EO model and improves it recursively on its own outputs. Settings long treated as separate research problems, from learning with a handful of labels to adapting across domains, become choices of harness and verifier. On four EO benchmarks spanning optical, SAR and multispectral time-series imagery, agent-built models surpass the state of the art and keep most of that accuracy from about 1% of the training labels. This establishes a new paradigm for EO, in which people design harnesses and verifiers and agents build the models, so EO models improve as agents do.

Recently, it was shown that small, looped architectures, such as Tiny Recursive Models (TRMs), can outperform Large Language Models (LLMs) on complex reasoning tasks, including the Abstraction and Reasoning Corpus (ARC). In this work, we investigate a core question: how can we further improve the efficiency of these methods with minimal changes? To address this, we frame the latent reasoning of TRMs as a form of classifier-free guidance and implicit policy improvement algorithm. Building on these insights, we propose a novel training scheme that provides a target for each loop during training. We demonstrate that our approach significantly enhances training efficiency. Our method reduces the total number of forward passes by 18x and eliminates halting mechanisms, while maintaining quality comparable to standard TRMs. Notably, we achieve 24% accuracy on ARC-1 with only 0.8M parameters, outperforming most LLMs.

Recent advances in depth-recurrent language models show that recurrence can decouple train-time compute and parameter count from test-time compute. In this work, we study how to convert existing pretrained non-recurrent language models into depth-recurrent models. We find that using a curriculum of recurrences to increase the effective depth of the model over the course of training preserves performance while reducing total computational cost. In our experiments, on mathematics, we observe that converting pretrained models to recurrent ones results in better performance at a given compute budget than simply post-training the original non-recurrent language model.

Foundation models in changing environments can encounter unfamiliar domain knowledge that their original training did not cover. However, new domains rarely provide large amounts of expert-created training data or reliable supervisory signals for further training. We introduce Recursa, a foundation model system that adapts to new domains by learning from its own experience without human experts or a stronger teacher model. Recursa uses a knowledge repository to store what it learns: domain-specific skills and instructions on when to apply them, along with memories of past task experiences and reflections on what to improve. Recursa bootstraps the repository from domain materials and then refines it through recursive self-improvement. It uses parallel learners to execute tasks and synthesize local improvements, then validates and merges the improvements into the knowledge repository. On Harvey LAB's Firm Knowledge benchmark, Recursa raises the all-pass rate on held-out test tasks from 30.0% to 55.0% with DeepSeek-V4.1-Flash and from 35.0% to 46.0% with Qwen3.8-Flash.

Recursive self-improvement (RSI) requires agents to diagnose system bottlenecks and coordinate improvements across training and inference. We refer to the agents' capability to jointly optimize training data, the trainer, and the inference harness as cross-component co-design. We introduce VibeTraining-Bench, a benchmark for evaluating this capability across tasks spanning terminal operation, software engineering, multi-turn tool use, and mathematical reasoning. Within each task, research agents start from an identical initial agent system under a fixed resource budget. Guided by validation feedback, they iteratively refine data, trainers, and inference harnesses, then select and submit a final agent system for evaluation on the test set. To prevent reward hacking, we enforce three safeguards: test data isolation, separate research and grading containers, and network restrictions for research agents. Our evaluation results show that frontier research agents substantially improve target agent systems. For example, on SWE-bench Verified, GPT-6-Astra raises the target agent system's performance from 32.9% to 53.7%, comparable to the human-developed instruct model's 55.4%. However, there is still room to improve their ability to co-design and iteratively refine data, trainer, and harness to achieve cumulative performance gains. We hope that VibeTraining-Bench will serve as a unified platform for advancing RSI, deepening our understanding of cross-component optimization for agent systems. Code and data are available at https://github.com/D2I-ai/VibeTraining-Bench.

While research on recursive self-improvement (RSI) has predominantly automated model training pipelines, reliable autonomous development demands a missing pillar: post-hoc monitoring and auditing to understand what models learn and ensure safe alignment. Mechanistic interpretability tools are essential to bridge this gap, among which Sparse Autoencoders (SAEs) serve as a cornerstone by isolating interpretable features for model inspection and steering. In this paper, we introduce SAEScientist-Bench to evaluate whether AI agents can act as scientists utilizing SAE tools for autonomous mechanistic discovery. Given a target concept, an agent designs contrastive probes and navigates a Gemma Scope dictionary of 131K+ features in Gemma-2-9B-IT to discover the optimal feature, evaluated against curated expert reference features anchored on Neuronpedia across activation rank, concept selectivity on contrastive texts, and causal steering. Across 10 agent configurations and 20 tasks, frontier agents demonstrate genuine discovery capabilities and lead different evaluation dimensions, but remain well behind the expert baseline, approaching expert levels on separating target concepts from contrastive controls while lagging substantially in causal generation steering. Further analysis reveals that although agents can design contrasts to rule out spurious candidates, they frequently misinterpret experimental measurements. These results establish experimental model understanding as a measurable capability for closed-loop autonomous AI R&D. Our code is available at https://github.com/Trae1ounG/SAEScientist.

