Daily Papers

The computation necessary for training Transformer-based language models has skyrocketed in recent years. This trend has motivated research on efficient training algorithms designed to improve training, validation, and downstream performance faster than standard training. In this work, we revisit three categories of such algorithms: dynamic architectures (layer stacking, layer dropping), batch selection (selective backprop, RHO loss), and efficient optimizers (Lion, Sophia). When pre-training BERT and T5 with a fixed computation budget using such methods, we find that their training, validation, and downstream gains vanish compared to a baseline with a fully-decayed learning rate. We define an evaluation protocol that enables computation to be done on arbitrary machines by mapping all computation time to a reference machine which we call reference system time. We discuss the limitations of our proposed protocol and release our code to encourage rigorous research in efficient training procedures: https://github.com/JeanKaddour/NoTrainNoGain.

It has become increasingly important to optimize backpropagation to reduce memory usage and computational overhead. Achieving this goal is highly challenging, as multiple objectives must be considered jointly while maintaining training quality. In this paper, we focus on matrix multiplication, which accounts for the largest portion of training costs, and analyze its backpropagation in detail to identify lightweight techniques that offer the best benefits. Based on this analysis, we introduce a novel method, Hadamard-based Optimized Training (HOT). In this approach, we apply Hadamard-based optimizations, such as Hadamard quantization and Hadamard low-rank approximation, selectively and with awareness of the suitability of each optimization for different backward paths. Additionally, we introduce two enhancements: activation buffer compression and layer-wise quantizer selection. Our extensive analysis shows that HOT achieves up to 75% memory savings and a 2.6 times acceleration on real GPUs, with negligible accuracy loss compared to FP32 precision.

Memory is a limiting resource for many deep learning tasks. Beside the neural network weights, one main memory consumer is the computation graph built up by automatic differentiation (AD) for backpropagation. We observe that PyTorch's current AD implementation neglects information about parameter differentiability when storing the computation graph. This information is useful though to reduce memory whenever gradients are requested for a parameter subset, as is the case in many modern fine-tuning tasks. Specifically, inputs to layers that act linearly in their parameters (dense, convolution, or normalization layers) can be discarded whenever the parameters are marked as non-differentiable. We provide a drop-in, differentiability-agnostic implementation of such layers and demonstrate its ability to reduce memory without affecting run time.

Machine unlearning seeks to remove the influence of designated training data from a trained model without retraining from scratch. Retrain-free methods such as Selective Synaptic Dampening (SSD) and its label-free variant LFSSD avoid full retraining but still require backpropagation and parameter importance computed over the entire dataset. We ask: what happens when a deletion request arrives with only a few images of the class to be forgotten? To answer this question, we introduce UnAct, a gradient-free class-unlearning method that needs only forward passes over the forget images. UnAct scores late-layer units by their responses, attenuates the most responsive connections, and repeats this for up to 20 rounds using no gradients, no labels, and no retained data. On ResNet-18 trained with CIFAR-10, CIFAR-20, and CIFAR-100, UnAct is competitive with SSD and LFSSD when forgetting entire classes and, unlike them, never collapses the network when forget data is scarce. On ResNet-18, across all tested sizes, UnAct's retain accuracy stays within 2.5 points of retraining, while SSD and LFSSD, at their full-class operating points, lose up to 86 points on some classes. With five forget images on CIFAR-10, UnAct's distance to retraining is 0.21 points, against 67 for LFSSD and 90 for SSD, and re-selecting SSD's threshold at each size with an oracle does not close the gap. In preliminary transfer to ViT-B/16, UnAct's distance to retraining is 11.5 against 33.7 for SSD, and a request is 19x faster than SSD when SSD computes its importance at request time. The code is available at https://github.com/abdulmuizz0903/UnAct

We consider the problem of selective prediction (also known as reject option) in deep neural networks, and introduce SelectiveNet, a deep neural architecture with an integrated reject option. Existing rejection mechanisms are based mostly on a threshold over the prediction confidence of a pre-trained network. In contrast, SelectiveNet is trained to optimize both classification (or regression) and rejection simultaneously, end-to-end. The result is a deep neural network that is optimized over the covered domain. In our experiments, we show a consistently improved risk-coverage trade-off over several well-known classification and regression datasets, thus reaching new state-of-the-art results for deep selective classification.

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty. Selective regression, also known as the "reject option," allows models to abstain from predictions in cases of considerable uncertainty. Initially proposed seven decades ago, approaches to selective regression have mostly focused on distribution-based proxies for measuring uncertainty, particularly conditional variance. However, this focus neglects the significant influence of model-specific biases on a model's performance. In this paper, we propose a novel approach to selective regression by leveraging conformal prediction, which provides grounded confidence measures for individual predictions based on model-specific biases. In addition, we propose a standardized evaluation framework to allow proper comparison of selective regression approaches. Via an extensive experimental approach, we demonstrate how our proposed approach, conformalized selective regression, demonstrates an advantage over multiple state-of-the-art baselines.

Selective classification techniques (also known as reject option) have not yet been considered in the context of deep neural networks (DNNs). These techniques can potentially significantly improve DNNs prediction performance by trading-off coverage. In this paper we propose a method to construct a selective classifier given a trained neural network. Our method allows a user to set a desired risk level. At test time, the classifier rejects instances as needed, to grant the desired risk (with high probability). Empirical results over CIFAR and ImageNet convincingly demonstrate the viability of our method, which opens up possibilities to operate DNNs in mission-critical applications. For example, using our method an unprecedented 2% error in top-5 ImageNet classification can be guaranteed with probability 99.9%, and almost 60% test coverage.

"Forward-only" algorithms, which train neural networks while avoiding a backward pass, have recently gained attention as a way of solving the biologically unrealistic aspects of backpropagation. Here, we first address compelling challenges related to the "forward-only" rules, which include reducing the performance gap with backpropagation and providing an analytical understanding of their dynamics. To this end, we show that the forward-only algorithm with top-down feedback is well-approximated by an "adaptive-feedback-alignment" algorithm, and we analytically track its performance during learning in a prototype high-dimensional setting. Then, we compare different versions of forward-only algorithms, focusing on the Forward-Forward and PEPITA frameworks, and we show that they share the same learning principles. Overall, our work unveils the connections between three key neuro-inspired learning rules, providing a link between "forward-only" algorithms, i.e., Forward-Forward and PEPITA, and an approximation of backpropagation, i.e., Feedback Alignment.

Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.

Selective Classification, wherein models can reject low-confidence predictions, promises reliable translation of machine-learning based classification systems to real-world scenarios such as clinical diagnostics. While current evaluation of these systems typically assumes fixed working points based on pre-defined rejection thresholds, methodological progress requires benchmarking the general performance of systems akin to the AUROC in standard classification. In this work, we define 5 requirements for multi-threshold metrics in selective classification regarding task alignment, interpretability, and flexibility, and show how current approaches fail to meet them. We propose the Area under the Generalized Risk Coverage curve (AUGRC), which meets all requirements and can be directly interpreted as the average risk of undetected failures. We empirically demonstrate the relevance of AUGRC on a comprehensive benchmark spanning 6 data sets and 13 confidence scoring functions. We find that the proposed metric substantially changes metric rankings on 5 out of the 6 data sets.

The expansion of machine learning into dynamic environments presents challenges in handling open-world problems where label shift, covariate shift, and unknown classes emerge. Post-training methods have been explored to address these challenges, adapting models to newly emerging data. However, these methods struggle when the initial pre-training is performed on class-imbalanced datasets, limiting generalization to minority classes. To address this, we propose a method that effectively handles open-world problems even when pre-training is conducted on imbalanced data. Our contrastive-based pre-training approach enhances classification performance, particularly for underrepresented classes. Our post-training mechanism generates reliable pseudo-labels, improving model robustness against open-world problems. We also introduce selective activation criteria to optimize the post-training process, reducing unnecessary computation. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art adaptation techniques in both accuracy and efficiency across diverse open-world scenarios.

Interventional counterfactuals evaluate statements such as "had A been a" by replacing the assignment for A while keeping the unit's exogenous background fixed. Backtracking counterfactuals reverse this logic: they preserve the structural assignments and instead vary background conditions across worlds. This semantics is natural for diagnostic explanation, but full backtracking may be too permissive because every exogenous coordinate can vary. We introduce scope-restricted backtracking counterfactuals, in which the modeler specifies which coordinates may vary while the remainder are shared across worlds. The scope determines the admissible carriers of the contrast, while a cross-world kernel governs the plausibility of their alternative values. We present model-based inference for general scope-restricted backtracking counterfactuals, derive sharp marginal bounds for a specified explanatory query, and establish frontier and compatibility conditions under which this explanatory query admits a modified-value policy representation. A linear-Gaussian example distinguishes local-noise, ancestor, irrelevant-noise, and infeasible explanations across scopes, while an application to the UCI Adult benchmark illustrates kernel specification, sensitivity, and how much of the explanation is carried by the cross-world coupling itself.

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 .

In critical applications, it is vital for classifiers to defer decision-making to humans. We propose a post-hoc method that makes existing classifiers selectively abstain from predicting certain samples. Our abstaining classifier is incentivized to maintain the original accuracy for each sub-population (i.e. no harm) while achieving a set of group fairness definitions to a user specified degree. To this end, we design an Integer Programming (IP) procedure that assigns abstention decisions for each training sample to satisfy a set of constraints. To generalize the abstaining decisions to test samples, we then train a surrogate model to learn the abstaining decisions based on the IP solutions in an end-to-end manner. We analyze the feasibility of the IP procedure to determine the possible abstention rate for different levels of unfairness tolerance and accuracy constraint for achieving no harm. To the best of our knowledge, this work is the first to identify the theoretical relationships between the constraint parameters and the required abstention rate. Our theoretical results are important since a high abstention rate is often infeasible in practice due to a lack of human resources. Our framework outperforms existing methods in terms of fairness disparity without sacrificing accuracy at similar abstention rates.

Recently, there is an emerging interest in adversarially training a classifier with a rejection option (also known as a selective classifier) for boosting adversarial robustness. While rejection can incur a cost in many applications, existing studies typically associate zero cost with rejecting perturbed inputs, which can result in the rejection of numerous slightly-perturbed inputs that could be correctly classified. In this work, we study adversarially-robust classification with rejection in the stratified rejection setting, where the rejection cost is modeled by rejection loss functions monotonically non-increasing in the perturbation magnitude. We theoretically analyze the stratified rejection setting and propose a novel defense method -- Adversarial Training with Consistent Prediction-based Rejection (CPR) -- for building a robust selective classifier. Experiments on image datasets demonstrate that the proposed method significantly outperforms existing methods under strong adaptive attacks. For instance, on CIFAR-10, CPR reduces the total robust loss (for different rejection losses) by at least 7.3% under both seen and unseen attacks.

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets layer-by-layer, without propagating gradients throughout the network. Although such an approach has several advantages over back-propagation and shows promising results, the fact that each layer is being trained independently limits the optimization process. Specifically, it prevents the network's layers from collaborating to learn complex and rich features. In this work, we study layer collaboration in the forward-forward algorithm. We show that the current version of the forward-forward algorithm is suboptimal when considering information flow in the network, resulting in a lack of collaboration between layers of the network. We propose an improved version that supports layer collaboration to better utilize the network structure, while not requiring any additional assumptions or computations. We empirically demonstrate the efficacy of the proposed version when considering both information flow and objective metrics. Additionally, we provide a theoretical motivation for the proposed method, inspired by functional entropy theory.

Backpropagation (BP), a foundational algorithm for training artificial neural networks, predominates in contemporary deep learning. Although highly successful, it is often considered biologically implausible. A significant limitation arises from the need for precise symmetry between connections in the backward and forward pathways to backpropagate gradient signals accurately, which is not observed in biological brains. Researchers have proposed several algorithms to alleviate this symmetry constraint, such as feedback alignment and direct feedback alignment. However, their divergence from backpropagation dynamics presents challenges, particularly in deeper networks and convolutional layers. Here we introduce the Product Feedback Alignment (PFA) algorithm. Our findings demonstrate that PFA closely approximates BP and achieves comparable performance in deep convolutional networks while avoiding explicit weight symmetry. Our results offer a novel solution to the longstanding weight symmetry problem, leading to more biologically plausible learning in deep convolutional networks compared to earlier methods.

