Daily Papers

Depth is a natural way to increase the computational capacity in Transformers, yet the contribution of deeper layers can diminish as depth grows larger. Recent approaches enhance normalization (e.g., LayerNorm Scaling) or residual connections (e.g., mHC, AttnRes) to enable better information flow and depth utilization. However, it remains unclear whether they truly translate increased architectural depth into effective computational depth, and whether their reported gains stem from better access to information across depth, or unaccounted-for confounding factors. In this paper, we introduce DepthBench, a controlled benchmark for studying computational depth across various architectures. We systematically vary the width--depth aspect ratio (d_{model}/n_{layer}) from shallow--wide to deep--narrow shapes, while keeping the model size and pre-training recipe fixed. Across 10 representative architectures, we find that the benefit of allocating more capacity to depth is strongly architecture-dependent. Standard Pre-LN and most of its norm- and scaling-based variants provide little benefit and can even degrade performance as models become deeper and narrower, whereas HC and Full AttnRes improve consistently even at extreme deep shapes. These gains extend beyond pre-training loss and consistently translate into improved domain-specific performance and effective computation. Controlled layer-level analyses further show that the gains of HC and Full AttnRes are associated with more effective utilization of additional layers, revealing distinct mechanisms of computational depth across architectures. Overall, our results identify residual connection design as a key determinant of whether depth can serve as a meaningful scaling axis by enabling additional architectural depth to translate into effective computation.

Recurrent Transformers increase computational depth through temporal recurrence, feeding each token's high-level hidden state into the computation of the next. This raises a natural question: is additional computation better spent on more temporal steps or greater physical depth? We investigate this question using Latent Recurrent Transformers (LRTs), which retain one backbone forward pass per vocabulary token during decoding and provide a controlled setting for comparing these two ways of adding computation. Specifically, we insert a latent thought token between consecutive vocabulary tokens. Each thought token passes through the same L layers as a vocabulary token, sharing the backbone parameters and providing an additional stage of hidden-state refinement before predicting the next token. We compare this L-layer LRT against a 2L-layer LRT without thought tokens. Both execute 2L Transformer blocks per vocabulary token during decoding, but the thought-token model uses fewer parameters. On 16- and 20-layer mixture-of-experts NanoChat backbones, one thought token brings the shallower model within 0.006 and 0.004 bits per byte of its double-depth counterpart, recovering 67% and 81% of the improvement with approximately 48% fewer total parameters. These results suggest that temporal thinking offers a parameter-efficient alternative to increasing physical depth in recurrent Transformers.

Current Vision-Language-Action (VLA) models rely on fixed computational depth, expending the same amount of compute on simple adjustments and complex multi-step manipulation. While Chain-of-Thought (CoT) prompting enables variable computation, it scales memory linearly and is ill-suited for continuous action spaces. We introduce Recurrent-Depth VLA (RD-VLA), an architecture that achieves computational adaptivity via latent iterative refinement rather than explicit token generation. RD-VLA employs a recurrent, weight-tied action head that supports arbitrary inference depth with a constant memory footprint. The model is trained using truncated backpropagation through time (TBPTT) to efficiently supervise the refinement process. At inference, RD-VLA dynamically allocates compute using an adaptive stopping criterion based on latent convergence. Experiments on challenging manipulation tasks show that recurrent depth is critical: tasks that fail entirely (0 percent success) with single-iteration inference exceed 90 percent success with four iterations, while simpler tasks saturate rapidly. RD-VLA provides a scalable path to test-time compute in robotics, replacing token-based reasoning with latent reasoning to achieve constant memory usage and up to 80x inference speedup over prior reasoning-based VLA models. Project page: https://rd-vla.github.io/

Large audio language models answer questions about speech, sound, and music, yet their accuracy drops sharply on tasks that need fine-grained acoustic analysis. Judging which of two speakers has the higher pitch demands iterative signal-level reasoning that a content question does not. Current models spend the same computational depth on both. We introduce AdaLoop, a lightweight recurrent module that learns how many latent refinement steps a given audio--question pair requires. A shared transformer block iterates over the audio representation, guided by the question, while a learned halting mechanism exits the loop once the representation is ready. AdaLoop adds fewer than 3\% of the base model's parameters and plugs into any audio encoder--language model pair without modifying either component. Evaluated on three architecturally distinct models across MMSU, MMAU-Pro, and MMAR, AdaLoop raises the average accuracy by 2.9 to 3.8 points, with the largest gains on perception-heavy subtasks where the model learns to apply deeper reasoning.

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped architectures possess an inductive bias toward latent reasoning. However, prior approaches fix the number of loop iterations during training and inference, leaving open the question of whether these models can flexibly adapt their computational depth under variable compute budgets. We introduce LoopFormer, a looped Transformer trained on variable-length trajectories to enable budget-conditioned reasoning. Our core contribution is a shortcut-consistency training scheme that aligns trajectories of different lengths, ensuring that shorter loops yield informative representations while longer loops continue to refine them. LoopFormer conditions each loop on the current time and step size, enabling representations to evolve consistently across trajectories of varying length rather than drifting or stagnating. Empirically, LoopFormer demonstrates robust performance on language modeling and reasoning benchmarks even under aggressive compute constraints, while scaling gracefully with additional budget. These results show that looped Transformers are inherently suited for adaptive language modeling, opening a path toward controllable and budget-aware large language models.

Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent Transformer that decouples computational depth from parameter count by iteratively applying a shared-weight Transformer block in latent space -- enabling the model to trade recurrence steps for deeper reasoning at inference time. Our architecture incorporates three mechanisms to make deep recurrence (20+ steps) stable: (1) a silent thinking objective that supervises only the final output, forcing genuine multi-step reasoning rather than intermediate heuristic shortcuts; (2) LayerScale initialization to protect fragile reasoning states from untrained layer noise; and (3) an identity-biased recurrence that creates a gradient highway across many steps. We evaluate on three compositional reasoning domains with decreasing inductive biases: graph reachability (strict adjacency masking), nested boolean logic (relative positioning), and unstructured relational text (where sequence position provides no structural hints). Across all tasks, we observe a clear computational frontier -- a boundary where performance transitions from chance to near-perfect as thinking steps scale with task complexity. Moreover, these tasks reveal qualitatively different generalization behaviors: precise but brittle (graph), approximate but robust (logic), and autonomous latent routing without structural hints (text). This progression illuminates how the interplay between a task-invariant recurrent reasoning core and task-specific perceptual interfaces shapes out-of-distribution (OOD) generalization, offering a mechanistic perspective on vertical chain-of-thought that complements the prevailing horizontal token-generation paradigm.

Traditional transformer models often allocate a fixed amount of computational resources to every input token, leading to inefficient and unnecessary computation. To address this, the Mixture of Depths (MoD) was introduced to dynamically adjust the computational depth by skipping less important layers. Despite its promise, current MoD approaches remain under-explored and face two main challenges: (1) high training costs due to the need to train the entire model along with the routers that determine which layers to skip, and (2) the risk of performance degradation when important layers are bypassed. In response to the first issue, we propose Router-Tuning, a method that fine-tunes only the router on a small dataset, drastically reducing the computational overhead associated with full model training. For the second challenge, we propose MindSkip, which deploys Attention with Dynamic Depths. This method preserves the model's performance while significantly enhancing computational and memory efficiency. Extensive experiments demonstrate that our approach delivers competitive results while dramatically improving the computation efficiency, e.g., 21\% speedup and only a 0.2\% performance drop. The code is released at https://github.com/CASE-Lab-UMD/Router-Tuning.

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 (looped) Transformers decouple computational depth from parameter depth by repeatedly applying shared layers, providing an explicit architectural primitive for iterative refinement and latent reasoning. However, early looped Transformers often underperform non-recursive baselines of equal compute. While recent literature has introduced more effective recursion mechanisms to mitigate this gap, existing architectures still operate at a fixed, full-token resolution, neglecting the potential efficiency of computing over compressed latent representations. In this paper, we propose SpiralFormer, a looped Transformer that executes recurrence under a multi-resolution recursion schedule. We provide probing evidence that multi-resolution recursion enables the model to learn hierarchical dependencies by inducing iteration-wise functional specialization across different scales. Empirically, SpiralFormer achieves better parameter and compute efficiency than both looped and non-looped baselines across model scales from 160M to 1.4B, establishing sequence resolution as a potential axis for scaling recursive architectures.

Looped language models separate computational depth from parameter count by repeatedly applying the same transformer block. Adapting these models requires a shared update that remains effective as hidden states evolve throughout the recurrent computation. Our empirical analysis reveals a pronounced late-loop bias in standard low-rank adaptation (LoRA): the shared update is more effective at later loop positions. This imbalance motivates training shared updates under varying combinations of their applications. Randomly omitting adapter applications alone, however, does not improve task performance; it reduces expected update strength during training while leaving inference unchanged. We introduce Loop Dropout, which couples stochastic masking of adapter applications with inverse-survival rescaling to preserve expected update strength and promote effective adaptation across loops. Extensive experiments demonstrate improved mathematical reasoning across model sizes, adapter ranks and training recipes, with benefits extending to general instruction tuning and code generation. Loop Dropout outperforms existing LoRA variants and adapter regularizers, while further analysis shows stronger early-loop adaptation. Every backbone loop remains active, and inference applies the adapter at all loops using standard LoRA without additional trainable parameters or inference computation.

Looped language models (LoopLMs) increase computational depth through parameter sharing, offering a path to scale inference computation without adding parameters. However, it remains unclear when additional recurrence is beneficial and how architectural choices affect its effectiveness. Through controlled experiments, we systematically examine (1) when recurrence helps, (2) where it should be applied, and (3) how its conditioning affects performance. Our evaluation covers inference budgets below, within, and beyond the training horizon under knowledge and reasoning tasks. (1) We find that recurrence can improve reasoning beyond the training horizon while degrading knowledge performance, but harder reasoning instances do not consistently benefit more. (2) Performance also depends on how distinct layers and recurrent iterations are allocated, showing that effective depth alone is insufficient to predict behavior. Non-recurrent output layers improve robustness to under-unrolling, while the preferred placement of input and output layers varies with inference budget. (3) Finally, we find that conventional initial-state injection offers limited robustness to varying recurrence depth. We therefore propose history-state injection as an alternative, and show that channel-wise history-state injection combined with timestep conditioning offers a low-cost and more effective design, better preserving knowledge under extended unrolling while improving robustness across inference budgets. Overall, our results clarify when recurrent computation helps, where it fails, and offer practical guidelines for designing LoopLMs across variable inference budgets.

Diffusion language models (DLMs) enable fast generation by predicting multiple tokens in parallel, but their practical adoption remains limited by a persistent quality gap relative to comparably sized autoregressive (AR) models. We attribute this gap to a computation-difficulty mismatch: within a partially observed sequence, some unknown tokens are easy to predict, while others require substantially more computation. Existing DLMs nevertheless apply uniform computational depth to all unknown positions at each denoising step. We introduce ALoDLM, which replaces uniform computation with token-adaptive latent recurrence. At each denoising step, ALoDLM iteratively refines latent representations and allocates computation according to token difficulty. Tokens ready to commit are fed back as discrete context, while unresolved tokens retain and further refine their latent states through additional recurrent passes. To learn token prediction and computation allocation jointly, we formulate token-wise computation schedules as latent variables and derive a conditional negative evidence lower bound (NELBO). We train ALoDLM at 1.7B and 8B parameter scales. Across eleven benchmarks, ALoDLM outperforms all evaluated DLMs and the corresponding AR baselines in average benchmark score at both scales. ALoDLM also retains fast parallel decoding, yielding a strong quality-efficiency trade-off among evaluated autoregressive and diffusion models under optimized inference engines.

Distribution Matching Distillation (DMD) distills score-based generative models into efficient one-step generators, without requiring a one-to-one correspondence with the sampling trajectories of their teachers. However, limited model capacity causes one-step distilled models underperform on complex generative tasks, e.g., synthesizing intricate object motions in text-to-video generation. Directly extending DMD to multi-step distillation increases memory usage and computational depth, leading to instability and reduced efficiency. While prior works propose stochastic gradient truncation as a potential solution, we observe that it substantially reduces the generation diversity of multi-step distilled models, bringing it down to the level of their one-step counterparts. To address these limitations, we propose Phased DMD, a multi-step distillation framework that bridges the idea of phase-wise distillation with Mixture-of-Experts (MoE), reducing learning difficulty while enhancing model capacity. Phased DMD is built upon two key ideas: progressive distribution matching and score matching within subintervals. First, our model divides the SNR range into subintervals, progressively refining the model to higher SNR levels, to better capture complex distributions. Next, to ensure the training objective within each subinterval is accurate, we have conducted rigorous mathematical derivations. We validate Phased DMD by distilling state-of-the-art image and video generation models, including Qwen-Image (20B parameters) and Wan2.2 (28B parameters). Experimental results demonstrate that Phased DMD preserves output diversity better than DMD while retaining key generative capabilities. We will release our code and models.

Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to power-law improvements in performance as computation increases. As an anchoring point, we consider the architectural formulation of looped transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly 20times less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla transformer, which normalizes and injects an earlier block, also provides an exponent increase, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the transformer, which can lead to efficiency gains that increase with scale.

Looped transformers reuse a shared block of layers to increase computational depth without increasing the number of trainable parameters. They are trained with backpropagation through time (BPTT). To save training compute, BPTT is often truncated to the last few loops, but truncation yields biased gradients that may weaken the benefit of looping. In this work, we study the value of truncation in looped transformer training in a systematic way: we jointly vary model size, training tokens, and forward and backward loop counts across nearly 600 training runs and fit a unified scaling law that captures the effects of looping and truncation through effective parameters. Despite the training-compute savings of truncation, our fitted law favors full BPTT when forward and backward loop counts are jointly optimized. In matched-compute runs, full BPTT through fewer loops consistently outperforms truncated settings of the same compute. The law further shows that at fixed model size, the compute-optimal loop count and training-token budget both grow with compute. When model size is also free, the law identifies two fully trained loops as the best looped setting. Experimentally, this setting achieves lower validation loss than the compute-optimal non-looped model with about 27% fewer non-embedding parameters and only 8% more training compute.

Information retrieval is a cornerstone of modern knowledge acquisition, enabling billions of queries each day across diverse domains. However, traditional keyword-based search engines are increasingly inadequate for handling complex, multi-step information needs. Our position is that Large Language Models (LLMs), endowed with reasoning and agentic capabilities, are ushering in a new paradigm termed Agentic Deep Research. These systems transcend conventional information search techniques by tightly integrating autonomous reasoning, iterative retrieval, and information synthesis into a dynamic feedback loop. We trace the evolution from static web search to interactive, agent-based systems that plan, explore, and learn. We also introduce a test-time scaling law to formalize the impact of computational depth on reasoning and search. Supported by benchmark results and the rise of open-source implementations, we demonstrate that Agentic Deep Research not only significantly outperforms existing approaches, but is also poised to become the dominant paradigm for future information seeking. All the related resources, including industry products, research papers, benchmark datasets, and open-source implementations, are collected for the community in https://github.com/DavidZWZ/Awesome-Deep-Research.

