Daily Papers

Existing reinforcement learning (RL) methods struggle with long-horizon robotic manipulation tasks, particularly those involving sparse rewards. While action chunking is a promising paradigm for robotic manipulation, using RL to directly learn continuous action chunks in a stable and data-efficient manner remains a critical challenge. This paper introduces AC3 (Actor-Critic for Continuous Chunks), a novel RL framework that learns to generate high-dimensional, continuous action sequences. To make this learning process stable and data-efficient, AC3 incorporates targeted stabilization mechanisms for both the actor and the critic. First, to ensure reliable policy improvement, the actor is trained with an asymmetric update rule, learning exclusively from successful trajectories. Second, to enable effective value learning despite sparse rewards, the critic's update is stabilized using intra-chunk n-step returns and further enriched by a self-supervised module providing intrinsic rewards at anchor points aligned with each action chunk. We conducted extensive experiments on 25 tasks from the BiGym and RLBench benchmarks. Results show that by using only a few demonstrations and a simple model architecture, AC3 achieves superior success rates on most tasks, validating its effective design.

In this paper, we propose a learning rule based on a back-propagation (BP) algorithm that can be applied to a hardware-based deep neural network (HW-DNN) using electronic devices that exhibit discrete and limited conductance characteristics. This adaptive learning rule, which enables forward, backward propagation, as well as weight updates in hardware, is helpful during the implementation of power-efficient and high-speed deep neural networks. In simulations using a three-layer perceptron network, we evaluate the learning performance according to various conductance responses of electronic synapse devices and weight-updating methods. It is shown that the learning accuracy is comparable to that obtained when using a software-based BP algorithm when the electronic synapse device has a linear conductance response with a high dynamic range. Furthermore, the proposed unidirectional weight-updating method is suitable for electronic synapse devices which have nonlinear and finite conductance responses. Because this weight-updating method can compensate the demerit of asymmetric weight updates, we can obtain better accuracy compared to other methods. This adaptive learning rule, which can be applied to full hardware implementation, can also compensate the degradation of learning accuracy due to the probable device-to-device variation in an actual electronic synapse device.

Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.

Asynchronous reinforcement learning improves rollout throughput for large language model agents by decoupling sample generation from policy optimization, but it also introduces a critical failure mode for PPO-style off-policy correction. In heterogeneous training systems, the total importance ratio should ideally be decomposed into two semantically distinct factors: a training--inference discrepancy term that aligns inference-side and training-side distributions at the same behavior-policy version, and a policy-staleness term that constrains the update from the historical policy to the current policy. We show that practical asynchronous pipelines with delayed updates and partial rollouts often lose the required historical training-side logits, or old logits. This missing-old-logit problem entangles discrepancy repair with staleness correction, breaks the intended semantics of decoupled correction, and makes clipping and masking thresholds interact undesirably. To address this issue, we study both exact and approximate correction routes. We propose three exact old-logit acquisition strategies: snapshot-based version tracking, a dedicated old-logit model, and synchronization via partial rollout interruption, and compare their system trade-offs. From the perspective of approximate correction, we focus on preserving the benefits of decoupled correction through a more appropriate approximate policy when exact old logits cannot be recovered at low cost, without incurring extra system overhead. Following this analysis, we adopt a revised PPO-EWMA method, which achieves significant gains in both training speed and optimization performance. Code at https://github.com/millioniron/ROLL.

Ensuring the long-term sustainability of recommender systems (RS) emerges as a crucial issue. Traditional offline evaluation methods for RS typically focus on immediate user feedback, such as clicks, but they often neglect the long-term impact of content creators. On real-world content platforms, creators can strategically produce and upload new items based on user feedback and preference trends. While previous studies have attempted to model creator behavior, they often overlook the role of information asymmetry. This asymmetry arises because creators primarily have access to feedback on the items they produce, while platforms possess data on the entire spectrum of user feedback. Current RS simulators, however, fail to account for this asymmetry, leading to inaccurate long-term evaluations. To address this gap, we propose CreAgent, a Large Language Model (LLM)-empowered creator simulation agent. By incorporating game theory's belief mechanism and the fast-and-slow thinking framework, CreAgent effectively simulates creator behavior under conditions of information asymmetry. Additionally, we enhance CreAgent's simulation ability by fine-tuning it using Proximal Policy Optimization (PPO). Our credibility validation experiments show that CreAgent aligns well with the behaviors between real-world platform and creator, thus improving the reliability of long-term RS evaluations. Moreover, through the simulation of RS involving CreAgents, we can explore how fairness- and diversity-aware RS algorithms contribute to better long-term performance for various stakeholders. CreAgent and the simulation platform are publicly available at https://github.com/shawnye2000/CreAgent.