Hybrid training methods for large language models combine supervised fine tuning (SFT) on expert demonstrations with reinforcement learning (RL) on model rollouts, typically at the sample level. We propose Entropy Gated Selective Policy Optimization (EGSPO), a three stage framework that extends sample level mixing with token level gradient modulation. Stage 1, SFT expert learning, establishes a reliable warm up policy using expert demonstrations with a pure SFT loss. Stage 2, RL rollout generation, samples trajectories from the current policy and computes per token predictive entropy. Stage 3, the EGSPO mechanism, applies entropy gated gradient allocation: a predictive entropy module routes high entropy tokens to full PPO updates to encourage exploration, and low entropy tokens to attenuated PPO updates to reduce variance and preserve knowledge. Critically, both branches incorporate the advantage function A_t, ensuring that incorrect trajectories receive consistent negative learning signals and preventing reinforcement of confident errors. EGSPO achieves consistent improvements on mathematical reasoning benchmarks, with gains of 3.8 percent on AIME and 2.9 percent on MATH over the CHORD phi baseline, while incurring only 3.4 percent additional computational overhead.

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

Typical reinforcement learning (RL) methods for LLM reasoning waste compute on hard problems, where correct on-policy traces are rare, policy gradients vanish, and learning stalls. To bootstrap more efficient RL, we consider reusing old sampling FLOPs (from prior inference or RL training) in the form of off-policy traces. Standard off-policy methods supervise against off-policy data, causing instabilities during RL optimization. We introduce PrefixRL, where we condition on the prefix of successful off-policy traces and run on-policy RL to complete them, side-stepping off-policy instabilities. PrefixRL boosts the learning signal on hard problems by modulating the difficulty of the problem through the off-policy prefix length. We prove that the PrefixRL objective is not only consistent with the standard RL objective but also more sample efficient. Empirically, we discover back-generalization: training only on prefixed problems generalizes to out-of-distribution unprefixed performance, with learned strategies often differing from those in the prefix. In our experiments, we source the off-policy traces by rejection sampling with the base model, creating a self-improvement loop. On hard reasoning problems, PrefixRL reaches the same training reward 2x faster than the strongest baseline (SFT on off-policy data then RL), even after accounting for the compute spent on the initial rejection sampling, and increases the final reward by 3x. The gains transfer to held-out benchmarks, and PrefixRL is still effective when off-policy traces are derived from a different model family, validating its flexibility in practical settings.

Leveraging learned strategies in unfamiliar scenarios is fundamental to human intelligence. In reinforcement learning, rationally reusing the policies acquired from other tasks or human experts is critical for tackling problems that are difficult to learn from scratch. In this work, we present a framework called Selective Myopic bEhavior Control~(SMEC), which results from the insight that the short-term behaviors of prior policies are sharable across tasks. By evaluating the behaviors of prior policies via a hybrid value function architecture, SMEC adaptively aggregates the sharable short-term behaviors of prior policies and the long-term behaviors of the task policy, leading to coordinated decisions. Empirical results on a collection of manipulation and locomotion tasks demonstrate that SMEC outperforms existing methods, and validate the ability of SMEC to leverage related prior policies.

Modern deployments require LLMs to enforce safety policies at scale, yet many controls rely on inference-time interventions that add recurring compute cost and serving complexity. Activation steering is widely used, but it requires runtime hooks and scales cost with the number of generations; conditional variants improve selectivity by gating when steering is applied but still retain an inference-time control path. We ask whether selective refusal can be moved entirely offline: can a mechanistic understanding of category-specific refusal be distilled into a circuit-restricted weight update that deploys as a standard checkpoint? We propose C-Δθ: Circuit Restricted Weight Arithmetic, which (i) localizes refusal-causal computation as a sparse circuit using EAP-IG and (ii) computes a constrained weight update ΔθC supported only on that circuit (typically <5% of parameters). Applying ΔθC yields a drop-in edited checkpoint with no inference-time hooks, shifting cost from per-request intervention to a one-time offline update. We evaluate category-targeted selectivity and capability retention on refusal and utility benchmarks.

A selector that allocates work across opaque components must evaluate them without being told how they performed. We study the least communication that suffices. Each parent maintains an allocation vector over its children and updates it from outcomes by proportional redistribution. Each child reads the sign of its own allocation change, one bit per round it is selected, so no evaluation message crosses the parent-child boundary. (1) The update preserves the simplex with strict positivity. (2) Conditional on being selected, a child's sign is exactly the root outcome at every depth, a sufficient statistic. The conditioning is necessary. (3) Under interiority a single selector has a unique interior equilibrium, exact and closed-form for N=2, with almost sure convergence under decreasing steps. For general N an equi-ratio condition gives an explicit affine equilibrium. (4) The linearised mean flow has real, strictly negative tangent eigenvalues with explicit bounds for all N >= 2. (5) The mean flow converges globally. An explicit potential, up to normalisation the KL divergence between the failure and slack distributions, decreases at a rate equal to the variance of the equi-ratio statistic. Without interiority the rule drops exactly the children below the surviving support's threshold. (6) The update law composes along a single active path, since ancestors select a node's active rounds but do not alter a realised signal. No joint convergence theorem for a hierarchy whose levels adapt simultaneously is claimed. (7) The one-bit interface admits exactly four deterministic memoryless distortions, and at a single selector passing the bit on unchanged delivers strictly higher mean quality upward than negation or constant transmission. Illustrations on synthetic hierarchies up to 16,384 leaves and three real datasets (3.4 billion comparisons, no mismatches) are consistent with the theory.

Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty gets exacerbated when employing regularizers involving a large number of hyperparameters. To overcome this challenge, bilevel learning can be employed to learn such parameters from data. However, neither exact function values nor exact gradients with respect to the hyperparameters are attainable, necessitating methods that only rely on inexact evaluation of such quantities. State-of-the-art inexact gradient-based methods a priori select a sequence of the required accuracies and cannot identify an appropriate step size since the Lipschitz constant of the hypergradient is unknown. In this work, we propose an algorithm with backtracking line search that only relies on inexact function evaluations and hypergradients and show convergence to a stationary point. Furthermore, the proposed algorithm determines the required accuracy dynamically rather than manually selected before running it. Our numerical experiments demonstrate the efficiency and feasibility of our approach for hyperparameter estimation on a range of relevant problems in imaging and data science such as total variation and field of experts denoising and multinomial logistic regression. Particularly, the results show that the algorithm is robust to its own hyperparameters such as the initial accuracies and step size.

A supervised learning algorithm searches over a set of functions A to B parametrised by a space P to find the best approximation to some ideal function fcolon A to B. It does this by taking examples (a,f(a)) in Atimes B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.

We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in high-stakes contexts, such as medical diagnosis and finance. We show that this inconsistent behavior extends beyond predictions to feature attributions, which may likewise have negative implications for the intelligibility of a model, and one's ability to find recourse for subjects. We then introduce selective ensembles to mitigate such inconsistencies by applying hypothesis testing to the predictions of a set of models trained using randomly-selected starting conditions; importantly, selective ensembles can abstain in cases where a consistent outcome cannot be achieved up to a specified confidence level. We prove that that prediction disagreement between selective ensembles is bounded, and empirically demonstrate that selective ensembles achieve consistent predictions and feature attributions while maintaining low abstention rates. On several benchmark datasets, selective ensembles reach zero inconsistently predicted points, with abstention rates as low 1.5%.

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL has close connections to neurobiological models of cortical function and has achieved equal performance to BP on supervised learning and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and also demonstrate IL achieves quicker convergence when trained with small mini-batches while matching the performance of BP for large mini-batches.

Mixup is a highly successful technique to improve generalization of neural networks by augmenting the training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs, e.g. only combining examples across classes or domains. These methods have claimed remarkable improvements on benchmarks with distribution shifts, but their mechanisms and limitations remain poorly understood. We examine an overlooked aspect of selective mixup that explains its success in a completely new light. We find that the non-random selection of pairs affects the training distribution and improve generalization by means completely unrelated to the mixing. For example in binary classification, mixup across classes implicitly resamples the data for a uniform class distribution - a classical solution to label shift. We show empirically that this implicit resampling explains much of the improvements in prior work. Theoretically, these results rely on a regression toward the mean, an accidental property that we identify in several datasets. We have found a new equivalence between two successful methods: selective mixup and resampling. We identify limits of the former, confirm the effectiveness of the latter, and find better combinations of their respective benefits.

The canonical deep learning approach for learning requires computing a gradient term at each layer by back-propagating the error signal from the output towards each learnable parameter. Given the stacked structure of neural networks, where each layer builds on the representation of the layer below, this approach leads to hierarchical representations. More abstract features live on the top layers of the model, while features on lower layers are expected to be less abstract. In contrast to this, we introduce a new learning method named NoProp, which does not rely on either forward or backwards propagation. Instead, NoProp takes inspiration from diffusion and flow matching methods, where each layer independently learns to denoise a noisy target. We believe this work takes a first step towards introducing a new family of gradient-free learning methods, that does not learn hierarchical representations -- at least not in the usual sense. NoProp needs to fix the representation at each layer beforehand to a noised version of the target, learning a local denoising process that can then be exploited at inference. We demonstrate the effectiveness of our method on MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks. Our results show that NoProp is a viable learning algorithm which achieves superior accuracy, is easier to use and computationally more efficient compared to other existing back-propagation-free methods. By departing from the traditional gradient based learning paradigm, NoProp alters how credit assignment is done within the network, enabling more efficient distributed learning as well as potentially impacting other characteristics of the learning process.

Backpropagation is the standard method for achieving state-of-the-art accuracy in neural network training, but it often imposes high memory costs and lacks biological plausibility. In this paper, we introduce the Mono-Forward algorithm, a purely local layerwise learning method inspired by Hinton's Forward-Forward framework. Unlike backpropagation, Mono-Forward optimizes each layer solely with locally available information, eliminating the reliance on global error signals. We evaluated Mono-Forward on multi-layer perceptrons and convolutional neural networks across multiple benchmarks, including MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100. The test results show that Mono-Forward consistently matches or surpasses the accuracy of backpropagation across all tasks, with significantly reduced and more even memory usage, better parallelizability, and a comparable convergence rate.

Many localized large language model (LLM) unlearning methods select a small parameter subset from a localization signal and keep it fixed during optimization. The parameters most associated with a target, however, need not be the best ones to update, and candidate interventions can change value as optimization proceeds. In a controlled experiment, a storage-localization score reaches an area under the receiver operating characteristic curve (AUROC) of 0.981, yet storage identity agrees with the better intervention on only 17/36 targets, while low-rank adaptation (LoRA) wins 35/36. We introduce Intervention Score, which ranks editable groups by the predicted effect of the actual unlearning update while accounting for collateral damage, and use it to form the static intervention-value baseline (Static-IV). We then introduce selective dynamic intervention re-ranking (DIR-R), which revisits that subset only when a calibrated probe justifies the comparison. On the Natural-TOFU dataset, our method has positive descriptive margins in 19/20 comparisons between methods and objectives, although several are near zero. On the LACUNA localization-precision benchmark, our mean terminal utility is higher in all six negative preference optimization (NPO) and SimNPO comparisons: NPO margins range from +0.431 to +0.848, and SimNPO margins range from +0.503 to +0.571. The gradient-difference (GradDiff) objective reveals substantial field dependence. Relative to Static-IV, the primary four-field GradDiff evaluation has six wins, six ties, and no losses, with mean and median paired gains of +0.165 and +0.0025. The evidence supports separating localization, initial intervention selection, and checkpoint-dependent support revision.

Formula alpha mining, which generates predictive signals from financial data, is critical for quantitative investment. Although various algorithmic approaches-such as genetic programming, reinforcement learning, and large language models-have significantly expanded the capacity for alpha discovery, systematic evaluation remains a key challenge. Existing evaluation metrics predominantly include backtesting and correlation-based measures. Backtesting is computationally intensive, inherently sequential, and sensitive to specific strategy parameters. Correlation-based metrics, though efficient, assess only predictive ability and overlook other crucial properties such as temporal stability, robustness, diversity, and interpretability. Additionally, the closed-source nature of most existing alpha mining models hinders reproducibility and slows progress in this field. To address these issues, we propose AlphaEval, a unified, parallelizable, and backtest-free evaluation framework for automated alpha mining models. AlphaEval assesses the overall quality of generated alphas along five complementary dimensions: predictive power, stability, robustness to market perturbations, financial logic, and diversity. Extensive experiments across representative alpha mining algorithms demonstrate that AlphaEval achieves evaluation consistency comparable to comprehensive backtesting, while providing more comprehensive insights and higher efficiency. Furthermore, AlphaEval effectively identifies superior alphas compared to traditional single-metric screening approaches. All implementations and evaluation tools are open-sourced to promote reproducibility and community engagement.