Large Language Models (LLMs) often exhibit a gap between their internal knowledge and their explicit linguistic outputs. In this report, we empirically investigate whether Looped Transformers (LTs)--architectures that increase computational depth by iterating shared layers--can bridge this gap by utilizing their iterative nature as a form of introspection. Our experiments reveal that while increasing loop iterations narrows the gap, it is partly driven by a degradation of their internal knowledge carried by representations. Moreover, another empirical analysis suggests that current LTs' ability to perceive representations does not improve across loops; it is only present in the final loop. These results suggest that while LTs offer a promising direction for scaling computational depth, they have yet to achieve the introspection required to truly link representation space and natural language.

Recent work on looped language models suggests that many reasoning problems benefit from greater computational depth rather than from additional independent parameters. Existing studies, however, focus almost exclusively on Transformer backbones, leaving open whether this principle also applies to state-space language models. We investigate Looped Mamba and Looped Hybrid Mamba-Transformer architectures, which repeatedly apply a shared Mamba (or hybrid) block to introduce explicit finite-depth recurrent computation. On two controlled reasoning tasks-Mano (modular-arithmetic manipulation) and p-hop induction-Looped Mamba consistently outperforms parameter-matched non-looped baselines and, in several settings, matches or exceeds non-looped models of equal effective depth. We then extend the study to language model pre-training under matched iso-parameter and iso-FLOPs protocols, which jointly disentangle the effects of parameter sharing and effective depth: looped models remain competitive on downstream benchmarks with substantially fewer distinct parameters, although deeper non-looped models retain an advantage in validation perplexity under strict iso-FLOPs comparisons. Finally, we adapt Ouro's two-stage exit gate to Looped Mamba for threshold-controlled selection among recurrent-step outputs. Since all recurrent steps are still executed, the selected exit step represents prediction depth rather than reduced wall-clock computation. At the scales studied, adaptive exit-state selection improves downstream performance at intermediate depths, while actual inference-time savings require additional state-handling mechanisms.

Looped Transformers have attracted substantial attention as a parameter-efficient approach to increasing computational depth through repeated application of shared Transformer blocks. However, their practical advantages over conventional Transformers remain under debate: each additional loop incurs another Transformer pass and requires caching another set of KV states, causing inference FLOPs and KV-cache memory to grow continuously with loop depth. This overhead becomes particularly severe at large loop counts and long context, preventing the parameter efficiency of Looped Transformers from translating into practical inference efficiency. In this paper, we find that much of the additional computation and storage introduced by looping is redundant. As recurrence proceeds, state changes become increasingly concentrated on a small subset of tokens; attention-output differences are dominated by a sparse and stable subset of key columns; and KV residuals between adjacent loops become progressively more amenable to low-bit quantization. Building on these observations, we introduce FlashLoop, a training-free inference framework that reduces cross-loop redundancy through token-sparse updates, sparse attention, and KV-residual quantization. Across several Looped Transformers models, FlashLoop delivers lossless accuracy while achieving up to 1.64times end-to-end speedup and up to 6times KV-cache memory reduction, substantially improving the practicality of scaling Looped Transformers to greater computational depths and longer context.

Looped transformers and Mixture-of-Experts (MoE) offer complementary routes to efficient scaling: recurrence increases computational depth at fixed parameters, while MoE sparsity expands total capacity at fixed active compute. Yet existing scaling laws model recurrence or sparsity in isolation. In this work, we introduce Loop Scaling Laws, the first scaling law to jointly model recurrence and sparsity alongside model size and data. At its core is a bounded, sparsity-conditional recurrence mapping that characterizes the effective-parameter gain from looping and how sparsity raises this gain. The laws predict the held-out loss of looped models more accurately than prior alternatives, and recover the standard dense and MoE scaling laws as special cases. Beyond prediction, the fitted laws provide a principled foundation for designing looped MoE models under compute and memory constraints. Downstream evaluations further demonstrate the complementary benefits of the two axes: sparsity delivers ~3x active-parameter efficiency, recurrence yields ~2x total-parameter efficiency on reasoning, and joint scaling further advances the performance frontier. As a practical extension, we show these gains hold at trillion-token scale: at matched training compute, a looped MoE with law-derived recurrence matches a ~2x larger non-looped MoE on the reasoning benchmarks, while enabling test-time scaling through recurrence.

Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs -- the Transformer -- has inherent limitations in computational depth, rendering them theoretically incapable of solving many reasoning tasks that demand increasingly deep computations. Chain of Thought (CoT) prompting has emerged as a technique to address these architectural limitations, as evidenced by several theoretical studies. It offers a promising approach to solving complex reasoning tasks that were previously beyond the capabilities of these models. Despite its successes, CoT and its variants (such as Tree of Thought, Graph of Thought, etc.) rely on a "one-prompt-for-all" approach, using a single prompt structure (e.g., "think step by step") for a wide range of tasks -- from counting and sorting to solving mathematical and algorithmic problems. This approach poses significant challenges for models to generate the correct reasoning steps, as the model must navigate through a vast prompt template space to find the appropriate template for each task. In this work, we build upon previous theoretical analyses of CoT to demonstrate how the one-prompt-for-all approach can negatively affect the computability of LLMs. We partition the solution search space into two: the prompt space and the answer space. Our findings show that task-specific supervision is essential for navigating the prompt space accurately and achieving optimal performance. Through experiments with state-of-the-art LLMs, we reveal a gap in reasoning performance when supervision is applied versus when it is not.

Sequential Recommendation (SeqRec) aims to predict the next item by capturing sequential patterns from users' historical interactions, playing a crucial role in many real-world recommender systems. However, existing approaches predominantly adopt a direct forward computation paradigm, where the final hidden state of the sequence encoder serves as the user representation. We argue that this inference paradigm, due to its limited computational depth, struggles to model the complex evolving nature of user preferences and lacks a nuanced understanding of long-tail items, leading to suboptimal performance. To address this issue, we propose ReaRec, the first inference-time computing framework for recommender systems, which enhances user representations through implicit multi-step reasoning. Specifically, ReaRec autoregressively feeds the sequence's last hidden state into the sequential recommender while incorporating special reasoning position embeddings to decouple the original item encoding space from the multi-step reasoning space. Moreover, we introduce two lightweight reasoning-based learning methods, Ensemble Reasoning Learning (ERL) and Progressive Reasoning Learning (PRL), to further effectively exploit ReaRec's reasoning potential. Extensive experiments on five public real-world datasets and different SeqRec architectures demonstrate the generality and effectiveness of our proposed ReaRec. Remarkably, post-hoc analyses reveal that ReaRec significantly elevates the performance ceiling of multiple sequential recommendation backbones by approximately 30\%-50\%. Thus, we believe this work can open a new and promising avenue for future research in inference-time computing for sequential recommendation.

Recent advances in visual reasoning have leveraged vision transformers to tackle the ARC-AGI benchmark. However, we argue that the feed-forward architecture, where computational depth is strictly bound to parameter size, falls short of capturing the iterative, algorithmic nature of human induction. In this work, we propose a recursive architecture called Loop-ViT, which decouples reasoning depth from model capacity through weight-tied recurrence. Loop-ViT iterates a weight-tied Hybrid Block, combining local convolutions and global attention, to form a latent chain of thought. Crucially, we introduce a parameter-free Dynamic Exit mechanism based on predictive entropy: the model halts inference when its internal state ``crystallizes" into a low-uncertainty attractor. Empirical results on the ARC-AGI-1 benchmark validate this perspective: our 18M model achieves 65.8% accuracy, outperforming massive 73M-parameter ensembles. These findings demonstrate that adaptive iterative computation offers a far more efficient scaling axis for visual reasoning than simply increasing network width. The code is available at https://github.com/WenjieShu/LoopViT.

Looped Transformers improve parameter efficiency by repeatedly applying shared Transformer blocks over multiple recurrent loops, increasing computational depth without increasing the parameter count. However, KV cache memory still scales with the number of loops, becoming a key memory bottleneck that limits batch size and inference throughput. KV cache quantization can alleviate this bottleneck, but existing methods often suffer substantial accuracy degradation at aggressive low-precision regimes. We observe that looped Transformers offer a unique opportunity: KV states across loops are highly similar. Based on this observation, we propose ResidualQuant, which uses the final-loop KV states as a reference and represents the remaining loops with low-precision residuals. Our method further combines least-square scaling and rotations applied to the residuals, as well as loop-wise mixed precision, to enable accurate quantization down to INT2 while retaining efficient reconstruction. Across multiple looped Transformer models and mathematical reasoning and code generation benchmarks, ResidualQuant consistently improves the accuracy-memory tradeoff over state-of-the-art rotation-based KV quantization. In particular, our method retains accuracy close to BF16 under mixed-precision settings while reducing theoretical KV storage by 80.7%, achieving up to 13.0% higher accuracy than the rotation-based baseline at the same memory budget. On an RTX 5090, the reduced KV memory traffic improves fixed-batch decode throughput by up to 2.73x, while the smaller memory footprint enables up to 2x larger batches, improving peak throughput by up to 4.15x.

Reasoning, the process of devising and executing complex goal-oriented action sequences, remains a critical challenge in AI. Current large language models (LLMs) primarily employ Chain-of-Thought (CoT) techniques, which suffer from brittle task decomposition, extensive data requirements, and high latency. Inspired by the hierarchical and multi-timescale processing in the human brain, we propose the Hierarchical Reasoning Model (HRM), a novel recurrent architecture that attains significant computational depth while maintaining both training stability and efficiency. HRM executes sequential reasoning tasks in a single forward pass without explicit supervision of the intermediate process, through two interdependent recurrent modules: a high-level module responsible for slow, abstract planning, and a low-level module handling rapid, detailed computations. With only 27 million parameters, HRM achieves exceptional performance on complex reasoning tasks using only 1000 training samples. The model operates without pre-training or CoT data, yet achieves nearly perfect performance on challenging tasks including complex Sudoku puzzles and optimal path finding in large mazes. Furthermore, HRM outperforms much larger models with significantly longer context windows on the Abstraction and Reasoning Corpus (ARC), a key benchmark for measuring artificial general intelligence capabilities. These results underscore HRM's potential as a transformative advancement toward universal computation and general-purpose reasoning systems.

Vision Transformers (ViTs) have achieved remarkable success in image recognition, yet standard ViT architectures are hampered by substantial parameter redundancy and high computational cost, limiting their practical deployment. While recent efforts on efficient ViTs primarily focus on static model compression or token-level sparsification, they remain constrained by fixed computational depth for all tokens. In this work, we present MoR-ViT, a novel vision transformer framework that, for the first time, incorporates a token-level dynamic recursion mechanism inspired by the Mixture-of-Recursions (MoR) paradigm. This approach enables each token to adaptively determine its processing depth, yielding a flexible and input-dependent allocation of computational resources. Extensive experiments on ImageNet-1K and transfer benchmarks demonstrate that MoR-ViT not only achieves state-of-the-art accuracy with up to 70% parameter reduction and 2.5x inference acceleration, but also outperforms leading efficient ViT baselines such as DynamicViT and TinyViT under comparable conditions. These results establish dynamic recursion as an effective strategy for efficient vision transformers and open new avenues for scalable and deployable deep learning models in real-world scenarios.

Current world models face a fundamental tension: faithful long-horizon simulation demands deep computation, but deeper models are expensive to deploy and prone to compounding errors. We resolve this by introducing Looped World Models (LoopWM), which are the first looped architectures for world modelling. Our method iteratively refines latent environment states through a parameter-shared transformer block. This yield up to 100x parameter efficiency over conventional approaches with adaptive computation that automatically scales depth to match the complexity of each prediction step. Orthogonal to scaling model size and training data, LoopWM establishes iterative latent depth as a new scaling axis for world simulation, which might significantly push the community forward.

Improving text-to-image models has traditionally relied on increasing model size or the number of denoising steps. In this work, we explore an alternative way to scale computation by repeatedly running shared Transformer blocks within each denoising step, effectively increasing computational depth while keeping the parameter count fixed. This looped computation enables iterative refinement of internal representations without explicit reasoning tokens. However, naive looping fails to consistently improve image quality. We trace this problem to weak supervision across intermediate loops and unregulated attention updates that progressively erode local information. To overcome these challenges, we propose Looped Diffusion Transformer (Looped-DiT), which combines deep supervision across intermediate loops with self-modulating attention to stabilize looped feature updates. Under matched-parameter and matched-compute settings, Looped-DiT consistently outperforms non-looped baselines. Notably, a 260M-parameter looped model can surpass a model 6.5x larger across multiple text-to-image benchmarks while requiring 4.9x lower inference compute. Beyond this performance gain, we find that looped computation can offer a more effective form of iterative computation for diffusion models, with increasing loop depth yielding larger gains than adding more denoising steps under a fixed inference budget. Furthermore, deeper loops can progressively correct mistakes made in earlier loops, exhibiting behaviors suggestive of latent reasoning. Together, these results show that looped computation offers a promising way to scale visual generation models.

The Liquid Reasoning Transformer (LRT) is a transformer architecture designed for inference with adaptive depths using iterative changes, discard-based correction, and a learned stopping mechanism. Instead of relying on a single feedforward pass, the model updates a recurrent reasoning token across multiple internal steps, allowing it to correct early errors and allocate computation based on input difficulty. We evaluate the LRT on Sudoku as a controlled testbed for structured reasoning and show that it achieves strong performance, reaching 98.68% digit accuracy and 36.30% full-puzzle accuracy without using symbolic rules or search. Analyzing internal patterns shows that the discard and stop gates play different, important roles in stabilizing inferences and adjusting computational depth. We discuss how these mechanisms extend naturally to chess-scale reasoning tasks and outline extensions for multi-token reasoning and larger domains.

Important tasks such as reasoning and planning are fundamentally algorithmic, meaning that solving them robustly requires acquiring true reasoning or planning algorithms, rather than shortcuts. Large Language Models lack true algorithmic ability primarily because of the limitations of neural network optimization algorithms, their optimization data and optimization objective, but also due to architectural inexpressivity. To solve this, our paper proposes augmenting LLMs with a library of fundamental operations and sophisticated differentiable programs, so that common algorithms do not need to be learned from scratch. We add memory, registers, basic operations, and adaptive recurrence to a transformer architecture built on LLaMA3. Then, we define a method for directly compiling algorithms into a differentiable starting library, which is used natively and propagates gradients for optimization. In this preliminary study, we explore the feasability of augmenting LLaMA3 with a differentiable computer, for instance by fine-tuning small transformers on simple algorithmic tasks with variable computational depth.