We pursue a vision for self-improving language models in which the model does not merely generate problems or traces to imitate, but constructs the environments that train it. In zero-data reasoning RL, this reframes self-improvement from a data-generation loop into an environment-construction loop, where each artifact is a reusable executable object that samples instances, computes references, and scores responses. Whether this vision sustains improvement hinges on a single property: the environments must exhibit stable solve--verify asymmetry, the model must be able to write an oracle once that it cannot reliably execute in natural language on fresh instances. This asymmetry takes two complementary forms. Some tasks are algorithmically hard to reason through but trivial as code: a dynamic program or graph traversal, compiled once, yields unboundedly many calibrated instances. Others are intrinsically hard to solve but easy to verify, like planted subset-sum or constraint satisfaction. Both create a durable gap between proposing and solving that the policy cannot close by gaming the verifier, and it is this gap that keeps reward informative as the learner improves. We instantiate this view in EvoEnv, a single-policy generator, solver method that synthesizes Python environments from ten seeds and admits them only after staged validation, semantic self-review, solver-relative difficulty calibration, and novelty checks. The strongest evidence comes from the already-strong regime: on Qwen3-4B-Thinking, fixed public-data RLVR and fixed hand-crafted environment RLVR reduce the average, while EvoEnv improves it from 72.4 to 74.8, a relative gain of 3.3%. Stable self-improvement, we suggest, depends not on producing more synthetic data, but on models learning to construct worlds whose difficulty stays structurally beyond their own reach.

Equilibrium propagation (EP) is a compelling alternative to the backpropagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to estimate unbiased gradients efficiently. Both requirements are challenging to implement in physical systems. Yet, whether and how weight asymmetry affects its applicability is unknown because, in practice, it may be masked by biases introduced through the finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias. For complex-differentiable non-symmetric networks, we show that the finite nudge does not pose a problem, as exact derivatives can still be estimated via a Cauchy integral. In contrast, weight asymmetry introduces bias resulting in low task performance due to poor alignment of EP's neuronal error vectors compared to BP. To mitigate this issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32x32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

We consider a binary classification problem under group fairness constraints, which can be one of Demographic Parity (DP), Equalized Opportunity (EOp), or Equalized Odds (EO). We propose an explicit characterization of Bayes optimal classifier under the fairness constraints, which turns out to be a simple modification rule of the unconstrained classifier. Namely, we introduce a novel instance-level measure of bias, which we call bias score, and the modification rule is a simple linear rule on top of the finite amount of bias scores.Based on this characterization, we develop a post-hoc approach that allows us to adapt to fairness constraints while maintaining high accuracy. In the case of DP and EOp constraints, the modification rule is thresholding a single bias score, while in the case of EO constraints we are required to fit a linear modification rule with 2 parameters. The method can also be applied for composite group-fairness criteria, such as ones involving several sensitive attributes.

We introduce a modern Hopfield network with continuous states and a corresponding update rule. The new Hopfield network can store exponentially (with the dimension of the associative space) many patterns, retrieves the pattern with one update, and has exponentially small retrieval errors. It has three types of energy minima (fixed points of the update): (1) global fixed point averaging over all patterns, (2) metastable states averaging over a subset of patterns, and (3) fixed points which store a single pattern. The new update rule is equivalent to the attention mechanism used in transformers. This equivalence enables a characterization of the heads of transformer models. These heads perform in the first layers preferably global averaging and in higher layers partial averaging via metastable states. The new modern Hopfield network can be integrated into deep learning architectures as layers to allow the storage of and access to raw input data, intermediate results, or learned prototypes. These Hopfield layers enable new ways of deep learning, beyond fully-connected, convolutional, or recurrent networks, and provide pooling, memory, association, and attention mechanisms. We demonstrate the broad applicability of the Hopfield layers across various domains. Hopfield layers improved state-of-the-art on three out of four considered multiple instance learning problems as well as on immune repertoire classification with several hundreds of thousands of instances. On the UCI benchmark collections of small classification tasks, where deep learning methods typically struggle, Hopfield layers yielded a new state-of-the-art when compared to different machine learning methods. Finally, Hopfield layers achieved state-of-the-art on two drug design datasets. The implementation is available at: https://github.com/ml-jku/hopfield-layers

Reinforcement Learning with Verifiable Rewards (RLVR) is commonly based on group sampling to estimate advantages and stabilize policy updates. In practice, large group sizes are not feasible due to computational limits, which biases learning toward trajectories that are already likely. Smaller groups often miss rare-correct trajectories while still containing mixed rewards, concentrating probability on common solutions. We derive the probability that updates miss rare-correct modes as a function of group size, showing non-monotonic behavior, and characterize how updates redistribute mass within the correct set, revealing that unsampled-correct mass can shrink even as total correct mass grows. Motivated by this analysis, we propose a difficulty-aware advantage scaling coefficient, inspired by Focal loss, that down-weights updates on high-success prompts. The lightweight modification can be directly integrated into any group-relative RLVR algorithm such as GRPO, DAPO, and CISPO. On Qwen2.5-7B across in-domain and out-of-domain benchmarks, our method improves pass@256 from 64.1 rightarrow 70.3 (GRPO), 69.3 rightarrow 72.5 (DAPO), and 73.2 rightarrow 76.8 (CISPO), while preserving or improving pass@1, without increasing group size or computational cost.