Feature selection is the problem of selecting a subset of features for a machine learning model that maximizes model quality subject to a budget constraint. For neural networks, prior methods, including those based on ell_1 regularization, attention, and other techniques, typically select the entire feature subset in one evaluation round, ignoring the residual value of features during selection, i.e., the marginal contribution of a feature given that other features have already been selected. We propose a feature selection algorithm called Sequential Attention that achieves state-of-the-art empirical results for neural networks. This algorithm is based on an efficient one-pass implementation of greedy forward selection and uses attention weights at each step as a proxy for feature importance. We give theoretical insights into our algorithm for linear regression by showing that an adaptation to this setting is equivalent to the classical Orthogonal Matching Pursuit (OMP) algorithm, and thus inherits all of its provable guarantees. Our theoretical and empirical analyses offer new explanations towards the effectiveness of attention and its connections to overparameterization, which may be of independent interest.

Almost every large language model that reaches a broad audience is quantized: trained in full precision, then compressed for efficiency. This step is assumed harmless and its safety is rarely re-checked. We find its principal side effect is increased bias that standard safety evaluation misses. Holding the model, its training, and the prompts fixed, a quantized model still refuses harmful requests, still avoids over-refusing benign prompts, and still selects the unbiased multiple-choice answer. Yet asked an open-ended question, the same model volunteers stereotypes in all eight languages we probe, in roughly one in four open-ended answers under an independent judge (~24% to ~27% across the compression ladder): it passes every standard check and still reaches users measurably more biased. The selective gap is a robust finding; whether open-ended bias further increases with compression is less certain, sensitive to the judge that scores it. We address both with QuantiBias, a benchmark that pairs a generative, multilingual stereotype probe with the refusal and multiple-choice controls that isolate open-ended generation, contrasts each build with and without reasoning, and rates the content severity of what it generates. Across two backbone models (Qwen and Gemma), a five-family screen, and eight benchmarks, quantizers allocate their extra precision by capability data that carries no bias-prevention signal, and reasoning before answering roughly halves the effect on some families while doing nothing on others. A quantized build must be re-evaluated for open-ended bias, not only on the short-form safeguards it already passes.

Deep Ensembles are a simple, reliable, and effective method of improving both the predictive performance and uncertainty estimates of deep learning approaches. However, they are widely criticised as being computationally expensive, due to the need to deploy multiple independent models. Recent work has challenged this view, showing that for predictive accuracy, ensembles can be more computationally efficient (at inference) than scaling single models within an architecture family. This is achieved by cascading ensemble members via an early-exit approach. In this work, we investigate extending these efficiency gains to tasks related to uncertainty estimation. As many such tasks, e.g. selective classification, are binary classification, our key novel insight is to only pass samples within a window close to the binary decision boundary to later cascade stages. Experiments on ImageNet-scale data across a number of network architectures and uncertainty tasks show that the proposed window-based early-exit approach is able to achieve a superior uncertainty-computation trade-off compared to scaling single models. For example, a cascaded EfficientNet-B2 ensemble is able to achieve similar coverage at 5% risk as a single EfficientNet-B4 with <30% the number of MACs. We also find that cascades/ensembles give more reliable improvements on OOD data vs scaling models up. Code for this work is available at: https://github.com/Guoxoug/window-early-exit.

Personalized treatment effect estimates are often of interest in high-stakes applications -- thus, before deploying a model estimating such effects in practice, one needs to be sure that the best candidate from the ever-growing machine learning toolbox for this task was chosen. Unfortunately, due to the absence of counterfactual information in practice, it is usually not possible to rely on standard validation metrics for doing so, leading to a well-known model selection dilemma in the treatment effect estimation literature. While some solutions have recently been investigated, systematic understanding of the strengths and weaknesses of different model selection criteria is still lacking. In this paper, instead of attempting to declare a global `winner', we therefore empirically investigate success- and failure modes of different selection criteria. We highlight that there is a complex interplay between selection strategies, candidate estimators and the data used for comparing them, and provide interesting insights into the relative (dis)advantages of different criteria alongside desiderata for the design of further illuminating empirical studies in this context.

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

Model selection/optimization in conformal inference is challenging, since it may break the exchangeability between labeled and unlabeled data. We study this problem in the context of conformal selection, which uses conformal p-values to select ``interesting'' instances with large unobserved labels from a pool of unlabeled data, while controlling the FDR in finite sample. For validity, existing solutions require the model choice to be independent of the data used to construct the p-values and calibrate the selection set. However, when presented with many model choices and limited labeled data, it is desirable to (i) select the best model in a data-driven manner, and (ii) mitigate power loss due to sample splitting. This paper presents OptCS, a general framework that allows valid statistical testing (selection) after flexible data-driven model optimization. We introduce general conditions under which OptCS constructs valid conformal p-values despite substantial data reuse and handles complex p-value dependencies to maintain finite-sample FDR control via a novel multiple testing procedure. We instantiate this general recipe to propose three FDR-controlling procedures, each optimizing the models differently: (i) selecting the most powerful one among multiple pre-trained candidate models, (ii) using all data for model fitting without sample splitting, and (iii) combining full-sample model fitting and selection. We demonstrate the efficacy of our methods via simulation studies and real applications in drug discovery and alignment of large language models in radiology report generation.

The Backpropagation algorithm has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, the recently introduced Forward-Forward algorithm replaces the forward and backward passes of Backpropagation with two forward passes. In this work, we show that the internal representations obtained by the Forward-Forward algorithm can organise into category-specific ensembles exhibiting high sparsity -- composed of a low number of active units. This situation is reminiscent of what has been observed in cortical sensory areas, where neuronal ensembles are suggested to serve as the functional building blocks for perception and action. Interestingly, while this sparse pattern does not typically arise in models trained with standard Backpropagation, it can emerge in networks trained with Backpropagation on the same objective proposed for the Forward-Forward algorithm.

Selective state space models (SSMs), such as Mamba, achieve strong per-token expressivity by making the time discretization step TildeΔ a learned function of the input. However, in doing so, TildeΔ no longer equals the physical time gap Δ between consecutive observations, limiting the ability of these models to handle irregular time series. Continuous time SSMs, such as S5, keep TildeΔequivΔ and therefore handle irregular timestamps natively, but their dynamics remain linear time invariant (LTI), limiting per token expressivity. We propose TIDES, a selective SSM variant that reconciles selective and continuous architectures by moving input dependence off the step size and onto the diagonal state matrix. As a result, TildeΔequivΔ as in S5, allowing the model to handle irregular timestamps natively without sacrificing the per-token expressivity that makes selective SSMs effective. We show this on a novel Fading Flash experimental benchmark, a compact controlled diagnostic for sequence models that jointly tests input dependence and extrapolation to out-of-distribution Δ values, and isolates the distinct failure modes of current state-of-the-art architectures that TIDES avoids by construction. On large-scale benchmarks, TIDES sets the new best average rank on UEA time series classification and the Physiome ODE regression benchmark, and matches or exceeds the reference baseline model on 6 of 8 natively irregular datasets from astronomy, agriculture, neuromorphic sensing, and climate events. Code available at: https://github.com/TaylanSoydan/TIDES.

The Mamba layer offers an efficient selective state space model (SSM) that is highly effective in modeling multiple domains including NLP, long-range sequences processing, and computer vision. Selective SSMs are viewed as dual models, in which one trains in parallel on the entire sequence via IO-aware parallel scan, and deploys in an autoregressive manner. We add a third view and show that such models can be viewed as attention-driven models. This new perspective enables us to compare the underlying mechanisms to that of the self-attention layers in transformers and allows us to peer inside the inner workings of the Mamba model with explainability methods. Our code is publicly available.

A widely used technique for improving policies is success conditioning, in which one collects trajectories, identifies those that achieve a desired outcome, and updates the policy to imitate the actions taken along successful trajectories. This principle appears under many names -- rejection sampling with SFT, goal-conditioned RL, Decision Transformers -- yet what optimization problem it solves, if any, has remained unclear. We prove that success conditioning exactly solves a trust-region optimization problem, maximizing policy improvement subject to a χ^2 divergence constraint whose radius is determined automatically by the data. This yields an identity: relative policy improvement, the magnitude of policy change, and a quantity we call action-influence -- measuring how random variation in action choices affects success rates -- are exactly equal at every state. Success conditioning thus emerges as a conservative improvement operator. Exact success conditioning cannot degrade performance or induce dangerous distribution shift, but when it fails, it does so observably, by hardly changing the policy at all. We apply our theory to the common practice of return thresholding, showing this can amplify improvement, but at the cost of potential misalignment with the true objective.

Perforated Backpropagation is a neural network optimization technique based on modern understanding of the computational importance of dendrites within biological neurons. This paper explores further experiments from the original publication, generated from a hackathon held at the Carnegie Mellon Swartz Center in February 2025. Students and local Pittsburgh ML practitioners were brought together to experiment with the Perforated Backpropagation algorithm on the datasets and models which they were using for their projects. Results showed that the system could enhance their projects, with up to 90% model compression without negative impact on accuracy, or up to 16% increased accuracy of their original models.

Adversarial training improves the robustness of neural networks against adversarial attacks, albeit at the expense of the trade-off between standard and robust generalization. To unveil the underlying factors driving this phenomenon, we examine the layer-wise learning capabilities of neural networks during the transition from a standard to an adversarial setting. Our empirical findings demonstrate that selectively updating specific layers while preserving others can substantially enhance the network's learning capacity. We therefore propose CURE, a novel training framework that leverages a gradient prominence criterion to perform selective conservation, updating, and revision of weights. Importantly, CURE is designed to be dataset- and architecture-agnostic, ensuring its applicability across various scenarios. It effectively tackles both memorization and overfitting issues, thus enhancing the trade-off between robustness and generalization and additionally, this training approach also aids in mitigating "robust overfitting". Furthermore, our study provides valuable insights into the mechanisms of selective adversarial training and offers a promising avenue for future research.

In many environments only a tiny subset of all states yield high reward. In these cases, few of the interactions with the environment provide a relevant learning signal. Hence, we may want to preferentially train on those high-reward states and the probable trajectories leading to them. To this end, we advocate for the use of a backtracking model that predicts the preceding states that terminate at a given high-reward state. We can train a model which, starting from a high value state (or one that is estimated to have high value), predicts and sample for which the (state, action)-tuples may have led to that high value state. These traces of (state, action) pairs, which we refer to as Recall Traces, sampled from this backtracking model starting from a high value state, are informative as they terminate in good states, and hence we can use these traces to improve a policy. We provide a variational interpretation for this idea and a practical algorithm in which the backtracking model samples from an approximate posterior distribution over trajectories which lead to large rewards. Our method improves the sample efficiency of both on- and off-policy RL algorithms across several environments and tasks.

Offline optimization has recently emerged as an increasingly popular approach to mitigate the prohibitively expensive cost of online experimentation. The key idea is to learn a surrogate of the black-box function that underlines the target experiment using a static (offline) dataset of its previous input-output queries. Such an approach is, however, fraught with an out-of-distribution issue where the learned surrogate becomes inaccurate outside the offline data regimes. To mitigate this, existing offline optimizers have proposed numerous conditioning techniques to prevent the learned surrogate from being too erratic. Nonetheless, such conditioning strategies are often specific to particular surrogate or search models, which might not generalize to a different model choice. This motivates us to develop a model-agnostic approach instead, which incorporates a notion of model sharpness into the training loss of the surrogate as a regularizer. Our approach is supported by a new theoretical analysis demonstrating that reducing surrogate sharpness on the offline dataset provably reduces its generalized sharpness on unseen data. Our analysis extends existing theories from bounding generalized prediction loss (on unseen data) with loss sharpness to bounding the worst-case generalized surrogate sharpness with its empirical estimate on training data, providing a new perspective on sharpness regularization. Our extensive experimentation on a diverse range of optimization tasks also shows that reducing surrogate sharpness often leads to significant improvement, marking (up to) a noticeable 9.6% performance boost. Our code is publicly available at https://github.com/cuong-dm/IGNITE

On-Policy distillation (OPD) transfers teacher capabilities by supervising student-sampled trajectories with dense token-level teacher signals. Recent selective OPD methods improve this process by prioritizing signals that are confident, informative, or learnable. However, the assumptions overlook a fundamental failure mode of language models: their token-level judgments can be driven by input-agnostic language priors, formatting conventions, or stereotyped reasoning templates rather than task-specific evidence. We refer to such optimization-relevant but weakly input-grounded supervision as spurious signals in OPD, which may produce large gradients while contributing little task-improving direction. To mitigate this issue, we propose SA-OPD, a Spurious-Signal-Aware On-Policy Distillation framework that identifies and filters misleading token-level supervision based on input-groundedness and optimization impact. SA-OPD introduces a lightweight input-groundedness proxy estimating whether a token-level distillation signal truly depends on the input. It then filters only tokens that simultaneously exhibit low input-groundedness and extreme distillation divergence, thereby removing high-impact spurious updates and achieving fine-grained OPD optimization. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that SA-OPD consistently outperforms Vanilla OPD and competitive selective methods. These results establish input-groundedness as a key dimension for OPD supervision selection and offer a simple, effective strategy for mitigating spurious updates.