Message-passing based approaches form the default backbone of most learning architectures on graph-structured data. However, the rapid progress of modern deep learning architectures in other domains, particularly sequence modeling, raises the question of how graph learning can benefit from these advances. We introduce Linearized Graph Sequence Models, a framework that recasts message-passing graph computation from the perspective of sequence modeling to simplify architectural choices. Our approach systematically separates the computational processing depth from the information propagation depth, allowing core graph architectural decisions to be treated as sequence modeling choices. Specifically, we analyze, both empirically and theoretically, what sequence properties make methods effective for learning and preserving the graph inductive bias. In particular, we validate our findings, demonstrating improved performance on long-range information tasks in graphs. Our findings provide a principled way to integrate modern sequence modeling advances into message-passing based graph learning. Beyond this, our work demonstrates how the separation of processing and information depth can recast central architectural questions as input modeling choices.

Advanced reasoning in large language models has achieved remarkable performance on challenging tasks, but the prevailing long-context reasoning paradigm faces critical limitations: quadratic computational scaling with sequence length, reasoning constrained by maximum context boundaries, and performance degradation beyond pre-training context windows. Existing approaches primarily compress reasoning chains without addressing the fundamental scaling problem. To overcome these challenges, we introduce InftyThink, a paradigm that transforms monolithic reasoning into an iterative process with intermediate summarization. By interleaving short reasoning segments with concise progress summaries, our approach enables unbounded reasoning depth while maintaining bounded computational costs. This creates a characteristic sawtooth memory pattern that significantly reduces computational complexity compared to traditional approaches. Furthermore, we develop a methodology for reconstructing long-context reasoning datasets into our iterative format, transforming OpenR1-Math into 333K training instances. Experiments across multiple model architectures demonstrate that our approach reduces computational costs while improving performance, with Qwen2.5-Math-7B showing 3-13% improvements across MATH500, AIME24, and GPQA_diamond benchmarks. Our work challenges the assumed trade-off between reasoning depth and computational efficiency, providing a more scalable approach to complex reasoning without architectural modifications.

We present a comprehensive framework for enhancing Retrieval-Augmented Generation (RAG) systems through dynamic retrieval strategies and reinforcement fine-tuning. This approach significantly improves large language models on knowledge-intensive tasks, including opendomain question answering and complex reasoning. Our framework integrates two complementary techniques: Policy-Optimized RetrievalAugmented Generation (PORAG), which optimizes the use of retrieved information, and Adaptive Token-Layer Attention Scoring (ATLAS), which dynamically determines retrieval timing and content based on contextual needs. Together, these techniques enhance both the utilization and relevance of retrieved content, improving factual accuracy and response quality. Designed as a lightweight solution compatible with any Transformer-based LLM without requiring additional training, our framework excels in knowledge-intensive tasks, boosting output accuracy in RAG settings. We further propose CRITIC, a novel method to selectively compress key-value caches by token importance, mitigating memory bottlenecks in long-context applications. The framework also incorporates test-time scaling techniques to dynamically balance reasoning depth and computational resources, alongside optimized decoding strategies for faster inference. Experiments on benchmark datasets show that our framework reduces hallucinations, strengthens domain-specific reasoning, and achieves significant efficiency and scalability gains over traditional RAG systems. This integrated approach advances the development of robust, efficient, and scalable RAG systems across diverse applications.

Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides a roadmap for advancing quantum algorithms and hardware toward achieving quantum advantage in molecular modeling.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Recent advances in large language models (LLMs) have predominantly focused on maximizing accuracy and reasoning capabilities, often overlooking crucial computational efficiency considerations. While this approach has yielded impressive accuracy improvements, it has led to methods that may be impractical for real-world deployment due to computational overhead and latency constraints. This paper investigates the potential synergy between reasoning enhancement and computational efficiency by analyzing the integration of two contrasting approaches: Quiet-STaR (Self-Taught Reasoner) and REBASE (REward BAlanced SEarch). Through comprehensive empirical analysis using the Mistral-7B model on the GSM8K dataset, we demonstrate that while each method excels in its primary objective-Quiet-STaR achieving superior accuracy (32.03%) despite high computational cost (554.66s runtime, 12.73T FLOPs), and REBASE providing exceptional efficiency (8.47s runtime, 2.35T FLOPs) while maintaining baseline-comparable accuracy (10.94%)-their integration reveals fundamental challenges in reconciling reasoning depth with computational efficiency. The combined approach unexpectedly results in degraded performance (9.38% accuracy, 143.66s runtime), highlighting critical insights about the complex interplay between reasoning enhancement and efficiency optimization in LLMs. Our findings illuminate the need for novel architectures and algorithms specifically designed to bridge the gap between these competing objectives, while providing concrete directions for future research in compute-efficient reasoning methods.

Consider a market of competing model providers selling query access to models with varying costs and capabilities. Customers submit problem instances and are willing to pay up to a budget for a verifiable solution. An arbitrageur efficiently allocates inference budget across providers to undercut the market, thus creating a competitive offering with no model-development risk. In this work, we initiate the study of arbitrage in AI model markets, empirically demonstrating the viability of arbitrage and illustrating its economic consequences. We conduct an in-depth case study of SWE-bench GitHub issue resolution using two representative models, GPT-5 mini and DeepSeek v3.2. In this verifiable domain, simple arbitrage strategies generate net profit margins of up to 40%. Robust arbitrage strategies that generalize across different domains remain profitable. Distillation further creates strong arbitrage opportunities, potentially at the expense of the teacher model's revenue. Multiple competing arbitrageurs drive down consumer prices, reducing the marginal revenue of model providers. At the same time, arbitrage reduces market segmentation and facilitates market entry for smaller model providers by enabling earlier revenue capture. Our results suggest that arbitrage can be a powerful force in AI model markets with implications for model development, distillation, and deployment.

The computational overhead of Vision Transformers in practice stems fundamentally from their deep architectures, yet existing acceleration strategies have primarily targeted algorithmic-level optimizations such as token pruning and attention speedup. This leaves an underexplored research question: can we reduce the number of stacked transformer layers while maintaining comparable representational capacity? To answer this, we propose a branch-based structural reparameterization technique that operates during the training phase. Our approach leverages parallel branches within transformer blocks that can be systematically consolidated into streamlined single-path models suitable for inference deployment. The consolidation mechanism works by gradually merging branches at the entry points of nonlinear components, enabling both feed-forward networks (FFN) and multi-head self-attention (MHSA) modules to undergo exact mathematical reparameterization without inducing approximation errors at test time. When applied to ViT-Tiny, the framework successfully reduces the original 12-layer architecture to 6, 4, or as few as 3 layers while maintaining classification accuracy on ImageNet-1K. The resulting compressed models achieve inference speedups of up to 37% on mobile CPU platforms. Our findings suggest that the conventional wisdom favoring extremely deep transformer stacks may be unnecessarily restrictive, and point toward new opportunities for constructing efficient vision transformers.

Recent advances in Gaussian Splatting have significantly advanced the field, achieving both panoptic and interactive segmentation of 3D scenes. However, existing methodologies often overlook the critical need for reconstructing specified targets with complex structures from sparse views. To address this issue, we introduce TSGaussian, a novel framework that combines semantic constraints with depth priors to avoid geometry degradation in challenging novel view synthesis tasks. Our approach prioritizes computational resources on designated targets while minimizing background allocation. Bounding boxes from YOLOv9 serve as prompts for Segment Anything Model to generate 2D mask predictions, ensuring semantic accuracy and cost efficiency. TSGaussian effectively clusters 3D gaussians by introducing a compact identity encoding for each Gaussian ellipsoid and incorporating 3D spatial consistency regularization. Leveraging these modules, we propose a pruning strategy to effectively reduce redundancy in 3D gaussians. Extensive experiments demonstrate that TSGaussian outperforms state-of-the-art methods on three standard datasets and a new challenging dataset we collected, achieving superior results in novel view synthesis of specific objects. Code is available at: https://github.com/leon2000-ai/TSGaussian.

We introduce Marigold-SSD, a single-step, late-fusion depth completion framework that leverages strong diffusion priors while eliminating the costly test-time optimization typically associated with diffusion-based methods. By shifting computational burden from inference to finetuning, our approach enables efficient and robust 3D perception under real-world latency constraints. Marigold-SSD achieves significantly faster inference with a training cost of only 4.5 GPU days. We evaluate our method across four indoor and two outdoor benchmarks, demonstrating strong cross-domain generalization and zero-shot performance compared to existing depth completion approaches. Our approach significantly narrows the efficiency gap between diffusion-based and discriminative models. Finally, we challenge common evaluation protocols by analyzing performance under varying input sparsity levels. Page: https://dtu-pas.github.io/marigold-ssd/

Transformer-based language models spread FLOPs uniformly across input sequences. In this work we demonstrate that transformers can instead learn to dynamically allocate FLOPs (or compute) to specific positions in a sequence, optimising the allocation along the sequence for different layers across the model depth. Our method enforces a total compute budget by capping the number of tokens (k) that can participate in the self-attention and MLP computations at a given layer. The tokens to be processed are determined by the network using a top-k routing mechanism. Since k is defined a priori, this simple procedure uses a static computation graph with known tensor sizes, unlike other conditional computation techniques. Nevertheless, since the identities of the k tokens are fluid, this method can expend FLOPs non-uniformly across the time and model depth dimensions. Thus, compute expenditure is entirely predictable in sum total, but dynamic and context-sensitive at the token-level. Not only do models trained in this way learn to dynamically allocate compute, they do so efficiently. These models match baseline performance for equivalent FLOPS and wall-clock times to train, but require a fraction of the FLOPs per forward pass, and can be upwards of 50\% faster to step during post-training sampling.

Point-spread-function (PSF) engineering is a powerful computational imaging techniques wherein a custom phase mask is integrated into an optical system to encode additional information into captured images. Used in combination with deep learning, such systems now offer state-of-the-art performance at monocular depth estimation, extended depth-of-field imaging, lensless imaging, and other tasks. Inspired by recent advances in spatial light modulator (SLM) technology, this paper answers a natural question: Can one encode additional information and achieve superior performance by changing a phase mask dynamically over time? We first prove that the set of PSFs described by static phase masks is non-convex and that, as a result, time-averaged PSFs generated by dynamic phase masks are fundamentally more expressive. We then demonstrate, in simulation, that time-averaged dynamic (TiDy) phase masks can offer substantially improved monocular depth estimation and extended depth-of-field imaging performance.

Depth Anything has achieved remarkable success in monocular depth estimation with strong generalization ability. However, it suffers from temporal inconsistency in videos, hindering its practical applications. Various methods have been proposed to alleviate this issue by leveraging video generation models or introducing priors from optical flow and camera poses. Nonetheless, these methods are only applicable to short videos (< 10 seconds) and require a trade-off between quality and computational efficiency. We propose Video Depth Anything for high-quality, consistent depth estimation in super-long videos (over several minutes) without sacrificing efficiency. We base our model on Depth Anything V2 and replace its head with an efficient spatial-temporal head. We design a straightforward yet effective temporal consistency loss by constraining the temporal depth gradient, eliminating the need for additional geometric priors. The model is trained on a joint dataset of video depth and unlabeled images, similar to Depth Anything V2. Moreover, a novel key-frame-based strategy is developed for long video inference. Experiments show that our model can be applied to arbitrarily long videos without compromising quality, consistency, or generalization ability. Comprehensive evaluations on multiple video benchmarks demonstrate that our approach sets a new state-of-the-art in zero-shot video depth estimation. We offer models of different scales to support a range of scenarios, with our smallest model capable of real-time performance at 30 FPS.

Due to the large number of parameters, the inference phase of Large Language Models (LLMs) is resource-intensive. Unlike traditional model compression, which needs retraining, recent dynamic computation methods show that not all components are required for inference, enabling a training-free pipeline. In this paper, we focus on the dynamic depth of LLM generation. A token-position aware layer skipping framework is proposed to save 1.5x times operations efficiently while maintaining performance. We first observed that tokens predicted later have lower perplexity and thus require less computation. Then, we propose a training-free algorithm called Position-Aware Depth Decay Decoding (D^3), which leverages a power-law decay function, leftlfloor L times (alpha^i) rightrfloor, to determine the number of layers to retain when generating token T_i. Remarkably, without any retraining, the D^3 achieves success across a wide range of generation tasks for the first time. Experiments on large language models (\ie the Llama) with 7 sim 70 billion parameters show that D^3 can achieve an average 1.5x speedup compared with the full-inference pipeline while maintaining comparable performance with nearly no performance drop (<1%) on the GSM8K and BBH benchmarks.

Monocular depth estimation aims to recover the depth information of 3D scenes from 2D images. Recent work has made significant progress, but its reliance on large-scale datasets and complex decoders has limited its efficiency and generalization ability. In this paper, we propose a lightweight and data-centric framework for zero-shot monocular depth estimation. We first adopt DINOv3 as the visual encoder to obtain high-quality dense features. Secondly, to address the inherent drawbacks of the complex structure of the DPT, we design the Simple Depth Transformer (SDT), a compact transformer-based decoder. Compared to the DPT, it uses a single-path feature fusion and upsampling process to reduce the computational overhead of cross-scale feature fusion, achieving higher accuracy while reducing the number of parameters by approximately 85%-89%. Furthermore, we propose a quality-based filtering strategy to filter out harmful samples, thereby reducing dataset size while improving overall training quality. Extensive experiments on five benchmarks demonstrate that our framework surpasses the DPT in accuracy. This work highlights the importance of balancing model design and data quality for achieving efficient and generalizable zero-shot depth estimation. Code: https://github.com/AIGeeksGroup/AnyDepth. Website: https://aigeeksgroup.github.io/AnyDepth.

Foundation-model-based monocular depth estimation offers a viable alternative to active sensors for robot perception, yet its computational cost often prohibits deployment on edge platforms. Existing methods perform independent per-frame inference, wasting the substantial computational redundancy between adjacent viewpoints in continuous robot operation. This paper presents AsyncMDE, an asynchronous depth perception system consisting of a foundation model and a lightweight model that amortizes the foundation model's computational cost over time. The foundation model produces high-quality spatial features in the background, while the lightweight model runs asynchronously in the foreground, fusing cached memory with current observations through complementary fusion, outputting depth estimates, and autoregressively updating the memory. This enables cross-frame feature reuse with bounded accuracy degradation. At a mere 3.83M parameters, it operates at 237 FPS on an RTX 4090, recovering 77% of the accuracy gap to the foundation model while achieving a 25X parameter reduction. Validated across indoor static, dynamic, and synthetic extreme-motion benchmarks, AsyncMDE degrades gracefully between refreshes and achieves 161FPS on a Jetson AGX Orin with TensorRT, clearly demonstrating its feasibility for real-time edge deployment.