Backward compatibility of model predictions is a desired property when updating a machine learning driven application. It allows to seamlessly improve the underlying model without introducing regression bugs. In classification tasks these bugs occur in the form of negative flips. This means an instance that was correctly classified by the old model is now classified incorrectly by the updated model. This has direct negative impact on the user experience of such systems e.g. a frequently used voice assistant query is suddenly misclassified. A common reason to update the model is when new training data becomes available and needs to be incorporated. Simply retraining the model with the updated data introduces the unwanted negative flips. We study the problem of regression during data updates and propose Backward Compatible Weight Interpolation (BCWI). This method interpolates between the weights of the old and new model and we show in extensive experiments that it reduces negative flips without sacrificing the improved accuracy of the new model. BCWI is straight forward to implement and does not increase inference cost. We also explore the use of importance weighting during interpolation and averaging the weights of multiple new models in order to further reduce negative flips.

Federated learning algorithms, such as FedAvg, are negatively affected by data heterogeneity and partial client participation. To mitigate the latter problem, global variance reduction methods, like FedVARP, leverage stale model updates for non-participating clients. These methods are effective under homogeneous client participation. Yet, this paper shows that, when some clients participate much less than others, aggregating updates with different levels of staleness can detrimentally affect the training process. Motivated by this observation, we introduce FedStale, a novel algorithm that updates the global model in each round through a convex combination of "fresh" updates from participating clients and "stale" updates from non-participating ones. By adjusting the weight in the convex combination, FedStale interpolates between FedAvg, which only uses fresh updates, and FedVARP, which treats fresh and stale updates equally. Our analysis of FedStale convergence yields the following novel findings: i) it integrates and extends previous FedAvg and FedVARP analyses to heterogeneous client participation; ii) it underscores how the least participating client influences convergence error; iii) it provides practical guidelines to best exploit stale updates, showing that their usefulness diminishes as data heterogeneity decreases and participation heterogeneity increases. Extensive experiments featuring diverse levels of client data and participation heterogeneity not only confirm these findings but also show that FedStale outperforms both FedAvg and FedVARP in many settings.

Recent Large Language Model (LLM) post-training methods rely on token-level clipping mechanisms during Reinforcement Learning (RL). However, we identify a fundamental flaw in this Outcome-Supervised RL (OSRL) paradigm: the Importance Sampling (IS) ratios of positive-advantage tokens are mismatched, leading to unbalanced token weighting for positive and negative tokens. This mismatch suppresses the update of low-probability tokens while over-amplifying already high-probability ones. To address this, we propose Asymmetric Importance Sampling Policy Optimization (ASPO), which uses a simple yet effective strategy that flips the IS ratios of positive-advantage tokens, aligning their update direction with the learning dynamics of negative ones. AIS further incorporates a soft dual-clipping mechanism to stabilize extreme updates while maintaining gradient flow. Comprehensive experiments on coding and mathematical reasoning benchmarks demonstrate that ASPO significantly mitigates premature convergence, improves training stability, and enhances final performance over strong GRPO-based baselines. Our analysis provides new insights into the role of token-level weighting in OSRL and highlights the critical importance of correcting IS in LLM RL. The code and models of ASPO are available at https://github.com/wizard-III/Archer2.0.

A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this involves minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations useful for subsequent tasks will arise as a side effect. In this work, we propose instead to directly target later desired tasks by meta-learning an unsupervised learning rule which leads to representations useful for those tasks. Specifically, we target semi-supervised classification performance, and we meta-learn an algorithm -- an unsupervised weight update rule -- that produces representations useful for this task. Additionally, we constrain our unsupervised update rule to a be a biologically-motivated, neuron-local function, which enables it to generalize to different neural network architectures, datasets, and data modalities. We show that the meta-learned update rule produces useful features and sometimes outperforms existing unsupervised learning techniques. We further show that the meta-learned unsupervised update rule generalizes to train networks with different widths, depths, and nonlinearities. It also generalizes to train on data with randomly permuted input dimensions and even generalizes from image datasets to a text task.