In standard Convolutional Neural Networks (CNNs), the receptive fields of artificial neurons in each layer are designed to share the same size. It is well-known in the neuroscience community that the receptive field size of visual cortical neurons are modulated by the stimulus, which has been rarely considered in constructing CNNs. We propose a dynamic selection mechanism in CNNs that allows each neuron to adaptively adjust its receptive field size based on multiple scales of input information. A building block called Selective Kernel (SK) unit is designed, in which multiple branches with different kernel sizes are fused using softmax attention that is guided by the information in these branches. Different attentions on these branches yield different sizes of the effective receptive fields of neurons in the fusion layer. Multiple SK units are stacked to a deep network termed Selective Kernel Networks (SKNets). On the ImageNet and CIFAR benchmarks, we empirically show that SKNet outperforms the existing state-of-the-art architectures with lower model complexity. Detailed analyses show that the neurons in SKNet can capture target objects with different scales, which verifies the capability of neurons for adaptively adjusting their receptive field sizes according to the input. The code and models are available at https://github.com/implus/SKNet.

The rapid advancements in artificial intelligence (AI) have primarily focused on the process of learning from data to acquire knowledgeable learning systems. As these systems are increasingly deployed in critical areas, ensuring their privacy and alignment with human values is paramount. Recently, selective forgetting (also known as machine unlearning) has shown promise for privacy and data removal tasks, and has emerged as a transformative paradigm shift in the field of AI. It refers to the ability of a model to selectively erase the influence of previously seen data, which is especially important for compliance with modern data protection regulations and for aligning models with human values. Despite its promise, selective forgetting raises significant privacy concerns, especially when the data involved come from sensitive domains. While new unlearning-induced privacy attacks are continuously proposed, each is shown to outperform its predecessors using different experimental settings, which can lead to overly optimistic and potentially unfair assessments that may disproportionately favor one particular attack over the others. In this work, we present the first comprehensive benchmark for evaluating privacy vulnerabilities in selective forgetting. We extensively investigate privacy vulnerabilities of machine unlearning techniques and benchmark privacy leakage across a wide range of victim data, state-of-the-art unlearning privacy attacks, unlearning methods, and model architectures. We systematically evaluate and identify critical factors related to unlearning-induced privacy leakage. With our novel insights, we aim to provide a standardized tool for practitioners seeking to deploy customized unlearning applications with faithful privacy assessments.

Model selection is a strategy aimed at creating accurate and robust models. A key challenge in designing these algorithms is identifying the optimal model for classifying any particular input sample. This paper addresses this challenge and proposes a novel framework for differentiable model selection integrating machine learning and combinatorial optimization. The framework is tailored for ensemble learning, a strategy that combines the outputs of individually pre-trained models, and learns to select appropriate ensemble members for a particular input sample by transforming the ensemble learning task into a differentiable selection program trained end-to-end within the ensemble learning model. Tested on various tasks, the proposed framework demonstrates its versatility and effectiveness, outperforming conventional and advanced consensus rules across a variety of settings and learning tasks.

Finding neural network weights that generalize well from small datasets is difficult. A promising approach is to learn a weight initialization such that a small number of weight changes results in low generalization error. We show that this form of meta-learning can be improved by letting the learning algorithm decide which weights to change, i.e., by learning where to learn. We find that patterned sparsity emerges from this process, with the pattern of sparsity varying on a problem-by-problem basis. This selective sparsity results in better generalization and less interference in a range of few-shot and continual learning problems. Moreover, we find that sparse learning also emerges in a more expressive model where learning rates are meta-learned. Our results shed light on an ongoing debate on whether meta-learning can discover adaptable features and suggest that learning by sparse gradient descent is a powerful inductive bias for meta-learning systems.

For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a set can be observed, but standard statistical estimation methods cannot be applied to estimate causal effects because of multicollinearity/high-dimensional data problems. We propose a novel two-stage penalized regression approach, the penalized covariate-mediator selection operator (PCM Selector), to estimate the causal effects in such scenarios. Unlike existing penalized regression analyses, when a set of intermediate variables is available, PCM Selector provides a consistent or less biased estimator of the causal effect. In addition, PCM Selector provides a variable selection procedure for intermediate variables to obtain better estimation accuracy of the causal effects than does the back-door criterion.

Enterprise agents must follow long-horizon, conditional, safety-critical standard operating procedures (SOPs). We compile machine-readable SOP constraints into executable pseudo-code and run them with a program-guided (PG) stack machine that pages the active frame while an LLM performs semantic execution. A three-arm SOPBench study across six models separates representation from runtime: compiled text never significantly hurts and gains up to 16.0 points where official prose underperforms. Runtime guidance is capability-gated. Two strong models independently show positive seven-domain PG contrasts (58:19 and 75:31 discordant pairs), whereas weak models are harmed. A full-program cursor ablation (active frame first, complete program retained) recovers much of the strong-model refusal gain; selective visibility adds a smaller improvement. Paired probe and audit measurements track this divide to spontaneous state discipline rather than reconstruction ability. On Bank the three primary arms rise from 70.4 to 86.4 to 92.8, with 100% refusal correctness. Practical guidance: compile first; enable active-frame paging only after a model-level discipline check.

Federated learning (FL) is a general principle for decentralized clients to train a server model collectively without sharing local data. FL is a promising framework with practical applications, but its standard training paradigm requires the clients to backpropagate through the model to compute gradients. Since these clients are typically edge devices and not fully trusted, executing backpropagation on them incurs computational and storage overhead as well as white-box vulnerability. In light of this, we develop backpropagation-free federated learning, dubbed BAFFLE, in which backpropagation is replaced by multiple forward processes to estimate gradients. BAFFLE is 1) memory-efficient and easily fits uploading bandwidth; 2) compatible with inference-only hardware optimization and model quantization or pruning; and 3) well-suited to trusted execution environments, because the clients in BAFFLE only execute forward propagation and return a set of scalars to the server. Empirically we use BAFFLE to train deep models from scratch or to finetune pretrained models, achieving acceptable results. Code is available in https://github.com/FengHZ/BAFFLE.

Several studies have compared the in-distribution (ID) and out-of-distribution (OOD) performance of models in computer vision and NLP. They report a frequent positive correlation and some surprisingly never even observe an inverse correlation indicative of a necessary trade-off. The possibility of inverse patterns is important to determine whether ID performance can serve as a proxy for OOD generalization capabilities. This paper shows with multiple datasets that inverse correlations between ID and OOD performance do happen in real-world data - not only in theoretical worst-case settings. We also explain theoretically how these cases can arise even in a minimal linear setting, and why past studies could miss such cases due to a biased selection of models. Our observations lead to recommendations that contradict those found in much of the current literature. - High OOD performance sometimes requires trading off ID performance. - Focusing on ID performance alone may not lead to optimal OOD performance. It may produce diminishing (eventually negative) returns in OOD performance. - In these cases, studies on OOD generalization that use ID performance for model selection (a common recommended practice) will necessarily miss the best-performing models, making these studies blind to a whole range of phenomena.

Selecting the best response from multiple small-model samples using a stronger scorer is a simple inference-time strategy, but fails when the small model has already committed to incorrect reasoning paths. PRM guided search avoids this by scoring candidate continuations during generation, but requires a reward model trained with step-level labels. We propose Chunk-Level Guided Generation, a training-free alternative that uses an off-the-shelf large language model as a process scorer. At each step, a small model samples k fixed-length candidate chunks, while the larger model scores the candidates using likelihoods without generating any text. The selected chunk is committed before the next step, steering generation before errors can propagate. We instantiate this framework with two selection rules: Likelihood-Guided Selection (LGS), which selects the chunk with the highest length-normalized large-model log-probability, and Contrastive-Guided Selection (CGS), which subtracts the small model's log-probability to favor chunks where the large model's preference diverges from the small model's. We show that scoring variable-length reasoning steps with large-model likelihoods is unreliable due to a systematic length bias that persists even after length normalization, and that fixed-length chunks avoid this confound. On GSM8K, MATH, Minerva Math, AMC23, and AIME24 with Qwen2.5-1.5B guided by Qwen2.5-32B and Llama-3.2-1B guided by Llama-3.1-70B, CGS outperforms majority voting by up to 28 pp and, under matched guidance budgets, matches or outperforms Qwen2.5-Math-PRM-72B guided search on most benchmarks without reward-model training. With Qwen2.5-7B guided by Qwen2.5-72B, CGS reaches 81.8% on MATH and 63.6% on Minerva Math at k=16, surpassing majority voting by 4--6 pp. Finally, Chunk-Level Guided Generation produces substantially shorter reasoning traces than PRM guided search.

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.

The Evidence Lower Bound (ELBO) is a quantity that plays a key role in variational inference. It can also be used as a criterion in model selection. However, though extremely popular in practice in the variational Bayes community, there has never been a general theoretic justification for selecting based on the ELBO. In this paper, we show that the ELBO maximization strategy has strong theoretical guarantees, and is robust to model misspecification while most works rely on the assumption that one model is correctly specified. We illustrate our theoretical results by an application to the selection of the number of principal components in probabilistic PCA.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

Graph neural networks (GNNs) have achieved remarkable success across a wide range of applications, such as recommendation, drug discovery, and question answering. Behind the success of GNNs lies the backpropagation (BP) algorithm, which is the de facto standard for training deep neural networks (NNs). However, despite its effectiveness, BP imposes several constraints, which are not only biologically implausible, but also limit the scalability, parallelism, and flexibility in learning NNs. Examples of such constraints include storage of neural activities computed in the forward pass for use in the subsequent backward pass, and the dependence of parameter updates on non-local signals. To address these limitations, the forward-forward algorithm (FF) was recently proposed as an alternative to BP in the image classification domain, which trains NNs by performing two forward passes over positive and negative data. Inspired by this advance, we propose ForwardGNN in this work, a new forward learning procedure for GNNs, which avoids the constraints imposed by BP via an effective layer-wise local forward training. ForwardGNN extends the original FF to deal with graph data and GNNs, and makes it possible to operate without generating negative inputs (hence no longer forward-forward). Further, ForwardGNN enables each layer to learn from both the bottom-up and top-down signals without relying on the backpropagation of errors. Extensive experiments on real-world datasets show the effectiveness and generality of the proposed forward graph learning framework. We release our code at https://github.com/facebookresearch/forwardgnn.

When the performance of a machine learning model varies over groups defined by sensitive attributes (e.g., gender or ethnicity), the performance disparity can be expressed in terms of the probability distributions of the input and output variables over each group. In this paper, we exploit this fact to reduce the disparate impact of a fixed classification model over a population of interest. Given a black-box classifier, we aim to eliminate the performance gap by perturbing the distribution of input variables for the disadvantaged group. We refer to the perturbed distribution as a counterfactual distribution, and characterize its properties for common fairness criteria. We introduce a descent algorithm to learn a counterfactual distribution from data. We then discuss how the estimated distribution can be used to build a data preprocessor that can reduce disparate impact without training a new model. We validate our approach through experiments on real-world datasets, showing that it can repair different forms of disparity without a significant drop in accuracy.

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio alpha when B=Omega(T) or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent O(T^{1/2}) regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

The validity screen (Cacioli, 2026d, 2026e) classifies LLM confidence signals as Valid, Indeterminate, or Invalid. We test whether these classifications predict selective prediction performance. Twenty frontier LLMs from seven families were evaluated on 524 items across six cognitive tracks. Valid models show mean Type 2 AUROC = .624 (SD = .048). Invalid models show mean AUROC = .357 (SD = .231). Cohen's d = 2.81, p = .002. The tiers order monotonically: Invalid (.357) < Indeterminate (.554) < Valid (.624). Split-half cross-validation yields median d = 1.77, P(d > 0) = 1.0 across 1,000 splits. The three-tier classification accounts for 47% of the variance in AUROC. DeepSeek-R1 drops from 85.3% accuracy at full coverage to 11.3% at 10% coverage. The screen predicts the criterion. For selective prediction, the screen matters.