A DJ mix is a sequence of music tracks concatenated seamlessly, typically rendered for audiences in a live setting by a DJ on stage. As a DJ mix is produced in a studio or the live version is recorded for music streaming services, computational methods to analyze DJ mixes, for example, extracting track information or understanding DJ techniques, have drawn research interests. Many of previous works are, however, limited to identifying individual tracks in a mix or segmenting it, and the sizes of the datasets are usually small. In this paper, we provide an in-depth analysis of DJ music by aligning a mix to its original music tracks. We set up the subsequence alignment such that the audio features are less sensitive to the tempo or key change of the original track in a mix. This approach provides temporally tight mix-to-track matching from which we can obtain cue-points, transition length, mix segmentation, and musical changes in DJ performance. Using 1,557 mixes from 1001Tracklists including 13,728 tracks and 20,765 transitions, we conduct the proposed analysis and show a wide range of statistics, which may elucidate the creative process of DJ music making.

Despite advancements in self-supervised monocular depth estimation, challenges persist in dynamic scenarios due to the dependence on assumptions about a static world. In this paper, we present Manydepth2, to achieve precise depth estimation for both dynamic objects and static backgrounds, all while maintaining computational efficiency. To tackle the challenges posed by dynamic content, we incorporate optical flow and coarse monocular depth to create a pseudo-static reference frame. This frame is then utilized to build a motion-aware cost volume in collaboration with the vanilla target frame. Furthermore, to improve the accuracy and robustness of the network architecture, we propose an attention-based depth network that effectively integrates information from feature maps at different resolutions by incorporating both channel and non-local attention mechanisms. Compared to methods with similar computational costs, Manydepth2 achieves a significant reduction of approximately five percent in root-mean-square error for self-supervised monocular depth estimation on the KITTI-2015 dataset. The code could be found at https://github.com/kaichen-z/Manydepth2.

Monocular depth estimation is crucial for numerous downstream vision tasks and applications. Current discriminative approaches to this problem are limited due to blurry artifacts, while state-of-the-art generative methods suffer from slow sampling due to their SDE nature. Rather than starting from noise, we seek a direct mapping from input image to depth map. We observe that this can be effectively framed using flow matching, since its straight trajectories through solution space offer efficiency and high quality. Our study demonstrates that a pre-trained image diffusion model can serve as an adequate prior for a flow matching depth model, allowing efficient training on only synthetic data to generalize to real images. We find that an auxiliary surface normals loss further improves the depth estimates. Due to the generative nature of our approach, our model reliably predicts the confidence of its depth estimates. On standard benchmarks of complex natural scenes, our lightweight approach exhibits state-of-the-art performance at favorable low computational cost despite only being trained on little synthetic data.

Depth Estimation plays a crucial role in recent applications in robotics, autonomous vehicles, and augmented reality. These scenarios commonly operate under constraints imposed by computational power. Stereo image pairs offer an effective solution for depth estimation since it only needs to estimate the disparity of pixels in image pairs to determine the depth in a known rectified system. Due to the difficulty in acquiring reliable ground-truth depth data across diverse scenarios, self-supervised techniques emerge as a solution, particularly when large unlabeled datasets are available. We propose a novel self-supervised convolutional approach that outperforms existing state-of-the-art Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) while balancing computational cost. The proposed CCNeXt architecture employs a modern CNN feature extractor with a novel windowed epipolar cross-attention module in the encoder, complemented by a comprehensive redesign of the depth estimation decoder. Our experiments demonstrate that CCNeXt achieves competitive metrics on the KITTI Eigen Split test data while being 10.18times faster than the current best model and achieves state-of-the-art results in all metrics in the KITTI Eigen Split Improved Ground Truth and Driving Stereo datasets when compared to recently proposed techniques. To ensure complete reproducibility, our project is accessible at https://github.com/alelopes/CCNext{https://github.com/alelopes/CCNext}.

Mathematical reasoning models are widely deployed in education, automated tutoring, and decision support systems despite exhibiting fundamental computational instabilities. We demonstrate that state-of-the-art models (Qwen2.5-Math-7B) achieve 61% accuracy through a mixture of reliable and unreliable reasoning pathways: 18.4% of correct predictions employ stable, faithful reasoning while 81.6% emerge through computationally inconsistent pathways. Additionally, 8.8% of all predictions are silent failures -- confident yet incorrect outputs. Through comprehensive analysis using novel faithfulness metrics, we reveal: (1) reasoning quality shows weak negative correlation with correctness (r=-0.21, p=0.002), reflecting a binary classification threshold artifact rather than a monotonic inverse relationship; (2) scaling from 1.5B to 7B parameters (4.7x increase) provides zero accuracy benefit on our evaluated subset (6% of GSM8K), requiring validation on the complete benchmark; and (3) latent reasoning employs diverse computational strategies, with ~20% sharing CoT-like patterns. These findings highlight that benchmark accuracy can mask computational unreliability, demanding evaluation reforms measuring stability beyond single-sample metrics.

In the era of "Software Engineering 2.0" (SE 2.0), where intelligent agents collaborate with human engineers, Generative AI is advancing beyond code generation into Software Architecture (SA). While Large Language Models (LLMs) demonstrate superior capabilities, computational costs and data privacy concerns drive interest in Small Language Models (SLMs) with fewer than 7 billion parameters. However, the reasoning limits of these resource-constrained models remain unexplored. This study benchmarks 10 state-of-the-art SLMs on Architectural Decision Records generation, introducing a multi-dimensional framework evaluating Technical Compliance and Semantic Diversity. Our empirical results reveal a significant reasoning gap: models above the 3B-parameter threshold demonstrate robust zero-shot capabilities, while sub-2B models show the strongest BERTScore gains from Fine-Tuning, though compliance improvements are not guaranteed. Contrary to assumptions regarding context saturation, Few-Shot prompting serves as a highly effective calibration mechanism for select mid-sized models with short context windows. Furthermore, high semantic diversity in off-the-shelf small models often correlates with hallucination rather than productive exploration. These findings establish a rigorous baseline for deploying sustainable, locally hosted architectural assistants.

We measure how much one extra recurrence is worth to a looped (depth-recurrent) language model, in equivalent unique parameters. From an iso-depth sweep of 116 pretraining runs across recurrence counts r in {1, 2, 4, 8} spanning {sim}50times in training compute, we fit a joint scaling law L = E + A,(N_once + r^φ N_rec)^{-α} + B,D^{-β} and recover a new recurrence-equivalence exponent φ= 0.46. Intuitively, φ tells us whether looping a block r times is equivalent in validation loss to r unique blocks of a non-looped model (full equivalence, φ{=}1) or to a single block run repeatedly with no capacity gain (φ{=}0). Our φ= 0.46 sits in between, so each additional recurrence predictably increases validation loss at matched training compute. For example, at r{=}4 a 410M looped model performs on par with a 580M non-looped model, but incurs the training cost of a 1B non-looped one. We demonstrate the utility of φ as a measurement tool on two probes. Truncated backpropagation lowers φ to 0.38, indicating that the loop mechanism is poorly trained under truncation, even though validation loss decreases. Conversely, hyperconnections raise φ to 0.65, a genuine capacity gain. Our method applies to any looped LM and separates true loop improvements from token-budget gains.

Monocular depth estimation has seen remarkable progress through foundation models achieving robust zero-shot generalization, yet their computational demands place them far beyond the reach of embedded and mobile platforms. Lightweight alternatives exist, but have been developed almost exclusively within single-domain, self-supervised paradigms, failing silently under domain shift. We present ZipDepth, a compact monocular depth network that bridges this gap by combining an efficient reparameterizable encoder-decoder with large-scale knowledge distillation from a foundation model over a large multi-domain training set. Comprising just 6.1M parameters, ZipDepth runs at real-time rates from server GPUs to power-constrained devices, achieving the best trade-off between zero-shot accuracy and deployment efficiency among lightweight models across five benchmarks, taking a significant step towards the accuracy of foundation models with 50x more parameters.

Monocular depth estimation is a ubiquitous yet highly ill-posed computer vision task, with downstream applications in scene reconstruction, computational photography, and robotics, among others. Despite the field's maturity, recent models still struggle to generalize to out-of-distribution inputs and to produce sharp and detailed depth maps. In this paper, we revisit Marigold, a set of techniques for repurposing modern image generation and editing models, powered by the diffusion transformer (DiT) architecture, into state-of-the-art monocular depth estimators. Our recipes target single-step inference from pretrained multi-step flow-matching models, with quantization where needed, preserving model capacity while remaining cheap to run. We analyze the artifacts of naive training and identify two effective remedies: aligning the model's internal representations with semantic features extracted from ground-truth, and adopting a 2-stage fine-tuning protocol built around a novel Sinkhorn-based loss. The results are crisper, cleaner depth maps that generalize well out-of-distribution, with 16-26% improvement in AbsRel over the previous best on KITTI and ETH3D. Qualitatively, our model resolves fur, foliage, and hair-thin edges that have eluded prior models. Furthermore, Marigold V2 achieves state-of-the-art results when applied to other dense regression tasks, such as surface normals estimation and intrinsic image decomposition. Project website: https://hf.co/spaces/huawei-bayerlab/marigold-v2-web

Depth sensing is a critical function for robotic tasks such as localization, mapping and obstacle detection. There has been a significant and growing interest in depth estimation from a single RGB image, due to the relatively low cost and size of monocular cameras. However, state-of-the-art single-view depth estimation algorithms are based on fairly complex deep neural networks that are too slow for real-time inference on an embedded platform, for instance, mounted on a micro aerial vehicle. In this paper, we address the problem of fast depth estimation on embedded systems. We propose an efficient and lightweight encoder-decoder network architecture and apply network pruning to further reduce computational complexity and latency. In particular, we focus on the design of a low-latency decoder. Our methodology demonstrates that it is possible to achieve similar accuracy as prior work on depth estimation, but at inference speeds that are an order of magnitude faster. Our proposed network, FastDepth, runs at 178 fps on an NVIDIA Jetson TX2 GPU and at 27 fps when using only the TX2 CPU, with active power consumption under 10 W. FastDepth achieves close to state-of-the-art accuracy on the NYU Depth v2 dataset. To the best of the authors' knowledge, this paper demonstrates real-time monocular depth estimation using a deep neural network with the lowest latency and highest throughput on an embedded platform that can be carried by a micro aerial vehicle.

Obtaining personalized 3D animatable avatars from a monocular camera has several real world applications in gaming, virtual try-on, animation, and VR/XR, etc. However, it is very challenging to model dynamic and fine-grained clothing deformations from such sparse data. Existing methods for modeling 3D humans from depth data have limitations in terms of computational efficiency, mesh coherency, and flexibility in resolution and topology. For instance, reconstructing shapes using implicit functions and extracting explicit meshes per frame is computationally expensive and cannot ensure coherent meshes across frames. Moreover, predicting per-vertex deformations on a pre-designed human template with a discrete surface lacks flexibility in resolution and topology. To overcome these limitations, we propose a novel method `\keyfeature: Neural Surface Fields' for modeling 3D clothed humans from monocular depth. NSF defines a neural field solely on the base surface which models a continuous and flexible displacement field. NSF can be adapted to the base surface with different resolution and topology without retraining at inference time. Compared to existing approaches, our method eliminates the expensive per-frame surface extraction while maintaining mesh coherency, and is capable of reconstructing meshes with arbitrary resolution without retraining. To foster research in this direction, we release our code in project page at: https://yuxuan-xue.com/nsf.

Transformer-based end-to-end speech recognition has achieved great success. However, the large footprint and computational overhead make it difficult to deploy these models in some real-world applications. Model compression techniques can reduce the model size and speed up inference, but the compressed model has a fixed architecture which might be suboptimal. We propose a novel Transformer encoder with Input-Dependent Dynamic Depth (I3D) to achieve strong performance-efficiency trade-offs. With a similar number of layers at inference time, I3D-based models outperform the vanilla Transformer and the static pruned model via iterative layer pruning. We also present interesting analysis on the gate probabilities and the input-dependency, which helps us better understand deep encoders.

Structured pruning of modern large language models (LLMs) has emerged as a way of decreasing their high computational needs. Width pruning reduces the size of projection weight matrices (e.g., by removing attention heads) while maintaining the number of layers. Depth pruning, in contrast, removes entire layers or blocks, while keeping the size of the remaining weights unchanged. Most current research focuses on either width-only or a blend of width and depth pruning, with little comparative analysis between the two units (width vs. depth) concerning their impact on LLM inference efficiency. In this work, we show that a simple depth pruning approach can compete with recent width pruning methods in terms of zero-shot task performance. Our pruning method boosts inference speeds, especially under memory-constrained conditions that require limited batch sizes for running LLMs, where width pruning is ineffective. We hope this work can help deploy LLMs on local and edge devices.

Estimating global tree canopy height is crucial for forest conservation and climate change applications. However, capturing high-resolution ground truth canopy height using LiDAR is expensive and not available globally. An efficient alternative is to train a canopy height estimator to operate on single-view remotely sensed imagery. The primary obstacle to this approach is that these methods require significant training data to generalize well globally and across uncommon edge cases. Recent monocular depth estimation foundation models have show strong zero-shot performance even for complex scenes. In this paper we leverage the representations learned by these models to transfer to the remote sensing domain for measuring canopy height. Our findings suggest that our proposed Depth Any Canopy, the result of fine-tuning the Depth Anything v2 model for canopy height estimation, provides a performant and efficient solution, surpassing the current state-of-the-art with superior or comparable performance using only a fraction of the computational resources and parameters. Furthermore, our approach requires less than \$1.30 in compute and results in an estimated carbon footprint of 0.14 kgCO2. Code, experimental results, and model checkpoints are openly available at https://github.com/DarthReca/depth-any-canopy.

Multi-view 3D object detection systems often struggle with generating precise predictions due to the challenges in estimating depth from images, increasing redundant and incorrect detections. Our paper presents Ray Denoising, an innovative method that enhances detection accuracy by strategically sampling along camera rays to construct hard negative examples. These examples, visually challenging to differentiate from true positives, compel the model to learn depth-aware features, thereby improving its capacity to distinguish between true and false positives. Ray Denoising is designed as a plug-and-play module, compatible with any DETR-style multi-view 3D detectors, and it only minimally increases training computational costs without affecting inference speed. Our comprehensive experiments, including detailed ablation studies, consistently demonstrate that Ray Denoising outperforms strong baselines across multiple datasets. It achieves a 1.9\% improvement in mean Average Precision (mAP) over the state-of-the-art StreamPETR method on the NuScenes dataset. It shows significant performance gains on the Argoverse 2 dataset, highlighting its generalization capability. The code will be available at https://github.com/LiewFeng/RayDN.