Automatic differentiation through digital signal processing algorithms for virtual analogue modelling has recently gained popularity. These algorithms are typically more computationally efficient than black-box neural networks that rely on dense matrix multiplications. Due to their differentiable nature, they can be integrated with neural networks and jointly trained using gradient descent algorithms, resulting in more efficient systems. Furthermore, signal processing algorithms have significantly fewer parameters than neural networks, allowing the application of the Newton-Raphson method. This method offers faster and more robust convergence than gradient descent at the cost of quadratic storage. This paper presents a method to emulate analogue levelling amplifiers using a feed-forward digital compressor with parameters optimised via the Newton-Raphson method. We demonstrate that a digital compressor can successfully approximate the behaviour of our target unit, the Teletronix LA-2A. Different strategies for computing the Hessian matrix are benchmarked. We leverage parallel algorithms for recursive filters to achieve efficient training on modern GPUs. The resulting model is made into a VST plugin and is open-sourced at https://github.com/aim-qmul/4a2a.

Antibodies are essential therapeutic molecules, and their complementarity-determining regions (CDRs) form the primary antigen-recognition interface. Recent protein generative models have demonstrated broad capabilities in biomolecular design, yet post-training strategies for downstream objectives remain limited. Standard denoising training operates on noisy states obtained by perturbing native structures, whereas recursive generation proceeds through model-generated intermediate states. For flexible antibody CDR loops such as CDR-H3, this mismatch can allow backbone deviations to accumulate along the denoising trajectory and compromise antigen-facing loop geometry. We introduce ABOPD, an antibody design framework based on on-policy distillation that leverages privileged native geometry during training to supervise states visited along the model's own denoising trajectories. With this fine-grained structural supervision, ABOPD substantially improves structural recovery on RAbD CDR-H3 generation, reducing RMSD by 0.42 Å (from 2.37 Å to 1.95 Å) and outperforming supervised fine-tuning and offline distillation controls, offering a path to higher-fidelity protein design.

Kolmogorov-Arnold Networks (KAN) are a new class of neural network architecture representing a promising alternative to the Multilayer Perceptron (MLP), demonstrating improved expressiveness and interpretability. However, KANs suffer from slow training and inference speeds relative to MLPs due in part to the recursive nature of the underlying B-spline calculations. This issue is particularly apparent with respect to KANs utilizing high-degree B-splines, as the number of required non-parallelizable recursions is proportional to B-spline degree. We solve this issue by proposing MatrixKAN, a novel optimization that parallelizes B-spline calculations with matrix representation and operations, thus significantly improving effective computation time for models utilizing high-degree B-splines. In this paper, we demonstrate the superior scaling of MatrixKAN's computation time relative to B-spline degree. Further, our experiments demonstrate speedups of approximately 40x relative to KAN, with significant additional speedup potential for larger datasets or higher spline degrees.

Loss Given Default (LGD) modeling faces a fundamental data quality constraint: 90% of available training data consists of proxy estimates based on pre-distress balance sheets rather than actual recovery outcomes from completed bankruptcy proceedings. We demonstrate that this mixture-contaminated training structure causes systematic failure of recursive partitioning methods, with Random Forest achieving negative r-squared (-0.664, worse than predicting the mean) on held-out test data. Information-theoretic approaches based on Shannon entropy and mutual information provide superior generalization, achieving r-squared of 0.191 and RMSE of 0.284 on 1,218 corporate bankruptcies (1980-2023). Analysis reveals that leverage-based features contain 1.510 bits of mutual information while size effects contribute only 0.086 bits, contradicting regulatory assumptions about scale-dependent recovery. These results establish practical guidance for financial institutions deploying LGD models under Basel III requirements when representative outcome data is unavailable at sufficient scale. The findings generalize to medical outcomes research, climate forecasting, and technology reliability-domains where extended observation periods create unavoidable mixture structure in training data.

Recursive self-improvement (RSI) requires an agentic system to design, train, and evaluate its own successor. Data-driven post-training is a central part of that loop, yet existing evaluations measure it on a single benchmark, where an agent selects from a static pool or distills a stronger model to push one score up in one run. Real post-training is multi-domain, and a gain in one domain has to be weighed against a regression in another. We propose ParetoRSI-Gym, in which an agent searches for data, curates it, trains, reads back per-domain results, and repeats, with everything but the data held fixed: the initial LLM, the five domains (math, code, finance, medicine, science), the toolset, and the SFT pipeline. Generalization benchmarks in each domain separate capability gains from overfitting to the scores the agent optimizes against. Across three agent systems, three base models, five rounds and multiple seeds, the strongest system, Claude Code with Opus-5, raises the generalization scores of its proxy-best checkpoint by 9.2% relative to the starting model (+2.3 absolute points), averaged with equal weight over three base models and five domains, with a single-domain relative gain of up to 63% (medicine on Ministral-3-3B). Further analysis shows that the harness matters as much as the model it drives, and that each agent keeps a unique data selection strategy. We see our work as a step towards evaluation of RSI systems in real-world machine learning engineering.

Scaling Transformer-based click-through rate (CTR) models by stacking more parameters brings growing computational and storage overhead, creating a widening gap between scaling ambitions and the stringent industrial deployment constraints. We propose LoopCTR, which introduces a loop scaling paradigm that increases training-time computation through recursive reuse of shared model layers, decoupling computation from parameter growth. LoopCTR adopts a sandwich architecture enhanced with Hyper-Connected Residuals and Mixture-of-Experts, and employs process supervision at every loop depth to encode multi-loop benefits into the shared parameters. This enables a train-multi-loop, infer-zero-loop strategy where a single forward pass without any loop already outperforms all baselines. Experiments on three public benchmarks and one industrial dataset demonstrate state-of-the-art performance. Oracle analysis further reveals 0.02--0.04 AUC of untapped headroom, with models trained with fewer loops exhibiting higher oracle ceilings, pointing to a promising frontier for adaptive inference.