Instrumental variable methods have been widely used to identify causal effects in the presence of unmeasured confounding. A key identification condition known as the exclusion restriction states that the instrument cannot have a direct effect on the outcome which is not mediated by the exposure in view. In the health and social sciences, such an assumption is often not credible. To address this concern, we consider identification conditions of the population average treatment effect with an invalid instrumental variable which does not satisfy the exclusion restriction, and derive the efficient influence function targeting the identifying functional under a nonparametric observed data model. We propose a novel multiply robust locally efficient estimator of the average treatment effect that is consistent in the union of multiple parametric nuisance models, as well as a multiply debiased machine learning estimator for which the nuisance parameters are estimated using generic machine learning methods, that effectively exploit various forms of linear or nonlinear structured sparsity in the nuisance parameter space. When one cannot be confident that any of these machine learners is consistent at sufficiently fast rates to ensure n-consistency for the average treatment effect, we introduce a new criteria for selective machine learning which leverages the multiple robustness property in order to ensure small bias. The proposed methods are illustrated through extensive simulations and a data analysis evaluating the causal effect of 401(k) participation on savings.

The conventional wisdom behind learning deep classification models is to focus on bad-classified examples and ignore well-classified examples that are far from the decision boundary. For instance, when training with cross-entropy loss, examples with higher likelihoods (i.e., well-classified examples) contribute smaller gradients in back-propagation. However, we theoretically show that this common practice hinders representation learning, energy optimization, and margin growth. To counteract this deficiency, we propose to reward well-classified examples with additive bonuses to revive their contribution to the learning process. This counterexample theoretically addresses these three issues. We empirically support this claim by directly verifying the theoretical results or significant performance improvement with our counterexample on diverse tasks, including image classification, graph classification, and machine translation. Furthermore, this paper shows that we can deal with complex scenarios, such as imbalanced classification, OOD detection, and applications under adversarial attacks because our idea can solve these three issues. Code is available at: https://github.com/lancopku/well-classified-examples-are-underestimated.

Counterfactual Risk Minimization (CRM) is a framework for dealing with the logged bandit feedback problem, where the goal is to improve a logging policy using offline data. In this paper, we explore the case where it is possible to deploy learned policies multiple times and acquire new data. We extend the CRM principle and its theory to this scenario, which we call "Sequential Counterfactual Risk Minimization (SCRM)." We introduce a novel counterfactual estimator and identify conditions that can improve the performance of CRM in terms of excess risk and regret rates, by using an analysis similar to restart strategies in accelerated optimization methods. We also provide an empirical evaluation of our method in both discrete and continuous action settings, and demonstrate the benefits of multiple deployments of CRM.

Rubric-based RL has recently shown promise in improving LLMs on open-ended tasks. A widely recognized limitation of rubric-based RL is limited exploration: criteria that no rollout manages to satisfy (Unexplored Criteria, UC) receive no optimization signal. Recent methods address this by incorporating rubric information as external guidance during rollout, yet they introduce a train-inference mismatch: the policy is optimized on rollouts produced under external guidance while this guidance is absent at inference time, causing error accumulation through autoregressive decoding. Moreover, these exploration-focused approaches overlook a fundamentally different failure mode that we term Suppressed Criteria (SC) -- criteria that are satisfied by some rollouts yet whose learning signals are lost during optimization because scalar reward aggregation assigns them non-positive aggregate advantages. Our analysis reveals that SC are remarkably prevalent: over 57% of samples exhibit this failure mode throughout training, with an average of 1.8 SC per sample. To simultaneously address both UC and SC without introducing training-inference mismatch, we propose Criterion-Distilled Policy Optimization (CriPO), which enhances rubric-based RL via on-policy self-distillation. For UC, CriPO constructs a criterion-injection self-teacher and computes a localized forward-KL loss to inject missing behaviors into the policy. For SC, CriPO employs a counterfactual self-teacher to locate criterion-relevant tokens in negative-advantage rollouts and flips their token-level advantages to positive values, preserving useful patterns that would otherwise be suppressed. Experiments on medicine and science benchmarks demonstrate that CriPO consistently outperforms rubric-based RL, achieving stronger final performance with approximately 2times fewer optimization steps.

Online conformal prediction can fail when predictions shape actions and actions determine which outcomes enter calibration. Standard adaptive methods may retain marginal coverage while systematically miscovering the counterfactual outcomes of rarely selected actions. This paper formalizes the failure through counterfactual coverage and introduces Propensity-Weighted Online Conformal Prediction, an inverse-propensity-weighted recursion that debiases calibration. A doubly robust variant further reduces nuisance bias to the product of outcome-model and propensity errors. Under positivity, the resulting coverage rate matches an information-theoretic lower bound up to logarithmic factors. Experiments on synthetic decision tasks, open bandit data, and financial rebalancing show that PW-OCP and DR-OCP improve counterfactual coverage and downstream regret without sacrificing prediction-set sharpness.

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks, their formal expressiveness and length generalization properties remain underexplored. In this work, we provide insight into the workings of selective SSMs by analyzing their expressiveness and length generalization performance on regular language tasks, i.e., finite-state automaton (FSA) emulation. We address certain limitations of modern SSM-based architectures by introducing the Selective Dense State-Space Model (SD-SSM), the first selective SSM that exhibits perfect length generalization on a set of various regular language tasks using a single layer. It utilizes a dictionary of dense transition matrices, a softmax selection mechanism that creates a convex combination of dictionary matrices at each time step, and a readout consisting of layer normalization followed by a linear map. We then proceed to evaluate variants of diagonal selective SSMs by considering their empirical performance on commutative and non-commutative automata. We explain the experimental results with theoretical considerations. Our code is available at https://github.com/IBM/selective-dense-state-space-model.

Since data is the fuel that drives machine learning models, and access to labeled data is generally expensive, semi-supervised methods are constantly popular. They enable the acquisition of large datasets without the need for too many expert labels. This work combines self-labeling techniques with active learning in a selective sampling scenario. We propose a new method that builds an ensemble classifier. Based on an evaluation of the inconsistency of the decisions of the individual base classifiers for a given observation, a decision is made on whether to request a new label or use the self-labeling. In preliminary studies, we show that naive application of self-labeling can harm performance by introducing bias towards selected classes and consequently lead to skewed class distribution. Hence, we also propose mechanisms to reduce this phenomenon. Experimental evaluation shows that the proposed method matches current selective sampling methods or achieves better results.

On-policy distillation (OPD) uses teacher correction on student-generated responses. Full-vocabulary correction can provide important corrections even for tokens that the student assigns low probability, but backpropagating through all token logits becomes memory-intensive for long sequences. Existing memory-saving approaches estimate corrections from sampled tokens or restrict supervision to the student's TopK tokens, introducing sampling noise or changing the full-vocabulary correction. We introduce SparseOPD, which uses full-vocabulary teacher correction to determine which corrections matter before selecting the token logits to differentiate. SparseOPD first constructs the full-vocabulary correction without retaining its backward graph, then selects tokens by correction magnitude rather than student probability. Signed residual compensation preserves the total promoting and suppressing correction mass, while correction-aware budget allocation distributes the sparse support across positions. Finally, the update backpropagates only through the selected token logits. Across six task--scale settings spanning mathematics, chemistry QA, and multimodal reasoning, SparseOPD outperforms Sampled Token and TopK in task-average accuracy and matches or exceeds Full Vocabulary. Gradient cosine similarity reaches 99\% on 4B mathematics, while 8K full-parameter profiling shows 70.5\% lower backward memory.

A training-data quality gate changes both which examples survive within regions of the input space and how training mass is distributed across those regions, so a gate-versus-random comparison does not isolate these mechanisms. We introduce Counterfactual Gate-Support Decomposition (CGSD), a four-arm, budget-matched design that crosses gate eligibility with support distribution and decomposes the observed gate effect into within-support selection, between-support redistribution, and their interaction. The practical constraint is finite-pool realizability: we characterize mass and token-assembly conditions under which the required arms can be constructed, together with a support-extinction case in which the ordinary design is undefined. On Korean-English and Korean-Japanese retrieval, the mean within-support selection component is the only one that exceeds its calibrated null band (+29.7 and +5.6 holdout items; 30/30 positive replicates), decisively in Korean-English and marginally in Korean-Japanese; redistribution and interaction remain unresolved at the available power. The same pattern holds for a second, unrelated gate family -- a model-confidence threshold rather than a deterministic verifier -- judged against its own null (+27.3 items, 9/9 positive), so the result is not a property of one gate's mechanism. On a mathematics gate, zero-eligibility supports leave the ordinary design undefined at every budget, while the extended design is constructible only inside narrow budget bands that an exhaustive scan locates and that the natural operating point misses -- the assembly condition separating a property of the pool from a limitation of the packer. CGSD therefore returns a decomposition, a constructible-but-underpowered design, or an explicit non-constructibility result, and says which; it prevents support redistribution from being silently interpreted as sample-level gate quality.

Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. Here we consider the entire posterior effects distribution by estimating full counterfactual outcome distributions. We propose a methodology for inference on counterfactual distributions which builds upon the martingale posterior framework of Fong et al. (2023). This provides a highly flexible approach to estimating densities, distribution functions, and derived quantities such as quantiles, which coherently quantifies the epistemic uncertainty on any target estimand of interest. As the predictive recursions are based on an underlying nonparametric model (a Dirichlet process mixture model), our method naturally inherits robustness with respect to restrictive parametric assumptions. In addition, implementation of our method is typically very fast. This approach can be applied to marginal or conditional counterfactual distributions and is easily extended to an instrumental variables setup. Using the concept of almost conditionally identically distributed random variables, we prove convergence of the martingale posterior inference on the counterfactual outcome distributions for the causal models considered in the paper. We illustrate our approach on both simulated and real data. Using the latter, we investigate the effect of zinc lozenges on common cold duration, the impact of vitamin A supplementation on children's survival rates with one-sided non-compliance (analysed in Imbens and Rubin, 1997a) and the effect of job training (LaLonde, 1986).

The input side of the Information Bottleneck may contain task-irrelevant variation that still costs rate. We identify this cost exactly. Let T be a source and C a relevance variable. Suppose the deterministic statistic Z = phi(T) satisfies C-Z-T. For any encoder p(X|T), its conditional average over the fibres of phi preserves I(X;C) and lowers the rate by I(X;T|Z). The reverse pullback preserves both coordinates. These maps establish equality of the relevance-rate curves and Lagrangian infima on standard Borel spaces for every tradeoff parameter. They also characterise all attained optima. Every full-source minimiser factors through Z, and every reduced minimiser pulls back to T. When C is finite and distortion is logarithmic loss, replacement of T^n by Z^n also preserves the optimal remote distortion at every blocklength and message budget. The operational rate-distortion functions are therefore equal.

Real-world classifiers can benefit from the option of abstaining from predicting on samples where they have low confidence. Such abstention is particularly useful on samples which are close to the learned decision boundary, or which are outliers with respect to the training sample. These settings have been the subject of extensive but disjoint study in the selective classification (SC) and out-of-distribution (OOD) detection literature. Recent work on selective classification with OOD detection (SCOD) has argued for the unified study of these problems; however, the formal underpinnings of this problem are still nascent, and existing techniques are heuristic in nature. In this paper, we propose new plugin estimators for SCOD that are theoretically grounded, effective, and generalise existing approaches from the SC and OOD detection literature. In the course of our analysis, we formally explicate how na\"{i}ve use of existing SC and OOD detection baselines may be inadequate for SCOD. We empirically demonstrate that our approaches yields competitive SC and OOD detection performance compared to baselines from both literatures.

Test-time reasoning is increasingly used as a serving-time control knob, but extra reasoning is not uniformly valuable: it can repair failed attempts, waste compute on already-correct answers, or introduce harmful answer changes. We study this as a deployment allocation problem rather than a new-verifier problem. We introduce \sevra, Selective Verification for Reasoning Allocation, a serving-layer controller that decides whether to preserve a frozen solver's initial answer or invoke active verification. Using a frozen Qwen3-4B solver, we log intervention outcomes and train recoverability-aware gates from serving-visible attempt state. On \mathfive, selective verification reaches 76.3\% accuracy, compared with 75.5\% for always verifying, while reducing post-generation tokens by 26.8\% and harmful flips from 2.2\% to 1.0\%. However, an 8,192-token initial solve reaches 76.0\% accuracy with 28\% fewer total model tokens, showing that selective recovery is useful but not the best tested cost frontier. In frozen transfer to \gsm, the selective policy verifies only 3.0\% of examples, improves accuracy from 93.4\% to 94.5\%, and reduces verification tokens by 91.2\% relative to always verifying; again, a longer initial solve matches its accuracy with fewer realized tokens. On CommonsenseQA, always-on verification hurts, while Self-Consistency@5 improves accuracy at about five times the realized token cost. The resulting deployment rule is: tune the initial budget first, then use selective recovery when explicit checks, bounded retries, auditability, or regression-risk control matter.