Despite the significant progress in multimodal large language models (MLLMs), their high computational cost remains a barrier to real-world deployment. Inspired by the mixture of depths (MoDs) in natural language processing, we aim to address this limitation from the perspective of ``activated tokens''. Our key insight is that if most tokens are redundant for the layer computation, then can be skipped directly via the MoD layer. However, directly converting the dense layers of MLLMs to MoD layers leads to substantial performance degradation. To address this issue, we propose an innovative MoD adaptation strategy for existing MLLMs called gamma-MoD. In gamma-MoD, a novel metric is proposed to guide the deployment of MoDs in the MLLM, namely rank of attention maps (ARank). Through ARank, we can effectively identify which layer is redundant and should be replaced with the MoD layer. Based on ARank, we further propose two novel designs to maximize the computational sparsity of MLLM while maintaining its performance, namely shared vision-language router and masked routing learning. With these designs, more than 90% dense layers of the MLLM can be effectively converted to the MoD ones. To validate our method, we apply it to three popular MLLMs, and conduct extensive experiments on 9 benchmark datasets. Experimental results not only validate the significant efficiency benefit of gamma-MoD to existing MLLMs but also confirm its generalization ability on various MLLMs. For example, with a minor performance drop, i.e., -1.5%, gamma-MoD can reduce the training and inference time of LLaVA-HR by 31.0% and 53.2%, respectively.

State-of-the-art Graph Neural Networks (GNNs) have limited scalability with respect to the graph and model sizes. On large graphs, increasing the model depth often means exponential expansion of the scope (i.e., receptive field). Beyond just a few layers, two fundamental challenges emerge: 1. degraded expressivity due to oversmoothing, and 2. expensive computation due to neighborhood explosion. We propose a design principle to decouple the depth and scope of GNNs -- to generate representation of a target entity (i.e., a node or an edge), we first extract a localized subgraph as the bounded-size scope, and then apply a GNN of arbitrary depth on top of the subgraph. A properly extracted subgraph consists of a small number of critical neighbors, while excluding irrelevant ones. The GNN, no matter how deep it is, smooths the local neighborhood into informative representation rather than oversmoothing the global graph into "white noise". Theoretically, decoupling improves the GNN expressive power from the perspectives of graph signal processing (GCN), function approximation (GraphSAGE) and topological learning (GIN). Empirically, on seven graphs (with up to 110M nodes) and six backbone GNN architectures, our design achieves significant accuracy improvement with orders of magnitude reduction in computation and hardware cost.

While current high-resolution depth estimation methods achieve strong results, they often suffer from computational inefficiencies due to reliance on heavyweight models and multiple inference steps, increasing inference time. To address this, we introduce PatchRefiner V2 (PRV2), which replaces heavy refiner models with lightweight encoders. This reduces model size and inference time but introduces noisy features. To overcome this, we propose a Coarse-to-Fine (C2F) module with a Guided Denoising Unit for refining and denoising the refiner features and a Noisy Pretraining strategy to pretrain the refiner branch to fully exploit the potential of the lightweight refiner branch. Additionally, we introduce a Scale-and-Shift Invariant Gradient Matching (SSIGM) loss to enhance synthetic-to-real domain transfer. PRV2 outperforms state-of-the-art depth estimation methods on UnrealStereo4K in both accuracy and speed, using fewer parameters and faster inference. It also shows improved depth boundary delineation on real-world datasets like CityScape, ScanNet++, and KITTI, demonstrating its versatility across domains.

What is the current state-of-the-art for image restoration and enhancement applied to degraded images acquired under less than ideal circumstances? Can the application of such algorithms as a pre-processing step to improve image interpretability for manual analysis or automatic visual recognition to classify scene content? While there have been important advances in the area of computational photography to restore or enhance the visual quality of an image, the capabilities of such techniques have not always translated in a useful way to visual recognition tasks. Consequently, there is a pressing need for the development of algorithms that are designed for the joint problem of improving visual appearance and recognition, which will be an enabling factor for the deployment of visual recognition tools in many real-world scenarios. To address this, we introduce the UG^2 dataset as a large-scale benchmark composed of video imagery captured under challenging conditions, and two enhancement tasks designed to test algorithmic impact on visual quality and automatic object recognition. Furthermore, we propose a set of metrics to evaluate the joint improvement of such tasks as well as individual algorithmic advances, including a novel psychophysics-based evaluation regime for human assessment and a realistic set of quantitative measures for object recognition performance. We introduce six new algorithms for image restoration or enhancement, which were created as part of the IARPA sponsored UG^2 Challenge workshop held at CVPR 2018. Under the proposed evaluation regime, we present an in-depth analysis of these algorithms and a host of deep learning-based and classic baseline approaches. From the observed results, it is evident that we are in the early days of building a bridge between computational photography and visual recognition, leaving many opportunities for innovation in this area.

In this paper, we analyze the computational limitations of Mamba and State-space Models (SSMs) by using the circuit complexity framework. Despite Mamba's stateful design and recent attention as a strong candidate to outperform Transformers, we have demonstrated that both Mamba and SSMs with poly(n)-precision and constant-depth layers reside within the DLOGTIME-uniform TC^0 complexity class. This result indicates Mamba has the same computational capabilities as Transformer theoretically, and it cannot solve problems like arithmetic formula problems, boolean formula value problems, and permutation composition problems if TC^0 neq NC^1. Therefore, it challenges the assumption Mamba is more computationally expressive than Transformers. Our contributions include rigorous proofs showing that Selective SSM and Mamba architectures can be simulated by DLOGTIME-uniform TC^0 circuits, and they cannot solve problems outside TC^0.

Zero-shot depth completion has gained attention for its ability to generalize across environments without sensor-specific datasets or retraining. However, most existing approaches rely on diffusion-based test-time optimization, which is computationally expensive due to iterative denoising. Recent visual-prompt-based methods reduce training cost but still require repeated forward--backward passes through the full frozen network to optimize input-level prompts, resulting in slow inference. In this work, we show that adapting only the decoder is sufficient for effective test-time optimization, as depth foundation models concentrate depth-relevant information within a low-dimensional decoder subspace. Based on this insight, we propose a lightweight test-time adaptation method that updates only this low-dimensional subspace using sparse depth supervision. Our approach achieves state-of-the-art performance, establishing a new Pareto frontier between accuracy and efficiency for test-time adaptation. Extensive experiments on five indoor and outdoor datasets demonstrate consistent improvements over prior methods, highlighting the practicality of fast zero-shot depth completion.

Spatial and temporal resource constraints are critical for both biological and artificial intelligent systems. Here we define differentiable cost terms for breadth, depth, and time within a recurrent convolutional neural network conceived as a finite subset of an infinite lattice. We optimize these costs jointly with task errors via backpropagation. We set different pressures on breadth, depth, and time, which leads to diverse computational graphs emerging organically through training. We find that all three resources can be traded off against each other to achieve a given level of accuracy. Networks grow in all three dimensions with task complexity and spontaneously take more recurrent steps when inputs are occluded. Surprisingly, time used by the model correlates with human reaction times in an object recognition task. Our framework provides a normative account of how resource constraints shape neural architectures, connecting to questions about brain design in neuroscience, and may help illuminate the diversity of neural solutions found in nature.

Standard transformer architectures apply the same number of layers to every token regardless of contextual difficulty. We present Token-Selective Attention (TSA), a learned per-token gate on residual updates between consecutive transformer blocks. Each gate is a lightweight two-layer multi-layer perceptron (MLP) that produces a continuous halting probability, making the mechanism end-to-end differentiable with 1.7% parameter overhead and no changes to the base architecture. Notably, TSA learns difficulty-proportional routing without any explicit depth pressure: even at λ=0 (no depth regularisation), the task-loss gradient alone drives the router to skip 20% of token-layer operations. On character-level language modeling, TSA saved 14-23% of token-layer operations (TLOps) across Tiny-Shakespeare and enwik8 at <0.5% quality loss. At matched efficiency, TSA achieved 0.7% lower validation loss than early exit, and the learned routing transfers directly to inference-time sparse execution for real wall-clock speedup.

As data propagates through a Transformer, the norm of its hidden states grows by orders of magnitude with depth, a phenomenon framed as 'curse of depth' and nearly universally treated as a pathology to be suppressed. We take the opposite view. Across 16 pre-trained LLMs from 9 families, spanning dense, mixture-of-experts and hybrid architectures and Pre-, Peri- and Post-Norm designs, we find that this growth reflects an emergent depth-positional encoding, carried by the only learned per-layer gain on the residual stream, the normalization weight γ: with depth, γ grows in magnitude and rotates in direction, jointly encoding the layer index. We make this depth-conditioned encoding explicit with LayerRoPE, an implicit analog of RoPE along the depth axis, which replaces all layerwise γ vectors with a single shared vector and depth-conditioned scalars, at a net reduction in parameters and <0.02% change in FLOPs. Across a model ladder scaled up to 100B+ tokens, LayerRoPE consistently outperforms Pre-, Post- and Peri-Norm and Layer-Norm Scaling, reaching Pre-Norm's 1.3B loss with 3.4times less compute; LayerRoPE is the only approach that shows strong convergence and improves near monotonically as depth scales to 512 layers. It improves learning-rate sensitivity by 3-10times, and transfers naively to and consistently improves looped latent models and Vision Transformers. Inspecting its learned schedule inverts the prevailing premise: LayerRoPE does not shrink the residual stream but widens it, damping what each block reads while amplifying what it writes. Depth stability, our results suggest, calls not for suppressing the residual stream, but for depth-conditioned regulation of the computational blocks it feeds.

Recent advances in medical image segmentation have been driven by deep learning; however, most existing methods remain limited by modality-specific designs and exhibit poor adaptability to dynamic medical imaging scenarios. The Segment Anything Model 2 (SAM2) and its related variants, which introduce a streaming memory mechanism for real-time video segmentation, present new opportunities for prompt-based, generalizable solutions. Nevertheless, adapting these models to medical video scenarios typically requires large-scale datasets for retraining or transfer learning, leading to high computational costs and the risk of catastrophic forgetting. To address these challenges, we propose DD-SAM2, an efficient adaptation framework for SAM2 that incorporates a Depthwise-Dilated Adapter (DD-Adapter) to enhance multi-scale feature extraction with minimal parameter overhead. This design enables effective fine-tuning of SAM2 on medical videos with limited training data. Unlike existing adapter-based methods focused solely on static images, DD-SAM2 fully exploits SAM2's streaming memory for medical video object tracking and segmentation. Comprehensive evaluations on TrackRad2025 (tumor segmentation) and EchoNet-Dynamic (left ventricle tracking) datasets demonstrate superior performance, achieving Dice scores of 0.93 and 0.97, respectively. To the best of our knowledge, this work provides an initial attempt at systematically exploring adapter-based SAM2 fine-tuning for medical video segmentation and tracking. Code, datasets, and models will be publicly available at https://github.com/apple1986/DD-SAM2.

Scaling depth is a key driver for large language models (LLMs). Yet, as LLMs become deeper, they often suffer from signal degradation: informative features formed in shallow layers are gradually diluted by repeated residual updates, making them harder to recover in deeper layers. We introduce mixture-of-depths attention (MoDA), a mechanism that allows each attention head to attend to sequence KV pairs at the current layer and depth KV pairs from preceding layers. We further describe a hardware-efficient algorithm for MoDA that resolves non-contiguous memory-access patterns, achieving 97.3% of FlashAttention-2's efficiency at a sequence length of 64K. Experiments on 1.5B-parameter models demonstrate that MoDA consistently outperforms strong baselines. Notably, it improves average perplexity by 0.2 across 10 validation benchmarks and increases average performance by 2.11% on 10 downstream tasks, with a negligible 3.7% FLOPs computational overhead. We also find that combining MoDA with post-norm yields better performance than using it with pre-norm. These results suggest that MoDA is a promising primitive for depth scaling. Code is released at https://github.com/hustvl/MoDA .

To obtain excellent deep neural architectures, a series of techniques are carefully designed in EfficientNets. The giant formula for simultaneously enlarging the resolution, depth and width provides us a Rubik's cube for neural networks. So that we can find networks with high efficiency and excellent performance by twisting the three dimensions. This paper aims to explore the twisting rules for obtaining deep neural networks with minimum model sizes and computational costs. Different from the network enlarging, we observe that resolution and depth are more important than width for tiny networks. Therefore, the original method, i.e., the compound scaling in EfficientNet is no longer suitable. To this end, we summarize a tiny formula for downsizing neural architectures through a series of smaller models derived from the EfficientNet-B0 with the FLOPs constraint. Experimental results on the ImageNet benchmark illustrate that our TinyNet performs much better than the smaller version of EfficientNets using the inversed giant formula. For instance, our TinyNet-E achieves a 59.9% Top-1 accuracy with only 24M FLOPs, which is about 1.9% higher than that of the previous best MobileNetV3 with similar computational cost. Code will be available at https://github.com/huawei-noah/ghostnet/tree/master/tinynet_pytorch, and https://gitee.com/mindspore/mindspore/tree/master/model_zoo/research/cv/tinynet.

Many natural language processing and information retrieval problems can be formalized as the task of semantic matching. Existing work in this area has been largely focused on matching between short texts (e.g., question answering), or between a short and a long text (e.g., ad-hoc retrieval). Semantic matching between long-form documents, which has many important applications like news recommendation, related article recommendation and document clustering, is relatively less explored and needs more research effort. In recent years, self-attention based models like Transformers and BERT have achieved state-of-the-art performance in the task of text matching. These models, however, are still limited to short text like a few sentences or one paragraph due to the quadratic computational complexity of self-attention with respect to input text length. In this paper, we address the issue by proposing the Siamese Multi-depth Transformer-based Hierarchical (SMITH) Encoder for long-form document matching. Our model contains several innovations to adapt self-attention models for longer text input. In order to better capture sentence level semantic relations within a document, we pre-train the model with a novel masked sentence block language modeling task in addition to the masked word language modeling task used by BERT. Our experimental results on several benchmark datasets for long-form document matching show that our proposed SMITH model outperforms the previous state-of-the-art models including hierarchical attention, multi-depth attention-based hierarchical recurrent neural network, and BERT. Comparing to BERT based baselines, our model is able to increase maximum input text length from 512 to 2048. We will open source a Wikipedia based benchmark dataset, code and a pre-trained checkpoint to accelerate future research on long-form document matching.

Motivated by the superior performance of image diffusion models, more and more researchers strive to extend these models to the text-based video editing task. Nevertheless, current video editing tasks mainly suffer from the dilemma between the high fine-tuning cost and the limited generation capacity. Compared with images, we conjecture that videos necessitate more constraints to preserve the temporal consistency during editing. Towards this end, we propose EVE, a robust and efficient zero-shot video editing method. Under the guidance of depth maps and temporal consistency constraints, EVE derives satisfactory video editing results with an affordable computational and time cost. Moreover, recognizing the absence of a publicly available video editing dataset for fair comparisons, we construct a new benchmark ZVE-50 dataset. Through comprehensive experimentation, we validate that EVE could achieve a satisfactory trade-off between performance and efficiency. We will release our dataset and codebase to facilitate future researchers.