Backpropagation, the cornerstone of deep learning, is limited to computing gradients for continuous variables. This limitation poses challenges for problems involving discrete latent variables. To address this issue, we propose a novel approach to approximate the gradient of parameters involved in generating discrete latent variables. First, we examine the widely used Straight-Through (ST) heuristic and demonstrate that it works as a first-order approximation of the gradient. Guided by our findings, we propose ReinMax, which achieves second-order accuracy by integrating Heun's method, a second-order numerical method for solving ODEs. ReinMax does not require Hessian or other second-order derivatives, thus having negligible computation overheads. Extensive experimental results on various tasks demonstrate the superiority of ReinMax over the state of the art. Implementations are released at https://github.com/microsoft/ReinMax.

We study causal logistic bandits with counterfactual fairness constraints. The causal structure is given through known factual and counterfactual feature maps that share an unknown logistic reward parameter, but the learner observes only factual rewards. Consequently, the directions determining counterfactual feasibility need not be identifiable from the available feedback. The closest prior analyses either omit a coverage condition or impose a comparatively strong one, and do not establish matching lower bounds. We first show that some coverage condition is necessary: without a coverage-type restriction, factually indistinguishable environments with different optimal fair actions force Ω(T) expected joint loss. Under a weaker full-rank condition on the factual covariance pooled across actions, we identify a target-specific information scale V_star that measures the difficulty of estimating rewards and counterfactual effects from factual feedback. We construct worst-case families satisfying this condition on which every policy incurs expected joint loss Ωleft(left[V_starmin{log K,d}right]^{1/3}T^{2/3}right). We also give an explore--then--exploit procedure tuned using V_star and an adaptive algorithm that does not require its value. Both algorithms achieve max{R_T,V_T}=Oleft(left[V_starmin{log K,d}right]^{1/3}T^{2/3}+κd/σ_0^2right), where R_T is regret relative to the best fair action and V_T denotes the cumulative stage-wise positive violations. Thus the upper and lower bounds match in their leading dependence on T, V_star, and min{log K,d}, up to logarithmic factors.

We present a novel network pruning algorithm called Dynamic Sparse Training that can jointly find the optimal network parameters and sparse network structure in a unified optimization process with trainable pruning thresholds. These thresholds can have fine-grained layer-wise adjustments dynamically via backpropagation. We demonstrate that our dynamic sparse training algorithm can easily train very sparse neural network models with little performance loss using the same number of training epochs as dense models. Dynamic Sparse Training achieves the state of the art performance compared with other sparse training algorithms on various network architectures. Additionally, we have several surprising observations that provide strong evidence for the effectiveness and efficiency of our algorithm. These observations reveal the underlying problems of traditional three-stage pruning algorithms and present the potential guidance provided by our algorithm to the design of more compact network architectures.

Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic or non-smooth neurons? I.e., can we "back-propagate" through these stochastic neurons? We examine this question, existing approaches, and compare four families of solutions, applicable in different settings. One of them is the minimum variance unbiased gradient estimator for stochatic binary neurons (a special case of the REINFORCE algorithm). A second approach, introduced here, decomposes the operation of a binary stochastic neuron into a stochastic binary part and a smooth differentiable part, which approximates the expected effect of the pure stochatic binary neuron to first order. A third approach involves the injection of additive or multiplicative noise in a computational graph that is otherwise differentiable. A fourth approach heuristically copies the gradient with respect to the stochastic output directly as an estimator of the gradient with respect to the sigmoid argument (we call this the straight-through estimator). To explore a context where these estimators are useful, we consider a small-scale version of {\em conditional computation}, where sparse stochastic units form a distributed representation of gaters that can turn off in combinatorially many ways large chunks of the computation performed in the rest of the neural network. In this case, it is important that the gating units produce an actual 0 most of the time. The resulting sparsity can be potentially be exploited to greatly reduce the computational cost of large deep networks for which conditional computation would be useful.

Masked diffusion language models (MDMs) admit flexible generation orders, making the unmasking strategy an inference decision. Existing methods vary in how they prioritize positions, control parallelism, restrict selection regions, revise predictions, or plan future denoising, yet it remains unclear when these choices should change during generation. We study this question through strategy reversals, where an alternative action becomes preferable to a fixed choice. We organize MDM inference into five axes--score, cardinality, region, commitment, and planning--and define adaptation opportunity as the one-step utility advantage of the best candidate action over a validation-selected fixed action. This view shows that adaptation value depends on both the frequency and magnitude of such reversals. Across three MDMs and ten tasks, adaptation opportunities are highly heterogeneous, with some regimes exhibiting concentrated and predictable one-step gains. This motivates selective adaptation: lightweight detectors calibrated on validation prompts identify high-opportunity states, capturing, for example, 56.9 percent of the candidate-set oracle opportunity by adapting only the top 10 percent of states on LLaDA-8B constrained JSON filling. Our transition-level results suggest that state adaptation is most useful when applied selectively rather than uniformly.

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true one, with precision growing only with the square root of the batch size. A theoretical justification is with the help of stochastic approximation theory. However, the conditions for the validity of this theory are not satisfied in the usual learning rate schedules. Batch processing is also difficult to combine with efficient second-order optimization methods. This proposal is based on another hypothesis: the loss minimum of the training set can be expected to be well-approximated by the minima of its subsets. Such subset minima can be computed in a fraction of the time necessary for optimizing over the whole training set. This hypothesis has been tested with the help of the MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks, optionally extended by training data augmentation. The experiments have confirmed that results equivalent to conventional training can be reached. In summary, even small subsets are representative if the overdetermination ratio for the given model parameter set sufficiently exceeds unity. The computing expense can be reduced to a tenth or less.

Deep Neural Networks (DNNs) are typically trained by backpropagation in a batch learning setting, which requires the entire training data to be made available prior to the learning task. This is not scalable for many real-world scenarios where new data arrives sequentially in a stream form. We aim to address an open challenge of "Online Deep Learning" (ODL) for learning DNNs on the fly in an online setting. Unlike traditional online learning that often optimizes some convex objective function with respect to a shallow model (e.g., a linear/kernel-based hypothesis), ODL is significantly more challenging since the optimization of the DNN objective function is non-convex, and regular backpropagation does not work well in practice, especially for online learning settings. In this paper, we present a new online deep learning framework that attempts to tackle the challenges by learning DNN models of adaptive depth from a sequence of training data in an online learning setting. In particular, we propose a novel Hedge Backpropagation (HBP) method for online updating the parameters of DNN effectively, and validate the efficacy of our method on large-scale data sets, including both stationary and concept drifting scenarios.

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade -- e.g., not modelling the errors of downstream models -- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called T-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

This paper formalizes threshold-based selection as an evaluation-gating architecture in which each incumbent is tested before variation and a replacement is generated and evaluated only when contextual pressure exceeds intrinsic strength. The mechanism is instantiated as Leaf Abscission Optimization (LAO), using rank-based strength, a phenological seasonal signal, diversity modulation, environmental pressure, and a base regrowth kernel. A blocked two-to-the-fourth-power factorial analysis at dimension 10 on the CEC 2017 suite reduces the original multi-layer design to a parsimonious core: drift is harmful, while the other three auxiliary layers show no robust independent evidence of benefit. The resulting LAO-Core attains the third-best mean Friedman rank among nine optimizers at dimensions 10, 30, and 50 under the equal evaluation budget. A four-budget sweep shows budget-dependent relative performance, with adaptive differential-evolution baselines gaining relative advantage at larger budgets; the nine-cell dimension-budget analysis establishes neither an evaluation-budget-per-dimension-only law nor a statistically significant dimension-budget interaction. A paired intervention shows that diversity modulation changes late-run replacement behaviour without a detectable effect on final error at the tested budget. The evidence supports LAO as a parsimonious evaluation-gating mechanism with regime-qualified competitiveness, rather than as a generally superior optimizer.

Group Relative Policy Optimization (GRPO) assigns a single scalar advantage to all tokens in a completion. For structured generations with explicit segments and objectives, this couples unrelated reward signals across segments, leading to objective interference and misattributed credit. We propose Blockwise Advantage Estimation, a family of GRPO-compatible methods that assigns each objective its own advantage and applies it only to the tokens in the corresponding text block, reducing reliance on hand-designed scalar rewards and scaling naturally to additional objectives. A key challenge is estimating advantages for later blocks whose rewards are conditioned on sampled prefixes; standard unbiased approaches require expensive nested rollouts from intermediate states. Concretely, we introduce an Outcome-Conditioned Baseline that approximates intermediate state values using only within-group statistics by stratifying samples according to a prefix-derived intermediate outcome. On math tasks with uncertainty estimation, our method mitigates reward interference, is competitive with a state-of-the-art reward-designed approach, and preserves test-time gains from confidence-weighted ensembling. More broadly, it provides a modular recipe for optimizing sequential objectives in structured generations without additional rollouts.

LLM-based agents often operate in a greedy, step-by-step manner, selecting actions solely based on the current observation without considering long-term consequences or alternative paths. This lack of foresight is particularly problematic in web environments, which are only partially observable-limited to browser-visible content (e.g., DOM and UI elements)-where a single misstep often requires complex and brittle navigation to undo. Without an explicit backtracking mechanism, agents struggle to correct errors or systematically explore alternative paths. Tree-search methods provide a principled framework for such structured exploration, but existing approaches lack mechanisms for safe backtracking, making them prone to unintended side effects. They also assume that all actions are reversible, ignoring the presence of irreversible actions-limitations that reduce their effectiveness in realistic web tasks. To address these challenges, we introduce WebOperator, a tree-search framework that enables reliable backtracking and strategic exploration. Our method incorporates a best-first search strategy that ranks actions by both reward estimates and safety considerations, along with a robust backtracking mechanism that verifies the feasibility of previously visited paths before replaying them, preventing unintended side effects. To further guide exploration, WebOperator generates action candidates from multiple, varied reasoning contexts to ensure diverse and robust exploration, and subsequently curates a high-quality action set by filtering out invalid actions pre-execution and merging semantically equivalent ones. Experimental results on WebArena and WebVoyager demonstrate the effectiveness of WebOperator. On WebArena, WebOperator achieves a state-of-the-art 54.6% success rate with gpt-4o, underscoring the critical advantage of integrating strategic foresight with safe execution.

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

In this study, we investigate the DIstribution Correction Estimation (DICE) methods, an important line of work in offline reinforcement learning (RL) and imitation learning (IL). DICE-based methods impose state-action-level behavior constraint, which is an ideal choice for offline learning. However, they typically perform much worse than current state-of-the-art (SOTA) methods that solely use action-level behavior constraint. After revisiting DICE-based methods, we find there exist two gradient terms when learning the value function using true-gradient update: forward gradient (taken on the current state) and backward gradient (taken on the next state). Using forward gradient bears a large similarity to many offline RL methods, and thus can be regarded as applying action-level constraint. However, directly adding the backward gradient may degenerate or cancel out its effect if these two gradients have conflicting directions. To resolve this issue, we propose a simple yet effective modification that projects the backward gradient onto the normal plane of the forward gradient, resulting in an orthogonal-gradient update, a new learning rule for DICE-based methods. We conduct thorough theoretical analyses and find that the projected backward gradient brings state-level behavior regularization, which reveals the mystery of DICE-based methods: the value learning objective does try to impose state-action-level constraint, but needs to be used in a corrected way. Through toy examples and extensive experiments on complex offline RL and IL tasks, we demonstrate that DICE-based methods using orthogonal-gradient updates (O-DICE) achieve SOTA performance and great robustness.

Multi-Grid Back-Projection (MGBP) is a fully-convolutional network architecture that can learn to restore images and videos with upscaling artifacts. Using the same strategy of multi-grid partial differential equation (PDE) solvers this multiscale architecture scales computational complexity efficiently with increasing output resolutions. The basic processing block is inspired in the iterative back-projection (IBP) algorithm and constitutes a type of cross-scale residual block with feedback from low resolution references. The architecture performs in par with state-of-the-arts alternatives for regression targets that aim to recover an exact copy of a high resolution image or video from which only a downscale image is known. A perceptual quality target aims to create more realistic outputs by introducing artificial changes that can be different from a high resolution original content as long as they are consistent with the low resolution input. For this target we propose a strategy using noise inputs in different resolution scales to control the amount of artificial details generated in the output. The noise input controls the amount of innovation that the network uses to create artificial realistic details. The effectiveness of this strategy is shown in benchmarks and it is explained as a particular strategy to traverse the perception-distortion plane.

Backpropagation-based approaches aim to align diffusion models with reward functions through end-to-end backpropagation of the reward gradient within the denoising chain, offering a promising perspective. However, due to the computational costs and the risk of gradient explosion associated with the lengthy denoising chain, existing approaches struggle to achieve complete gradient backpropagation, leading to suboptimal results. In this paper, we introduce Shortcut-based Fine-Tuning (ShortFT), an efficient fine-tuning strategy that utilizes the shorter denoising chain. More specifically, we employ the recently researched trajectory-preserving few-step diffusion model, which enables a shortcut over the original denoising chain, and construct a shortcut-based denoising chain of shorter length. The optimization on this chain notably enhances the efficiency and effectiveness of fine-tuning the foundational model. Our method has been rigorously tested and can be effectively applied to various reward functions, significantly improving alignment performance and surpassing state-of-the-art alternatives.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

Foundation models are often used as fixed black-box predictors for downstream tasks with limited labeled data, but their predictions may be biased and unsafe to trust blindly. We study this setting through black-box assisted nonparametric regression: a learner observes labeled samples and can query a fixed predictor f_0, while the target f^* is close to f_0 in L_2(P_X) up to an unknown radius δ. We give a finite-sample minimax characterization showing a phase transition at δ_c(n) asymp n^{-β/(2β+d)}, with leading risk min{δ^2, n^{-2β/(2β+d)}}. We then analyze a Safe Residual Estimator: it learns a correction around f_0, initializes the residual head at zero so the initial predictor equals f_0, and uses holdout selection to revert to f_0 when the learned correction is not supported by validation data. Here, "safe" means avoiding negative transfer, i.e., performing worse than the black-box predictor alone. The estimator matches the leading minimax term up to an additive validation-selection cost. Synthetic regression experiments verify the predicted phase transition, while CIFAR-100 with CLIP and AG News with Qwen3-8B provide practice-facing evidence that the same residual-correction tradeoff is useful beyond the formal squared-loss regression setting.

Block drafters propose several tokens in one forward pass, before earlier target tokens are realised. Their rejection mixes two losses: missing within-block path information and imperfect modelling of observable information. Accepted length cannot distinguish them. We separate the two with an information floor, the minimum expected rejection at a specified conditioning order; rejection above this floor is the model gap. Estimating both from target rollouts across four domains, four open-weight targets, and a frontier API target yields three findings. First, the all-parallel floor reaches 0.286 at the final slot on Qwen3-4B, limiting even the best proposal to 71% per-slot acceptance. Second, one realised token removes 86--100% of this floor, a locality also recovered by an independent mutual-information analysis. Third, current drafters remain far above their floors: the final-slot model gap accounts for 43--64% of DFlash rejection and 85--92% of DSpark's oracle-conditioned rejection. These findings separate the value of short-range conditioning from proposal quality. Guided by this distinction, we replace a context-independent predecessor correction with a prefix-attention head that reads committed context conditional on the predecessor. With supporting backbone components, the resulting Qwen3-4B drafter improves mean serving accepted length by 3.83% over the released DSpark checkpoint across nine tasks, without increasing the conditioning order.

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

In regression and causal inference, controlled subgroup selection aims to identify, with inferential guarantees, a subgroup (defined as a subset of the covariate space) on which the average response or treatment effect is above a given threshold. E.g., in a clinical trial, it may be of interest to find a subgroup with a positive average treatment effect. However, existing methods either lack inferential guarantees, heavily restrict the search for the subgroup, or sacrifice efficiency by naive data splitting. We propose a novel framework called chiseling that allows the analyst to interactively refine and test a candidate subgroup by iteratively shrinking it. The sole restriction is that the shrinkage direction only depends on the points outside the current subgroup, but otherwise the analyst may leverage any prior information or machine learning algorithm. Despite this flexibility, chiseling controls the probability that the discovered subgroup is null (e.g., has a non-positive average treatment effect) under minimal assumptions: for example, in randomized experiments, this inferential validity guarantee holds under only bounded moment conditions. When applied to a variety of simulated datasets and a real survey experiment, chiseling identifies substantially better subgroups than existing methods with inferential guarantees.

Algorithmic trading systems on decentralised exchanges (DEXs) reject most candidate tokens they evaluate. The counterfactual outcome of rejected candidates (what would have happened had the system entered) is rarely measured. This paper introduces Post-Rejection Follow-up Sampling (PRFS). A separate tracking subsystem samples each rejected token's price and liquidity at a configurable cadence, over a horizon of up to twenty-four hours. PRFS produces the data needed to evaluate filter precision against actual market outcomes of rejected candidates, not against synthetic backtest reconstructions. The methodology, data architecture, and deposit format are described in Section III. The companion dataset contains 67,000 forward-outcome observation rows across 2,997 rejection events spanning 457 unique mints, collected over a continuous eight-day window (2026-04-10 to 2026-04-19, UTC). Approximately 55 percent of rejection events receive at least one forward observation; coverage at the mint level is complete. The principal binding constraint on downstream classification is per-event horizon density, not event-level coverage. PRFS is dataset-independent. It generalises to any algorithmic decision system in which rejections substantially outnumber executions.

The aim of this paper is to introduce a new learning procedure for neural networks and to demonstrate that it works well enough on a few small problems to be worth further investigation. The Forward-Forward algorithm replaces the forward and backward passes of backpropagation by two forward passes, one with positive (i.e. real) data and the other with negative data which could be generated by the network itself. Each layer has its own objective function which is simply to have high goodness for positive data and low goodness for negative data. The sum of the squared activities in a layer can be used as the goodness but there are many other possibilities, including minus the sum of the squared activities. If the positive and negative passes could be separated in time, the negative passes could be done offline, which would make the learning much simpler in the positive pass and allow video to be pipelined through the network without ever storing activities or stopping to propagate derivatives.

Layer-wise Relevance Propagation (LRP) provides principled attribution for neural networks through conservation properties and foundations in Deep Taylor Decomposition. However, existing implementations operate at the module level, requiring architecture-specific propagation rules and modifications. These limit the generality of target model and sustainability of implementations as architectures evolve. We introduce DynamicLRP, a model-agnostic LRP framework operating at the tensor operation level. By decomposing attribution to individual operations within computation graphs and introducing a novel mechanism for deferred activation resolution, named the Promise System, our approach achieves true architecture agnosticity while maintaining LRP's theoretical guarantees. This design operates independently of backpropagation machinery, enabling operation on arbitrary computation graphs without model modification and side-by-side execution with gradient backpropagation. Being based on computation graphs, this method is theoretically extensible to other deep learning libraries that support auto-differentiation. We demonstrate faithfulness matching or exceeding specialized implementations (1.77 vs 1.69 ABPC on VGG, equivalent performance on ViT, 93.70\% and 95.06\% top-1 attribution accuracy for explaining RoBERTa-large and Flan-T5-large answers on SQuADv2, respectively) while maintaining practical efficiency on models with hundreds of millions of parameters. We achieved 99.92\% node coverage across 31,465 computation graph nodes from 15 diverse architectures, including state-space models (Mamba), audio transformers (Whisper), and multimodal systems (DePlot) without any model-specific code with rules for 47 fundamental operations implemented. Our operation-level decomposition and Promise System establish a sustainable, extensible foundation for LRP across evolving architectures.

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

Learning algorithms are often used in conjunction with expert decision makers in practical scenarios, however this fact is largely ignored when designing these algorithms. In this paper we explore how to learn predictors that can either predict or choose to defer the decision to a downstream expert. Given only samples of the expert's decisions, we give a procedure based on learning a classifier and a rejector and analyze it theoretically. Our approach is based on a novel reduction to cost sensitive learning where we give a consistent surrogate loss for cost sensitive learning that generalizes the cross entropy loss. We show the effectiveness of our approach on a variety of experimental tasks.

Backpropagation algorithm has driven the remarkable success of deep neural networks, but its lack of biological plausibility and high computational costs have motivated the ongoing search for alternative training methods. Hebbian learning has attracted considerable interest as a biologically plausible alternative to backpropagation. Nevertheless, its exclusive reliance on local information, without consideration of global task objectives, fundamentally limits its scalability. Inspired by the biological synergy between neuromodulators and local plasticity, we introduce a novel model-agnostic Global-guided Hebbian Learning (GHL) framework, which seamlessly integrates local and global information to scale up across diverse networks and tasks. In specific, the local component employs Oja's rule with competitive learning to ensure stable and effective local updates. Meanwhile, the global component introduces a sign-based signal that guides the direction of local Hebbian plasticity updates. Extensive experiments demonstrate that our method consistently outperforms existing Hebbian approaches. Notably, on large-scale network and complex datasets like ImageNet, our framework achieves the competitive results and significantly narrows the gap with standard backpropagation.

Prompt optimization methods either analyze individual failures in isolation or compare prompt variants across examples, operating on single execution traces with no access to the reasoning process distinguishing success from failure on the same input. We introduce ContraPrompt, built on the observation that when a model fails but succeeds on a retry with feedback, the difference between its two chain-of-thought traces constitutes an optimization signal not captured by prior methods. Unlike prior contrastive methods, we compare complete intermediate reasoning processes: the two traces share model, input, and base prompt, so remaining differences reflect reasoning strategy and appended error feedback -- we call this dyadic reasoning trace analysis. The multi-attempt solving phase is an instrumented agentic retry loop that generates contrastive data automatically without human annotation. Extracted rules are organized into an input-aware decision tree routing instructions by observable input characteristics. On four reasoning and compliance benchmarks, ContraPrompt outperforms GEPA (Agrawal et al., 2026) on all four, with absolute gains of +8.29 pp on HotPotQA (+20.8% rel.), +2.21 pp on GDPR-Bench (+18.2% rel.), +7.14 pp on GPQA Diamond (+10.6% rel.), and +0.74 pp on BBH (+0.85% rel.). Ablations confirm dyadic trace contrastivity is the critical component, with a -16% relative average drop upon its removal. On 53 EvalSet black-box optimization problems, ContraPrompt beats GEPA on 11, ties on 41, and loses on 1 at equal budget. On FiNER-139 financial named entity recognition (Loukas et al., 2022), ContraPrompt achieves +7.77 pp over the unoptimized baseline (+11.6% rel.) and +1.94 pp over GEPA (+2.66% rel.), with branch conditions aligning with standard US GAAP financial-instrument categories.

Fine-tuning pretrained large models to downstream tasks is an important problem, which however suffers from huge memory overhead due to large-scale parameters. This work strives to reduce memory overhead in fine-tuning from perspectives of activation function and layer normalization. To this end, we propose the Approximate Backpropagation (Approx-BP) theory, which provides the theoretical feasibility of decoupling the forward and backward passes. We apply our Approx-BP theory to backpropagation training and derive memory-efficient alternatives of GELU and SiLU activation functions, which use derivative functions of ReLUs in the backward pass while keeping their forward pass unchanged. In addition, we introduce a Memory-Sharing Backpropagation strategy, which enables the activation memory to be shared by two adjacent layers, thereby removing activation memory usage redundancy. Our method neither induces extra computation nor reduces training efficiency. We conduct extensive experiments with pretrained vision and language models, and the results demonstrate that our proposal can reduce up to sim30% of the peak memory usage. Our code is released at https://github.com/yyyyychen/LowMemoryBP.

We present Direct Reward Fine-Tuning (DRaFT), a simple and effective method for fine-tuning diffusion models to maximize differentiable reward functions, such as scores from human preference models. We first show that it is possible to backpropagate the reward function gradient through the full sampling procedure, and that doing so achieves strong performance on a variety of rewards, outperforming reinforcement learning-based approaches. We then propose more efficient variants of DRaFT: DRaFT-K, which truncates backpropagation to only the last K steps of sampling, and DRaFT-LV, which obtains lower-variance gradient estimates for the case when K=1. We show that our methods work well for a variety of reward functions and can be used to substantially improve the aesthetic quality of images generated by Stable Diffusion 1.4. Finally, we draw connections between our approach and prior work, providing a unifying perspective on the design space of gradient-based fine-tuning algorithms.