Monocular metric depth estimation (MMDE) is a crucial task to solve for indoor scene reconstruction on edge devices. Despite this importance, existing models are sensitive to factors such as boundary frequency of objects in the scene and scene complexity, failing to fully capture many indoor scenes. In this work, we propose to close this gap through the task of monocular metric depth refinement (MMDR) by leveraging state-of-the-art MMDE models. MultiDepth proposes a solution by taking samples of the image along with the initial depth map prediction made by a pre-trained MMDE model. Compared to existing iterative depth refinement techniques, MultiDepth does not employ normal map prediction as part of its architecture, effectively lowering the model size and computation overhead while outputting impactful changes from refining iterations. MultiDepth implements a lightweight encoder-decoder architecture for the refinement network, processing multiple samples from the given image, including segmentation masking. We evaluate MultiDepth on four datasets and compare them to state-of-the-art methods to demonstrate its effective refinement with minimal overhead, displaying accuracy improvement upward of 45%.

We introduce ReplaceMe, a generalized training-free depth pruning method that effectively replaces transformer blocks with a linear operation, while maintaining high performance for low compression ratios. In contrast to conventional pruning approaches that require additional training or fine-tuning, our approach requires only a small calibration dataset that is used to estimate a linear transformation, which approximates the pruned blocks. The estimated linear mapping can be seamlessly merged with the remaining transformer blocks, eliminating the need for any additional network parameters. Our experiments show that ReplaceMe consistently outperforms other training-free approaches and remains highly competitive with state-of-the-art pruning methods that involve extensive retraining/fine-tuning and architectural modifications. Applied to several large language models (LLMs), ReplaceMe achieves up to 25\% pruning while retaining approximately 90\% of the original model's performance on open benchmarks - without any training or healing steps, resulting in minimal computational overhead. We provide an open-source library implementing ReplaceMe alongside several state-of-the-art depth pruning techniques, available at https://github.com/mts-ai/ReplaceMe

Generative AI models have made significant progress in automating the creation of 3D shapes, which has the potential to transform car design. In engineering design and optimization, evaluating engineering metrics is crucial. To make generative models performance-aware and enable them to create high-performing designs, surrogate modeling of these metrics is necessary. However, the currently used representations of three-dimensional (3D) shapes either require extensive computational resources to learn or suffer from significant information loss, which impairs their effectiveness in surrogate modeling. To address this issue, we propose a new two-dimensional (2D) representation of 3D shapes. We develop a surrogate drag model based on this representation to verify its effectiveness in predicting 3D car drag. We construct a diverse dataset of 9,070 high-quality 3D car meshes labeled by drag coefficients computed from computational fluid dynamics (CFD) simulations to train our model. Our experiments demonstrate that our model can accurately and efficiently evaluate drag coefficients with an R^2 value above 0.84 for various car categories. Moreover, the proposed representation method can be generalized to many other product categories beyond cars. Our model is implemented using deep neural networks, making it compatible with recent AI image generation tools (such as Stable Diffusion) and a significant step towards the automatic generation of drag-optimized car designs. We have made the dataset and code publicly available at https://decode.mit.edu/projects/dragprediction/.

Backpropagation is still the de facto algorithm used today to train neural networks. With the exponential growth of recent architectures, the computational cost of this algorithm also becomes a burden. The recent PEPITA and forward-only frameworks have proposed promising alternatives, but they failed to scale up to a handful of hidden layers, yet limiting their use. In this paper, we first analyze theoretically the main limitations of these approaches. It allows us the design of a forward-only algorithm, which is equivalent to backpropagation under the linear and orthogonal assumptions. By relaxing the linear assumption, we then introduce FOTON (Forward-Only Training of Orthogonal Networks) that bridges the gap with the backpropagation algorithm. Experimental results show that it outperforms PEPITA, enabling us to train neural networks of any depth, without the need for a backward pass. Moreover its performance on convolutional networks clearly opens up avenues for its application to more advanced architectures. The code is open-sourced at https://github.com/p0lcAi/FOTON .

Bird's-eye view (BEV) perception has gained significant attention because it provides a unified representation to fuse multiple view images and enables a wide range of down-stream autonomous driving tasks, such as forecasting and planning. Recent state-of-the-art models utilize projection-based methods which formulate BEV perception as query learning to bypass explicit depth estimation. While we observe promising advancements in this paradigm, they still fall short of real-world applications because of the lack of uncertainty modeling and expensive computational requirement. In this work, we introduce GaussianLSS, a novel uncertainty-aware BEV perception framework that revisits unprojection-based methods, specifically the Lift-Splat-Shoot (LSS) paradigm, and enhances them with depth un-certainty modeling. GaussianLSS represents spatial dispersion by learning a soft depth mean and computing the variance of the depth distribution, which implicitly captures object extents. We then transform the depth distribution into 3D Gaussians and rasterize them to construct uncertainty-aware BEV features. We evaluate GaussianLSS on the nuScenes dataset, achieving state-of-the-art performance compared to unprojection-based methods. In particular, it provides significant advantages in speed, running 2.5x faster, and in memory efficiency, using 0.3x less memory compared to projection-based methods, while achieving competitive performance with only a 0.4% IoU difference.

Residual connections are central to modern deep neural networks, enabling stable optimization and efficient information flow across depth. In this work, we propose SCORE (Skip-Connection ODE Recurrent Embedding), a discrete recurrent alternative to classical layer stacking. Instead of composing multiple independent layers, SCORE iteratively applies a single shared neural block using an ODE (Ordinary Differential Equation)-inspired contractive update: ht+1 = (1 - dt) * ht + dt * F(ht) This formulation can be interpreted as a depth-by-iteration refinement process, where the step size dt explicitly controls stability and update magnitude. Unlike continuous Neural ODE approaches, SCORE uses a fixed number of discrete iterations and standard backpropagation without requiring ODE solvers or adjoint methods. We evaluate SCORE across graph neural networks (ESOL molecular solubility), multilayer perceptrons, and Transformer-based language models (nanoGPT). Across architectures, SCORE generally improves convergence speed and often accelerates training. SCORE is reducing parameter count through shared weights. In practice, simple Euler integration provides the best trade-off between computational cost and performance, while higher-order integrators yield marginal gains at increased compute. These results suggest that controlled recurrent depth with contractive residual updates offers a lightweight and effective alternative to classical stacking in deep neural networks.

The rise of test-time scaling has remarkably boosted the reasoning and agentic proficiency of Large Language Models (LLMs). Yet, standard Transformers struggle to scale inference-time compute efficiently, as conventional looping strategies suffer from high computational overhead and a KV cache that inflates alongside model depth. We present Universal YOCO (YOCO-U), which combines the YOCO decoder-decoder architecture with recursive computation to achieve a synergistic effect greater than either alone. Built on the YOCO framework, YOCO-U implements a Universal Self-Decoder that performs multiple iterations via parameter sharing, while confining the iterative process to shallow, efficient-attention layers. This combination yields a favorable capability-efficiency tradeoff that neither YOCO nor recursion achieves independently. The YOCO architecture provides a constant global KV cache and linear pre-filling, while partial recursion enhances representational depth with limited overhead. Together, YOCO-U improves token utility and scaling behavior while maintaining efficient inference. Empirical results confirm that YOCO-U remains highly competitive in general and long-context benchmarks, demonstrating that the integration of efficient-attention architectures and recursive computation is a promising direction for scalable LLMs.

Navigation and mapping on the lunar surface require robust perception under challenging conditions, including poorly textured environments, high-contrast lighting, and limited computational resources. This paper presents a real-time mapping framework that integrates dense perception models with a 3D Gaussian Splatting (3DGS) representation. We first benchmark several models on synthetic datasets generated with the LuPNT simulator, selecting a stereo dense depth estimation model based on Gated Recurrent Units for its balance of speed and accuracy in depth estimation, and a convolutional neural network for its superior performance in detecting semantic segments. Using ground truth poses to decouple the local scene understanding from the global state estimation, our pipeline reconstructs a 120-meter traverse with a geometric height accuracy of approximately 3 cm, outperforming a traditional point cloud baseline without LiDAR. The resulting 3DGS map enables novel view synthesis and serves as a foundation for a full SLAM system, where its capacity for joint map and pose optimization would offer significant advantages. Our results demonstrate that combining semantic segmentation and dense depth estimation with learned map representations is an effective approach for creating detailed, large-scale maps to support future lunar surface missions.

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.

Depth estimation from a single image is an important task that can be applied to various fields in computer vision, and has grown rapidly with the development of convolutional neural networks. In this paper, we propose a novel structure and training strategy for monocular depth estimation to further improve the prediction accuracy of the network. We deploy a hierarchical transformer encoder to capture and convey the global context, and design a lightweight yet powerful decoder to generate an estimated depth map while considering local connectivity. By constructing connected paths between multi-scale local features and the global decoding stream with our proposed selective feature fusion module, the network can integrate both representations and recover fine details. In addition, the proposed decoder shows better performance than the previously proposed decoders, with considerably less computational complexity. Furthermore, we improve the depth-specific augmentation method by utilizing an important observation in depth estimation to enhance the model. Our network achieves state-of-the-art performance over the challenging depth dataset NYU Depth V2. Extensive experiments have been conducted to validate and show the effectiveness of the proposed approach. Finally, our model shows better generalisation ability and robustness than other comparative models.

Focusing on the task of point-to-point navigation for an autonomous driving vehicle, we propose a novel deep learning model trained with end-to-end and multi-task learning manners to perform both perception and control tasks simultaneously. The model is used to drive the ego vehicle safely by following a sequence of routes defined by the global planner. The perception part of the model is used to encode high-dimensional observation data provided by an RGBD camera while performing semantic segmentation, semantic depth cloud (SDC) mapping, and traffic light state and stop sign prediction. Then, the control part decodes the encoded features along with additional information provided by GPS and speedometer to predict waypoints that come with a latent feature space. Furthermore, two agents are employed to process these outputs and make a control policy that determines the level of steering, throttle, and brake as the final action. The model is evaluated on CARLA simulator with various scenarios made of normal-adversarial situations and different weathers to mimic real-world conditions. In addition, we do a comparative study with some recent models to justify the performance in multiple aspects of driving. Moreover, we also conduct an ablation study on SDC mapping and multi-agent to understand their roles and behavior. As a result, our model achieves the highest driving score even with fewer parameters and computation load. To support future studies, we share our codes at https://github.com/oskarnatan/end-to-end-driving.

Estimating the depths of equirectangular (360) images (EIs) is challenging given the distorted 180 x 360 field-of-view, which is hard to be addressed via convolutional neural network (CNN). Although a transformer with global attention achieves significant improvements over CNN for EI depth estimation task, it is computationally inefficient, which raises the need for transformer with local attention. However, to apply local attention successfully for EIs, a specific strategy, which addresses distorted equirectangular geometry and limited receptive field simultaneously, is required. Prior works have only cared either of them, resulting in unsatisfactory depths occasionally. In this paper, we propose an equirectangular geometry-biased transformer termed EGformer, which enables local attention extraction in a global manner considering the equirectangular geometry. To achieve this, we actively utilize the equirectangular geometry as the bias for the local attention instead of struggling to reduce the distortion of EIs. As compared to the most recent transformer based EI depth estimation studies, the proposed approach yields the best depth outcomes overall with the lowest computational cost and the fewest parameters, demonstrating the effectiveness of the proposed methods.

This research paper presents an innovative multi-task learning framework that allows concurrent depth estimation and semantic segmentation using a single camera. The proposed approach is based on a shared encoder-decoder architecture, which integrates various techniques to improve the accuracy of the depth estimation and semantic segmentation task without compromising computational efficiency. Additionally, the paper incorporates an adversarial training component, employing a Wasserstein GAN framework with a critic network, to refine model's predictions. The framework is thoroughly evaluated on two datasets - the outdoor Cityscapes dataset and the indoor NYU Depth V2 dataset - and it outperforms existing state-of-the-art methods in both segmentation and depth estimation tasks. We also conducted ablation studies to analyze the contributions of different components, including pre-training strategies, the inclusion of critics, the use of logarithmic depth scaling, and advanced image augmentations, to provide a better understanding of the proposed framework. The accompanying source code is accessible at https://github.com/PardisTaghavi/SwinMTL.

Monocular Depth Estimation (MDE) has emerged as a pivotal task in computer vision, supporting numerous real-world applications. However, deploying accurate depth estimation models on resource-limited edge devices, especially Application-Specific Integrated Circuits (ASICs), is challenging due to the high computational and memory demands. Recent advancements in foundational depth estimation deliver impressive results but further amplify the difficulty of deployment on ASICs. To address this, we propose QuartDepth which adopts post-training quantization to quantize MDE models with hardware accelerations for ASICs. Our approach involves quantizing both weights and activations to 4-bit precision, reducing the model size and computation cost. To mitigate the performance degradation, we introduce activation polishing and compensation algorithm applied before and after activation quantization, as well as a weight reconstruction method for minimizing errors in weight quantization. Furthermore, we design a flexible and programmable hardware accelerator by supporting kernel fusion and customized instruction programmability, enhancing throughput and efficiency. Experimental results demonstrate that our framework achieves competitive accuracy while enabling fast inference and higher energy efficiency on ASICs, bridging the gap between high-performance depth estimation and practical edge-device applicability. Code: https://github.com/shawnricecake/quart-depth

Recent advances in generalizable 3D Gaussian Splatting have demonstrated promising results in real-time high-fidelity rendering without per-scene optimization, yet existing approaches still struggle to handle unfamiliar visual content during inference on novel scenes due to limited generalizability. To address this challenge, we introduce MonoSplat, a novel framework that leverages rich visual priors from pre-trained monocular depth foundation models for robust Gaussian reconstruction. Our approach consists of two key components: a Mono-Multi Feature Adapter that transforms monocular features into multi-view representations, coupled with an Integrated Gaussian Prediction module that effectively fuses both feature types for precise Gaussian generation. Through the Adapter's lightweight attention mechanism, features are seamlessly aligned and aggregated across views while preserving valuable monocular priors, enabling the Prediction module to generate Gaussian primitives with accurate geometry and appearance. Through extensive experiments on diverse real-world datasets, we convincingly demonstrate that MonoSplat achieves superior reconstruction quality and generalization capability compared to existing methods while maintaining computational efficiency with minimal trainable parameters. Codes are available at https://github.com/CUHK-AIM-Group/MonoSplat.

Stereo depth estimation is fundamental to underwater robotic perception, yet suffers from severe domain shifts caused by wavelength-dependent light attenuation, scattering, and refraction. Recent approaches leverage monocular foundation models with GRU-based iterative refinement for underwater adaptation; however, the sequential gating and local convolutional kernels in GRUs necessitate multiple iterations for long-range disparity propagation, limiting performance in large-disparity and textureless underwater regions. In this paper, we propose StereoAdapter-2, which replaces the conventional ConvGRU updater with a novel ConvSS2D operator based on selective state space models. The proposed operator employs a four-directional scanning strategy that naturally aligns with epipolar geometry while capturing vertical structural consistency, enabling efficient long-range spatial propagation within a single update step at linear computational complexity. Furthermore, we construct UW-StereoDepth-80K, a large-scale synthetic underwater stereo dataset featuring diverse baselines, attenuation coefficients, and scattering parameters through a two-stage generative pipeline combining semantic-aware style transfer and geometry-consistent novel view synthesis. Combined with dynamic LoRA adaptation inherited from StereoAdapter, our framework achieves state-of-the-art zero-shot performance on underwater benchmarks with 17% improvement on TartanAir-UW and 7.2% improvment on SQUID, with real-world validation on the BlueROV2 platform demonstrates the robustness of our approach. Code: https://github.com/AIGeeksGroup/StereoAdapter-2. Website: https://aigeeksgroup.github.io/StereoAdapter-2.

As object detection techniques continue to evolve, understanding their relationships with complementary visual tasks becomes crucial for optimising model architectures and computational resources. This paper investigates the correlations between object detection accuracy and two fundamental visual tasks: depth prediction and visual saliency prediction. Through comprehensive experiments using state-of-the-art models (DeepGaze IIE, Depth Anything, DPT-Large, and Itti's model) on COCO and Pascal VOC datasets, we find that visual saliency shows consistently stronger correlations with object detection accuracy (mArho up to 0.459 on Pascal VOC) compared to depth prediction (mArho up to 0.283). Our analysis reveals significant variations in these correlations across object categories, with larger objects showing correlation values up to three times higher than smaller objects. These findings suggest incorporating visual saliency features into object detection architectures could be more beneficial than depth information, particularly for specific object categories. The observed category-specific variations also provide insights for targeted feature engineering and dataset design improvements, potentially leading to more efficient and accurate object detection systems.

This paper presents a vision-only autonomous flight system for small UAVs operating in controlled indoor environments. The system combines semantic segmentation with monocular depth estimation to enable obstacle avoidance, scene exploration, and autonomous safe landing operations without requiring GPS or expensive sensors such as LiDAR. A key innovation is an adaptive scale factor algorithm that converts non-metric monocular depth predictions into accurate metric distance measurements by leveraging semantic ground plane detection and camera intrinsic parameters, achieving a mean distance error of 14.4 cm. The approach uses a knowledge distillation framework where a color-based Support Vector Machine (SVM) teacher generates training data for a lightweight U-Net student network (1.6M parameters) capable of real-time semantic segmentation. For more complex environments, the SVM teacher can be replaced with a state-of-the-art segmentation model. Testing was conducted in a controlled 5x4 meter laboratory environment with eight cardboard obstacles simulating urban structures. Extensive validation across 30 flight tests in a real-world environment and 100 flight tests in a digital-twin environment demonstrates that the combined segmentation and depth approach increases the distance traveled during surveillance and reduces mission time while maintaining 100% success rates. The system is further optimized through end-to-end learning, where a compact student neural network learns complete flight policies from demonstration data generated by our best-performing method, achieving an 87.5% autonomous mission success rate. This work advances practical vision-based drone navigation in structured environments, demonstrating solutions for metric depth estimation and computational efficiency challenges that enable deployment on resource-constrained platforms.

The pursuit of a generalizable stereo matching model, capable of performing well across varying resolutions and disparity ranges without dataset-specific fine-tuning, has revealed a fundamental trade-off. Iterative local search methods achieve high scores on constrained benchmarks, but their core mechanism inherently limits the global consistency required for true generalization. However, global matching architectures, while theoretically more robust, have historically been rendered infeasible by prohibitive computational and memory costs. We resolve this dilemma with {S2M2}: a global matching architecture that achieves state-of-the-art accuracy and high efficiency without relying on cost volume filtering or deep refinement stacks. Our design integrates a multi-resolution transformer for robust long-range correspondence, trained with a novel loss function that concentrates probability on feasible matches. This approach enables a more robust joint estimation of disparity, occlusion, and confidence. {S2M2} establishes a new state of the art on Middlebury v3 and ETH3D benchmarks, significantly outperforming prior methods in most metrics while reconstructing high-quality details with competitive efficiency.

This paper presents StereoNet, the first end-to-end deep architecture for real-time stereo matching that runs at 60 fps on an NVidia Titan X, producing high-quality, edge-preserved, quantization-free disparity maps. A key insight of this paper is that the network achieves a sub-pixel matching precision than is a magnitude higher than those of traditional stereo matching approaches. This allows us to achieve real-time performance by using a very low resolution cost volume that encodes all the information needed to achieve high disparity precision. Spatial precision is achieved by employing a learned edge-aware upsampling function. Our model uses a Siamese network to extract features from the left and right image. A first estimate of the disparity is computed in a very low resolution cost volume, then hierarchically the model re-introduces high-frequency details through a learned upsampling function that uses compact pixel-to-pixel refinement networks. Leveraging color input as a guide, this function is capable of producing high-quality edge-aware output. We achieve compelling results on multiple benchmarks, showing how the proposed method offers extreme flexibility at an acceptable computational budget.

Vision-Language Models (VLMs) have revolutionized document parsing by enabling end-to-end mapping from images to structured text, imposing a significant latency bottleneck, particularly for token-dense documents. While Multi-Token Prediction (MTP) has emerged as a promising approach for accelerating inference, its potential is constrained by optimization instability when scaling to deeper look-ahead depth. In this paper, we propose P-MTP, a framework that leverages Progressive Multi-Token Prediction with a lightweight MTP module to scale the look-ahead depth for high-throughput document parsing. Specifically, we introduce Progressive Curriculum Loss that adaptively re-weights different look-ahead depths using cumulative path reliability and retrospective target consistency. By effectively suppressing gradient noise in long-range predictions, P-MTP, facilitates an automated easy-to-hard optimization transition, enabling the model to master increasingly distant look-ahead depths. Furthermore, we propose Confidence-Gated Dynamic Drafting to maximize the effective look-ahead depth and acceptance rate by adaptively calibrating speculative length during inference, thereby minimizing computational waste and further pushing the boundaries of inference speedup. Experimental results across multiple benchmarks and architectures demonstrate that P-MTP, achieves up to a 5times speedup with negligible loss in accuracy, providing the first successful validation of extensive look-ahead MTP in the document parsing domain.

A well-known dilemma in large vision-language models (e.g., GPT-4, LLaVA) is that while increasing the number of vision tokens generally enhances visual understanding, it also significantly raises memory and computational costs, especially in long-term, dense video frame streaming scenarios. Although learnable approaches like Q-Former and Perceiver Resampler have been developed to reduce the vision token burden, they overlook the context causally modeled by LLMs (i.e., key-value cache), potentially leading to missed visual cues when addressing user queries. In this paper, we introduce a novel approach to reduce vision compute by leveraging redundant vision tokens "skipping layers" rather than decreasing the number of vision tokens. Our method, VideoLLM-MoD, is inspired by mixture-of-depths LLMs and addresses the challenge of numerous vision tokens in long-term or streaming video. Specifically, for each transformer layer, we learn to skip the computation for a high proportion (e.g., 80\%) of vision tokens, passing them directly to the next layer. This approach significantly enhances model efficiency, achieving approximately \textasciitilde42\% time and \textasciitilde30\% memory savings for the entire training. Moreover, our method reduces the computation in the context and avoid decreasing the vision tokens, thus preserving or even improving performance compared to the vanilla model. We conduct extensive experiments to demonstrate the effectiveness of VideoLLM-MoD, showing its state-of-the-art results on multiple benchmarks, including narration, forecasting, and summarization tasks in COIN, Ego4D, and Ego-Exo4D datasets.

Self-Supervised Monocular Depth Estimation (MDE) has garnered attention in recent years due to its independence from ground truth. However, most existing models are limited to a single scale and exhibit considerable performance degradation in complex driving environments. Networks specifically designed to handle dynamic traffic participants tend to be overly complex, hindering their deployment on resource-constrained automotive edge devices. To address these limitations and move towards robust driving perception, we propose FlexDepth, a scale-driven and flexible family of self-supervised MDE models tailored for challenging road scenarios. FlexDepth employs a two-stage static-dynamic decoupled training strategy, enabling the independent assessment of confidence for both static backgrounds and dynamic road objects. Furthermore, it introduces a meticulously designed Scale-Driven Decoder (SDD) to dynamically select components based on scale size, facilitating efficient feature fusion and the output of high-precision depth maps. Extensive experiments on standard driving benchmarks demonstrate that without any auxiliary information, our model achieves state-of-the-art performance across arbitrary scales with minimal computational overhead. Our smallest model, Flex-Nano, requires only 0.7 GFLOPs and achieves 37.6 FPS on mobile platforms, ensuring reliable real-time perception while maintaining excellent zero-shot generalization. Our source code is avalible: https://github.com/startnew/flexdepth

This paper proposes CAMOT, a simple camera angle estimator for multi-object tracking to tackle two problems: 1) occlusion and 2) inaccurate distance estimation in the depth direction. Under the assumption that multiple objects are located on a flat plane in each video frame, CAMOT estimates the camera angle using object detection. In addition, it gives the depth of each object, enabling pseudo-3D MOT. We evaluated its performance by adding it to various 2D MOT methods on the MOT17 and MOT20 datasets and confirmed its effectiveness. Applying CAMOT to ByteTrack, we obtained 63.8% HOTA, 80.6% MOTA, and 78.5% IDF1 in MOT17, which are state-of-the-art results. Its computational cost is significantly lower than the existing deep-learning-based depth estimators for tracking.

Looping, reusing a block of layers across depth, and depth growing, training shallow-to-deep models by duplicating middle layers, have both been linked to stronger reasoning, but their relationship remains unclear. We provide a mechanistic unification: looped and depth-grown models exhibit convergent depth-wise signatures, including increased reliance on late layers and recurring patterns aligned with the looped or grown block. These shared signatures support the view that their gains stem from a common form of iterative computation. Building on this connection, we show that the two techniques are adaptable and composable: applying inference-time looping to the middle blocks of a depth-grown model improves accuracy on some reasoning primitives by up to 2times, despite the model never being trained to loop. Both approaches also adapt better than the baseline when given more in-context examples or additional supervised fine-tuning data. Additionally, depth-grown models achieve the largest reasoning gains when using higher-quality, math-heavy cooldown mixtures, which can be further boosted by adapting a middle block to loop. Overall, our results position depth growth and looping as complementary, practical methods for inducing and scaling iterative computation to improve reasoning.

Different real-time speech applications impose distinct latency budgets, often requiring separately trained enhancement models for each scenario. In this paper, we propose a one-for-all, real-time universal speech enhancement model that provides explicit control over both algorithmic and computational latency. Algorithmic latency is flexibly adjusted via configurable look-ahead frames. To avoid learning inefficiency caused by varying padding configurations, we introduce parallel convolutional layers corresponding to different look-ahead settings. Computational latency is controlled through an early-exit mechanism, enabling inference at different network depths. To narrow the performance gap between specialized and flexible models, we propose a two-stage training strategy with a shared-to-multiple decoder transition. Overall, the proposed framework enables a single model to be deployed across diverse latency budgets without retraining separate models.

We present PORTAL, a novel framework for developing artificial intelligence agents capable of playing thousands of 3D video games through language-guided policy generation. By transforming decision-making problems into language modeling tasks, our approach leverages large language models (LLMs) to generate behavior trees represented in domain-specific language (DSL). This method eliminates the computational burden associated with traditional reinforcement learning approaches while preserving strategic depth and rapid adaptability. Our framework introduces a hybrid policy structure that combines rule-based nodes with neural network components, enabling both high-level strategic reasoning and precise low-level control. A dual-feedback mechanism incorporating quantitative game metrics and vision-language model analysis facilitates iterative policy improvement at both tactical and strategic levels. The resulting policies are instantaneously deployable, human-interpretable, and capable of generalizing across diverse gaming environments. Experimental results demonstrate PORTAL's effectiveness across thousands of first-person shooter (FPS) games, showcasing significant improvements in development efficiency, policy generalization, and behavior diversity compared to traditional approaches. PORTAL represents a significant advancement in game AI development, offering a practical solution for creating sophisticated agents that can operate across thousands of commercial video games with minimal development overhead. Experiment results on the 3D video games are best viewed on https://zhongwen.one/projects/portal .

LLMs are computationally expensive to pre-train due to their large scale. Model growth emerges as a promising approach by leveraging smaller models to accelerate the training of larger ones. However, the viability of these model growth methods in efficient LLM pre-training remains underexplored. This work identifies three critical textit{O}bstacles: (O1) lack of comprehensive evaluation, (O2) untested viability for scaling, and (O3) lack of empirical guidelines. To tackle O1, we summarize existing approaches into four atomic growth operators and systematically evaluate them in a standardized LLM pre-training setting. Our findings reveal that a depthwise stacking operator, called G_{stack}, exhibits remarkable acceleration in training, leading to decreased loss and improved overall performance on eight standard NLP benchmarks compared to strong baselines. Motivated by these promising results, we conduct extensive experiments to delve deeper into G_{stack} to address O2 and O3. For O2 (untested scalability), our study shows that G_{stack} is scalable and consistently performs well, with experiments up to 7B LLMs after growth and pre-training LLMs with 750B tokens. For example, compared to a conventionally trained 7B model using 300B tokens, our G_{stack} model converges to the same loss with 194B tokens, resulting in a 54.6\% speedup. We further address O3 (lack of empirical guidelines) by formalizing guidelines to determine growth timing and growth factor for G_{stack}, making it practical in general LLM pre-training. We also provide in-depth discussions and comprehensive ablation studies of G_{stack}. Our code and pre-trained model are available at https://llm-stacking.github.io/{https://llm-stacking.github.io/}.

Vaccine hesitancy has been a common concern, probably since vaccines were created and, with the popularisation of social media, people started to express their concerns about vaccines online alongside those posting pro- and anti-vaccine content. Predictably, since the first mentions of a COVID-19 vaccine, social media users posted about their fears and concerns or about their support and belief into the effectiveness of these rapidly developing vaccines. Identifying and understanding the reasons behind public hesitancy towards COVID-19 vaccines is important for policy markers that need to develop actions to better inform the population with the aim of increasing vaccine take-up. In the case of COVID-19, where the fast development of the vaccines was mirrored closely by growth in anti-vaxx disinformation, automatic means of detecting citizen attitudes towards vaccination became necessary. This is an important computational social sciences task that requires data analysis in order to gain in-depth understanding of the phenomena at hand. Annotated data is also necessary for training data-driven models for more nuanced analysis of attitudes towards vaccination. To this end, we created a new collection of over 3,101 tweets annotated with users' attitudes towards COVID-19 vaccination (stance). Besides, we also develop a domain-specific language model (VaxxBERT) that achieves the best predictive performance (73.0 accuracy and 69.3 F1-score) as compared to a robust set of baselines. To the best of our knowledge, these are the first dataset and model that model vaccine hesitancy as a category distinct from pro- and anti-vaccine stance.