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later resolved using residual connections. Variants of these are now widely used in modern architecture. However, the computational cost of backpropagation remains a major burden, accounting for most of the training time. Taking advantage of residual-like architectural designs, we introduce Highway backpropagation, a parallelizable iterative algorithm that approximates backpropagation, by alternatively i) accumulating the gradient estimates along the residual path, and ii) backpropagating them through every layer in parallel. This algorithm is naturally derived from a decomposition of the gradient as the sum of gradients flowing through all paths and is adaptable to a diverse set of common architectures, ranging from ResNets and Transformers to recurrent neural networks. Through an extensive empirical study on a large selection of tasks and models, we evaluate Highway-BP and show that major speedups can be achieved with minimal performance degradation.

Despite being the workhorse of deep learning, the backpropagation algorithm is no panacea. It enforces sequential layer updates, thus preventing efficient parallelization of the training process. Furthermore, its biological plausibility is being challenged. Alternative schemes have been devised; yet, under the constraint of synaptic asymmetry, none have scaled to modern deep learning tasks and architectures. Here, we challenge this perspective, and study the applicability of Direct Feedback Alignment to neural view synthesis, recommender systems, geometric learning, and natural language processing. In contrast with previous studies limited to computer vision tasks, our findings show that it successfully trains a large range of state-of-the-art deep learning architectures, with performance close to fine-tuned backpropagation. At variance with common beliefs, our work supports that challenging tasks can be tackled in the absence of weight transport.

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed "unilateral concentrability". Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

On-policy distillation (OPD) has emerged as a promising post-training technique for enhancing LLM reasoning. Under the reverse KL objective, the idealized optimum of OPD aligns the student distribution with that of the teacher. When the teacher consistently outperforms the student, this naturally suggests that OPD should yield broad improvements over the pre-OPD student. However, do such improvements extend across the entire range of test-time sampling budgets? In this work, we revisit this expectation through the lens of test-time scaling by varying the sampling budget K and evaluating performance with pass@K. Across multiple settings, we observe two distinct patterns: OPD can improve pass@K at both small and large sampling budgets, but it can also improve small-budget performance while reducing large-budget pass@K. We show one condition that guarantees such a reversal and an idealized reverse KL counterexample where it occurs even when the teacher has higher accuracy on every problem. To choose between two candidate teachers at a target sampling budget, we propose the Teacher Advantage Score at K (TAS@K), which can be computed before OPD training to predict which teacher will lead to a larger improvement in pass@K. Across three domains and thirteen benchmarks, the ordering predicted by TAS@K agrees with the observed pass@K improvements of the resulting OPD models in 83.6\% of experiments, providing a useful signal for teacher selection at the target pass@K.

Traditional weight of evidence assigns a credit characteristic a value based on its association with default across a population. Credit analysis also requires an assessment of that characteristic in the context of an individual applicant's record. We study conditional weight of evidence for this purpose. It measures the change in default log odds from observing a characteristic after the remaining credit information is known. Its sign identifies whether the characteristic adds adverse or favorable information for that applicant, and its magnitude measures the strength of that information. The same characteristic value can therefore receive different assessments for applicants with different payment histories or other credit attributes. We develop estimators using gradient-boosted trees and evaluate their accuracy in a bureau-style simulation. Regressions of the full model's predicted probabilities recover conditional evidence more accurately than separate models fitted to default outcomes, provided the full model is accurate. They also recover a deliberately constructed file-age effect whose direction varies with utilization and is often missed by marginal weight of evidence. Local class-frequency estimates improve on marginal weight of evidence but remain inaccurate for some weak effects. An application to FICO HELOC data illustrates estimation when the population evidence is unknown. Conditional weight of evidence provides an applicant-specific interpretation of the information in a credit characteristic; its population summary, a conditional information value, splits the joint information in the record across blocks when averaged over orderings. Neither is an adverse action reason, which explains the fitted score difference between the applicant and chosen passing records.

Proactive Recommender Systems (PRSs) aim to guide user preference shift toward target items by generating paths of intermediate recommendations. Reinforcement learning (RL) provides a principled framework for optimizing such sequential decision tasks, as path rewards can naturally capture both short-term acceptance and long-term guidance effectiveness. However, naively applying policy gradients to PRS results in deficient gradient estimation. We identify two deficiencies: (1) path-level rewards decompose into step-level rewards with positive mean, creating a length-dependent bias that causes gradients to favor path extension over meaningful exploration; (2) weighting each step by the entire path-level reward ignores the decomposition structure, leading to high gradient variance. To rectify these two deficiencies, we propose an effective RL framework ProRL with two novel mechanisms for proactive recommendation. First, Stepwise Reward Centering subtracts expected rewards to neutralize length-dependent bias, ensuring that path extension yields zero expected gradient signal. Second, Position-Specific Advantage Estimation leverages the reward decomposition structure to compute step-dependent baselines, reducing gradient variance. Together, these mechanisms yield policy gradients that precisely target path quality. Our experiments on three real-world datasets demonstrate that ProRL significantly outperforms state-of-the-art PRSs. Our code is available at https://github.com/hongruhou89/ProRL.

In many real-world deployments of machine learning systems, data arrive piecemeal. These learning scenarios may be passive, where data arrive incrementally due to structural properties of the problem (e.g., daily financial data) or active, where samples are selected according to a measure of their quality (e.g., experimental design). In both of these cases, we are building a sequence of models that incorporate an increasing amount of data. We would like each of these models in the sequence to be performant and take advantage of all the data that are available to that point. Conventional intuition suggests that when solving a sequence of related optimization problems of this form, it should be possible to initialize using the solution of the previous iterate -- to "warm start" the optimization rather than initialize from scratch -- and see reductions in wall-clock time. However, in practice this warm-starting seems to yield poorer generalization performance than models that have fresh random initializations, even though the final training losses are similar. While it appears that some hyperparameter settings allow a practitioner to close this generalization gap, they seem to only do so in regimes that damage the wall-clock gains of the warm start. Nevertheless, it is highly desirable to be able to warm-start neural network training, as it would dramatically reduce the resource usage associated with the construction of performant deep learning systems. In this work, we take a closer look at this empirical phenomenon and try to understand when and how it occurs. We also provide a surprisingly simple trick that overcomes this pathology in several important situations, and present experiments that elucidate some of its properties.

Multi-negative preference optimization under the Plackett--Luce (PL) model extends Direct Preference Optimization (DPO) by leveraging comparative signals across one preferred and multiple rejected responses. However, optimizing over large negative pools is costly, and many candidates contribute redundant gradients due to their similar effects on policy updates. We introduce MASS-DPO, a multi-negative active sample selection method that derives a PL-specific Fisher-information objective for selecting compact, informative negative subsets within each prompt. The resulting log-determinant objective selects negatives that contribute complementary information for policy updates, yielding compact subsets that retain the full pool's information while reducing redundancy. In practice, this favors negatives whose gradients cover different update directions, reducing redundant signal from near-duplicate candidates while preserving the most useful training information. Across four benchmarks spanning recommendation and multiple-choice QA and three model families, MASS-DPO consistently exceeds or matches existing methods in accuracy, improves Recall/NDCG and margin-based optimization dynamics, and delivers stronger alignment with substantially fewer negatives.

Strictly proper scoring rules identify the true conditional class distribution at population level, but their curvature can alter optimization and finite-sample behavior. We study three multiclass objectives: a class-aware quadratic Bregman score (CAPM), a strongly convex generator with constrained log-cosh ridges (HPG), and an HPG objective with an annealed probability-margin penalty (APMS). CAPM is treated as a structured instance of established quadratic scoring-rule theory. We derive conditional-regret, curvature, range, and logit-gradient bounds for CAPM and HPG, and prove exact penalty-range and conditional-target displacement bounds for APMS. Controlled five-seed experiments use Digits, Wisconsin breast cancer, and synthetic confusion and long-tail problems under clean labels, symmetric and pair-flip corruption, class imbalance, calibration evaluation, input corruption, and first-order adversarial perturbations. The candidates are close to cross-entropy on clean data and show descriptive gains in some noisy-label cells, but the five-seed comparisons are interpreted descriptively rather than as significance evidence. The selected noisy-label baselines perform better on Digits with 40% symmetric label noise, and explicit prior-adjustment methods perform better in the 30:1 synthetic long-tail experiment. Ablations do not show a consistent benefit from the candidate-specific graph, ridge, or margin components. The mathematical analysis establishes the stated properties, and the experiments delimit the empirical evidence; together they do not support a claim of general superiority.

We propose a novel algorithm called Backpropagation Neural Tree (BNeuralT), which is a stochastic computational dendritic tree. BNeuralT takes random repeated inputs through its leaves and imposes dendritic nonlinearities through its internal connections like a biological dendritic tree would do. Considering the dendritic-tree like plausible biological properties, BNeuralT is a single neuron neural tree model with its internal sub-trees resembling dendritic nonlinearities. BNeuralT algorithm produces an ad hoc neural tree which is trained using a stochastic gradient descent optimizer like gradient descent (GD), momentum GD, Nesterov accelerated GD, Adagrad, RMSprop, or Adam. BNeuralT training has two phases, each computed in a depth-first search manner: the forward pass computes neural tree's output in a post-order traversal, while the error backpropagation during the backward pass is performed recursively in a pre-order traversal. A BNeuralT model can be considered a minimal subset of a neural network (NN), meaning it is a "thinned" NN whose complexity is lower than an ordinary NN. Our algorithm produces high-performing and parsimonious models balancing the complexity with descriptive ability on a wide variety of machine learning problems: classification, regression, and pattern recognition.

Deep Reinforcement Learning approaches to Online Portfolio Selection have grown in popularity in recent years. The sensitive nature of training Reinforcement Learning agents implies a need for extensive efforts in market representation, behavior objectives, and training processes, which have often been lacking in previous works. We propose a training and evaluation process to assess the performance of classical DRL algorithms for portfolio management. We found that most Deep Reinforcement Learning algorithms were not robust, with strategies generalizing poorly and degrading quickly during backtesting.

Agentic reinforcement learning requires assigning credit to environment-facing actions such as searches, clicks, edits, navigation commands, and object interactions. Standard GRPO uses the final verifier outcome as a uniform advantage over all action tokens. This outcome signal is useful but structurally incomplete: it punishes useful exploration in failed rollouts and reinforces redundant or regressive actions in successful rollouts. We propose TRIAGE, a role-typed credit assignment framework that adds a semantic role axis to outcome credit. A structured judge classifies each segment as decisive progress, useful exploration, no-progress infrastructure, or regression, and a fixed role-conditioned rule maps these labels to bounded segment-level process rewards. This keeps verifier outcomes as the source of optimization direction while correcting the two main blind spots of outcome-only credit. We further show that role-conditioned credit is the optimal segment-level correction expressible from role labels alone -- a projection of the per-segment advantage residual onto the role variable -- so that the fixed role constants reduce advantage estimation error whenever the judge is reliable, and we connect this to lower-variance policy gradients. Across ALFWorld, Search-QA, and WebShop, TRIAGE improves success rates over GRPO for two policy models and outperforms both a scalar judge-derived process reward and an outcome-supervised shared-backbone value baseline. Ablations show that the gain comes from role typing rather than merely adding dense rewards: reliable detection of regression inside successful trajectories is the dominant contributor, while exploration credit provides a consistent secondary gain; on completed ALFWorld and WebShop rollouts, TRIAGE also reduces environment-facing turns by an additional 10.4% and 14.8% relative to GRPO.

Zero-shot reinforcement learning (RL) promises to provide agents that can perform any task in an environment after an offline pre-training phase. Forward-backward (FB) representations represent remarkable progress towards this ideal, achieving 85% of the performance of task-specific agents in this setting. However, such performance is contingent on access to large and diverse datasets for pre-training, which cannot be expected for most real problems. Here, we explore how FB performance degrades when trained on small datasets that lack diversity, and mitigate it with conservatism, a well-established feature of performant offline RL algorithms. We evaluate our family of methods across various datasets, domains and tasks, reaching 150% of vanilla FB performance in aggregate. Somewhat surprisingly, conservative FB algorithms also outperform the task-specific baseline, despite lacking access to reward labels and being required to maintain policies for all tasks. Conservative FB algorithms perform no worse than FB on full datasets, and so present little downside over their predecessor. Our code is available open-source via https://enjeeneer.io/projects/conservative-world-models/.