Transformers have been recently explored for 3D point cloud understanding with impressive progress achieved. A large number of points, over 0.1 million, make the global self-attention infeasible for point cloud data. Thus, most methods propose to apply the transformer in a local region, e.g., spherical or cubic window. However, it still contains a large number of Query-Key pairs, which requires high computational costs. In addition, previous methods usually learn the query, key, and value using a linear projection without modeling the local 3D geometric structure. In this paper, we attempt to reduce the costs and model the local geometry prior by developing a new transformer block, named ConDaFormer. Technically, ConDaFormer disassembles the cubic window into three orthogonal 2D planes, leading to fewer points when modeling the attention in a similar range. The disassembling operation is beneficial to enlarging the range of attention without increasing the computational complexity, but ignores some contexts. To provide a remedy, we develop a local structure enhancement strategy that introduces a depth-wise convolution before and after the attention. This scheme can also capture the local geometric information. Taking advantage of these designs, ConDaFormer captures both long-range contextual information and local priors. The effectiveness is demonstrated by experimental results on several 3D point cloud understanding benchmarks. Code is available at https://github.com/LHDuan/ConDaFormer .

Streaming video understanding is a critical capability for real-world applications, including embodied intelligence, autonomous driving, industrial monitoring, surveillance and early warning, and wearable assistants. However, processing continuous video streams with multimodal large language models (MLLMs) is computationally expensive. Existing efforts have explored reducing streaming overhead through visual token pruning, token merging, quantization, on-demand frame retrieval, and context offloading. However, most existing methods overlook the dimension of model depth. Repeatedly executing full-depth MLLM prefill over incoming frames is prohibitively expensive, incurring substantial computational overhead and causing the KV cache to grow at a rate directly proportional to the prefill depth. To address these challenges, we propose ShallowStream, a novel framework that leverages the shallow layers of an MLLM to simultaneously perform frame encoding and retrieval index building. During stream processing, ShallowStream maintains an always-on lightweight index using the KV cache of shallow layers. During query-time answering, we leverage the attention scores generated by the shallow layers to score context frames and employ a diversity-aware selection strategy to retrieve precise and comprehensive evidence. ShallowStream achieves performance on par with the strongest existing streaming methods, while reducing per-frame prefill latency and 10-second end-to-end latency by up to 52.1x and 11.9x, respectively. Our code is available at https://github.com/CURRENTF/ShallowStream.

In this study, we propose a method to find an optimal central angle in deep learning-based depth map estimation used to produce realistic holographic content. The acquisition of RGB-depth map images as detailed as possible must be performed to generate holograms of high quality, despite the high computational cost. Therefore, we introduce a novel pipeline designed to analyze various values of central angles between adjacent camera viewpoints equidistant from the origin of an object-centered environment. Then we propose the optimal central angle to generate high-quality holographic content. The proposed pipeline comprises key steps such as comparing estimated depth maps and comparing reconstructed CGHs (Computer-Generated Holograms) from RGB images and estimated depth maps. We experimentally demonstrate and discuss the relationship between the central angle and the quality of digital holographic content.

High demand for computation resources severely hinders deployment of large-scale Deep Neural Networks (DNN) in resource constrained devices. In this work, we propose a Structured Sparsity Learning (SSL) method to regularize the structures (i.e., filters, channels, filter shapes, and layer depth) of DNNs. SSL can: (1) learn a compact structure from a bigger DNN to reduce computation cost; (2) obtain a hardware-friendly structured sparsity of DNN to efficiently accelerate the DNNs evaluation. Experimental results show that SSL achieves on average 5.1x and 3.1x speedups of convolutional layer computation of AlexNet against CPU and GPU, respectively, with off-the-shelf libraries. These speedups are about twice speedups of non-structured sparsity; (3) regularize the DNN structure to improve classification accuracy. The results show that for CIFAR-10, regularization on layer depth can reduce 20 layers of a Deep Residual Network (ResNet) to 18 layers while improve the accuracy from 91.25% to 92.60%, which is still slightly higher than that of original ResNet with 32 layers. For AlexNet, structure regularization by SSL also reduces the error by around ~1%. Open source code is in https://github.com/wenwei202/caffe/tree/scnn

Existing visual localization methods are typically either 2D image-based, which are easy to build and maintain but limited in effective geometric reasoning, or 3D structure-based, which achieve high accuracy but require a centralized reconstruction and are difficult to update. In this work, we revisit visual localization with a 2D image-based representation and propose to augment each image with estimated depth maps to capture the geometric structure. Supported by the effective use of dense matchers, this representation is not only easy to build and maintain, but achieves highest accuracy in challenging conditions. With compact compression and a GPU-accelerated LO-RANSAC implementation, the whole pipeline is efficient in both storage and computation and allows for a flexible trade-off between accuracy and highest memory efficiency. Our method achieves a new state-of-the-art accuracy on various standard benchmarks and outperforms existing memory-efficient methods at comparable map sizes. Code will be available at https://github.com/cvg/Hierarchical-Localization.

Structured pruning is essential for efficient deployment of Large Language Models (LLMs). The varying sensitivity of LLM sub-blocks to pruning necessitates the identification of optimal non-uniformly pruned models. Existing methods evaluate the importance of layers, attention heads, or weight channels in isolation. Such localized focus ignores the complex global structural dependencies that exist across the model. Training-aware structured pruning addresses global dependencies, but its computational cost can be just as expensive as post-pruning training. To alleviate the computational burden of training-aware pruning and capture global structural dependencies, we propose TraceNAS, a training-free Neural Architecture Search (NAS) framework that jointly explores structured pruning of LLM depth and width. TraceNAS identifies pruned models that maintain a high degree of loss landscape alignment with the pretrained model using a scale-invariant zero-shot proxy, effectively selecting models that exhibit maximal performance potential during post-pruning training. TraceNAS is highly efficient, enabling high-fidelity discovery of pruned models on a single GPU in 8.5 hours, yielding a 10times reduction in GPU-hours compared to training-aware methods. Evaluations on the Llama and Qwen families demonstrate that TraceNAS is competitive with training-aware baselines across commonsense and reasoning benchmarks.

LLM-powered systems require complex multi-step decision-making abilities to solve real-world tasks, yet current planning approaches face a trade-off between the high latency of inference-time search and the limited generalization of supervised fine-tuning. To address this limitation, we introduce SGA-MCTS, a framework that casts LLM planning as non-parametric retrieval. Offline, we leverage Monte Carlo Tree Search (MCTS) to explore the solution space and distill high-fidelity trajectories into State-Goal-Action (SGA) atoms. These atoms are de-lexicalized primitives that abstract concrete entities into symbolic slots, preserving reusable causal logic while discarding domain-specific noise. Online, a retrieval-augmented agent employs a hybrid symbolic-semantic mechanism to fetch relevant SGAs and re-ground them into the current context as soft reasoning hints. Empirical results on complex benchmarks demonstrate that this paradigm enables frozen, open-weights models to match the performance of SOTA systems (e.g., GPT-5) without task-specific fine-tuning. By effectively amortizing the heavy computational cost of search, SGA-MCTS achieves System 2 reasoning depth at System 1 inference speeds, rendering autonomous planning both scalable and real-time feasible.

Computer vision techniques have empowered underwater robots to effectively undertake a multitude of tasks, including object tracking and path planning. However, underwater optical factors like light refraction and absorption present challenges to underwater vision, which cause degradation of underwater images. A variety of underwater image enhancement methods have been proposed to improve the effectiveness of underwater vision perception. Nevertheless, for real-time vision tasks on underwater robots, it is necessary to overcome the challenges associated with algorithmic efficiency and real-time capabilities. In this paper, we introduce Lightweight Underwater Unet (LU2Net), a novel U-shape network designed specifically for real-time enhancement of underwater images. The proposed model incorporates axial depthwise convolution and the channel attention module, enabling it to significantly reduce computational demands and model parameters, thereby improving processing speed. The extensive experiments conducted on the dataset and real-world underwater robots demonstrate the exceptional performance and speed of proposed model. It is capable of providing well-enhanced underwater images at a speed 8 times faster than the current state-of-the-art underwater image enhancement method. Moreover, LU2Net is able to handle real-time underwater video enhancement.

The task of synthesizing novel views from a single image has useful applications in virtual reality and mobile computing, and a number of approaches to the problem have been proposed in recent years. A Multiplane Image (MPI) estimates the scene as a stack of RGBA layers, and can model complex appearance effects, anti-alias depth errors and synthesize soft edges better than methods that use textured meshes or layered depth images. And unlike neural radiance fields, an MPI can be efficiently rendered on graphics hardware. However, MPIs are highly redundant and require a large number of depth layers to achieve plausible results. Based on the observation that the depth complexity in local image regions is lower than that over the entire image, we split an MPI into many small, tiled regions, each with only a few depth planes. We call this representation a Tiled Multiplane Image (TMPI). We propose a method for generating a TMPI with adaptive depth planes for single-view 3D photography in the wild. Our synthesized results are comparable to state-of-the-art single-view MPI methods while having lower computational overhead.

Implicit models separate the definition of a layer from the description of its solution process. While implicit layers allow features such as depth to adapt to new scenarios and inputs automatically, this adaptivity makes its computational expense challenging to predict. In this manuscript, we increase the "implicitness" of the DEQ by redefining the method in terms of an infinite time neural ODE, which paradoxically decreases the training cost over a standard neural ODE by 2-4x. Additionally, we address the question: is there a way to simultaneously achieve the robustness of implicit layers while allowing the reduced computational expense of an explicit layer? To solve this, we develop Skip and Skip Reg. DEQ, an implicit-explicit (IMEX) layer that simultaneously trains an explicit prediction followed by an implicit correction. We show that training this explicit predictor is free and even decreases the training time by 1.11-3.19x. Together, this manuscript shows how bridging the dichotomy of implicit and explicit deep learning can combine the advantages of both techniques.

Deep neural networks are typically trained using global error signals that backpropagate (BP) end-to-end, which is not only biologically implausible but also suffers from the update locking problem and requires huge memory consumption. Local learning, which updates each layer independently with a gradient-isolated auxiliary network, offers a promising alternative to address the above problems. However, existing local learning methods are confronted with a large accuracy gap with the BP counterpart, particularly for large-scale networks. This is due to the weak coupling between local layers and their subsequent network layers, as there is no gradient communication across layers. To tackle this issue, we put forward an augmented local learning method, dubbed AugLocal. AugLocal constructs each hidden layer's auxiliary network by uniformly selecting a small subset of layers from its subsequent network layers to enhance their synergy. We also propose to linearly reduce the depth of auxiliary networks as the hidden layer goes deeper, ensuring sufficient network capacity while reducing the computational cost of auxiliary networks. Our extensive experiments on four image classification datasets (i.e., CIFAR-10, SVHN, STL-10, and ImageNet) demonstrate that AugLocal can effectively scale up to tens of local layers with a comparable accuracy to BP-trained networks while reducing GPU memory usage by around 40%. The proposed AugLocal method, therefore, opens up a myriad of opportunities for training high-performance deep neural networks on resource-constrained platforms.Code is available at https://github.com/ChenxiangMA/AugLocal.

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scaling properties, and limitations remain insufficiently understood. Current evaluations primarily focus on established math and coding benchmarks, emphasizing final answer accuracy. However, this evaluation paradigm often suffers from contamination and does not provide insights into the reasoning traces. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs think. Through extensive experiments, we show that LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counterintuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having remaining token budget. By comparing LRMs with their standard LLM counterparts under same inference compute, we identify three performance regimes: (1) low-complexity tasks where standard models outperform LRMs, (2) medium-complexity tasks where LRMs demonstrates advantage, and (3) high-complexity tasks where both models face complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across scales. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models' computational behavior, shedding light on their strengths, limitations, and raising questions about their reasoning capabilities.

In this paper, we propose LIR-LIVO, a lightweight and robust LiDAR-inertial-visual odometry system designed for challenging illumination and degraded environments. The proposed method leverages deep learning-based illumination-resilient features and LiDAR-Inertial-Visual Odometry (LIVO). By incorporating advanced techniques such as uniform depth distribution of features enabled by depth association with LiDAR point clouds and adaptive feature matching utilizing Superpoint and LightGlue, LIR-LIVO achieves state-of-the-art (SOTA) accuracy and robustness with low computational cost. Experiments are conducted on benchmark datasets, including NTU-VIRAL, Hilti'22, and R3LIVE-Dataset. The corresponding results demonstrate that our proposed method outperforms other SOTA methods on both standard and challenging datasets. Particularly, the proposed method demonstrates robust pose estimation under poor ambient lighting conditions in the Hilti'22 dataset. The code of this work is publicly accessible on GitHub to facilitate advancements in the robotics community.

We propose a deep convolutional neural network architecture codenamed "Inception", which was responsible for setting the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC 2014). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. This was achieved by a carefully crafted design that allows for increasing the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC 2014 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

We present DFormer, a novel RGB-D pretraining framework to learn transferable representations for RGB-D segmentation tasks. DFormer has two new key innovations: 1) Unlike previous works that encode RGB-D information with RGB pretrained backbone, we pretrain the backbone using image-depth pairs from ImageNet-1K, and hence the DFormer is endowed with the capacity to encode RGB-D representations; 2) DFormer comprises a sequence of RGB-D blocks, which are tailored for encoding both RGB and depth information through a novel building block design. DFormer avoids the mismatched encoding of the 3D geometry relationships in depth maps by RGB pretrained backbones, which widely lies in existing methods but has not been resolved. We finetune the pretrained DFormer on two popular RGB-D tasks, i.e., RGB-D semantic segmentation and RGB-D salient object detection, with a lightweight decoder head. Experimental results show that our DFormer achieves new state-of-the-art performance on these two tasks with less than half of the computational cost of the current best methods on two RGB-D semantic segmentation datasets and five RGB-D salient object detection datasets. Our code is available at: https://github.com/VCIP-RGBD/DFormer.

Originally proposed for handling time series data, Auto-regressive Decision Trees (ARDTs) have not yet been explored for language modeling. This paper delves into both the theoretical and practical applications of ARDTs in this new context. We theoretically demonstrate that ARDTs can compute complex functions, such as simulating automata, Turing machines, and sparse circuits, by leveraging "chain-of-thought" computations. Our analysis provides bounds on the size, depth, and computational efficiency of ARDTs, highlighting their surprising computational power. Empirically, we train ARDTs on simple language generation tasks, showing that they can learn to generate coherent and grammatically correct text on par with a smaller Transformer model. Additionally, we show that ARDTs can be used on top of transformer representations to solve complex reasoning tasks. This research reveals the unique computational abilities of ARDTs, aiming to broaden the architectural diversity in language model development.