Progressive Learning (PL) reduces pre-training computational overhead by gradually increasing model scale. While prior work has extensively explored depth expansion, width expansion remains significantly understudied, with the few existing methods limited to the early stages of training. However, expanding width during the mid-stage is essential for maximizing computational savings, yet it remains a formidable challenge due to severe training instabilities. Empirically, we show that naive initialization at this stage disrupts activation statistics, triggering loss spikes, while copy-based initialization introduces gradient symmetry that hinders feature diversity. To address these issues, we propose SPARKLING (balancing {S}ignal {P}reservation {A}nd symmet{R}y brea{K}ing for width-progressive {L}earn{ING}), a novel framework for mid-stage width expansion. Our method achieves signal preservation via RMS-scale consistency, stabilizing activation statistics during expansion. Symmetry breaking is ensured through asymmetric optimizer state resetting and learning rate re-warmup. Extensive experiments on Mixture-of-Experts (MoE) models demonstrate that, across multiple width axes and optimizer families, SPARKLING consistently outperforms training from scratch and reduces training cost by up to 35% under 2times width expansion.

Scalable oversight protocols aim to enable humans to accurately supervise superhuman AI. In this paper we study debate, where two AI's compete to convince a judge; consultancy, where a single AI tries to convince a judge that asks questions; and compare to a baseline of direct question-answering, where the judge just answers outright without the AI. We use large language models (LLMs) as both AI agents and as stand-ins for human judges, taking the judge models to be weaker than agent models. We benchmark on a diverse range of asymmetries between judges and agents, extending previous work on a single extractive QA task with information asymmetry, to also include mathematics, coding, logic and multimodal reasoning asymmetries. We find that debate outperforms consultancy across all tasks when the consultant is randomly assigned to argue for the correct/incorrect answer. Comparing debate to direct question answering, the results depend on the type of task: in extractive QA tasks with information asymmetry debate outperforms direct question answering, but in other tasks without information asymmetry the results are mixed. Previous work assigned debaters/consultants an answer to argue for. When we allow them to instead choose which answer to argue for, we find judges are less frequently convinced by the wrong answer in debate than in consultancy. Further, we find that stronger debater models increase judge accuracy, though more modestly than in previous studies.

Why do language models sometimes prefer correct statements even when trained on mixed-quality data? We introduce the Compression--Consistency Principle: next-token prediction favors hypotheses that allow shorter and more internally consistent descriptions of the training data. Truth bias emerges only when false alternatives are structurally harder to compress. We test this using small GPT-2-style character-level transformers (3.5M--86M parameters) on synthetic math corpora with controlled mixtures of correct and incorrect rules. In the random-error setting, models strongly prefer correct completions in paired evaluation: 83.1% accuracy at balanced data and 67.0% even when correct rules appear in only 10% of the corpus. Replacing random errors with a coherent but mathematically incorrect rule system largely eliminates the preference (near-chance accuracy). In a more natural-language-like synthetic world, the effect is weaker but still present (57.7%). Additional experiments show that embedding verification steps can restore preference for correctness even at small scale, while increasing the number of consistent rules produces a graded improvement in accuracy. Our results suggest that what appears as a "truth bias" is largely a side effect of compression pressure and preference for internal consistency, rather than an intrinsic drive toward truth. Full code and data are available at https://github.com/Rai220/compression-drives-truth.

Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO and DAPO), which improperly penalizes negative-advantage samples under reward outliers. We propose {Quantile Advantage Estimation} (QAE), replacing the mean with a group-wise K-quantile baseline. QAE induces a response-level, two-regime gate: on hard queries (p <= 1 - K) it reinforces rare successes, while on easy queries (p > 1 - K) it targets remaining failures. Under first-order softmax updates, we prove {two-sided entropy safety}, giving lower and upper bounds on one-step entropy change that curb explosion and prevent collapse. Empirically, this minimal modification stabilizes entropy, sparsifies credit assignment (with tuned K, roughly 80% of responses receive zero advantage), and yields sustained pass@1 gains on Qwen3-8B/14B-Base across AIME 2024/2025 and AMC 2023. These results identify {baseline design} -- rather than token-level heuristics -- as the primary mechanism for scaling RLVR.

AI systems are increasingly governed by natural language principles, yet a key challenge arising from reliance on language remains underexplored: interpretive ambiguity. As in legal systems, ambiguity arises both from how these principles are written and how they are applied. But while legal systems use institutional safeguards to manage such ambiguity, such as transparent appellate review policing interpretive constraints, AI alignment pipelines offer no comparable protections. Different interpretations of the same rule can lead to inconsistent or unstable model behavior. Drawing on legal theory, we identify key gaps in current alignment pipelines by examining how legal systems constrain ambiguity at both the rule creation and rule application steps. We then propose a computational framework that mirrors two legal mechanisms: (1) a rule refinement pipeline that minimizes interpretive disagreement by revising ambiguous rules (analogous to agency rulemaking or iterative legislative action), and (2) prompt-based interpretive constraints that reduce inconsistency in rule application (analogous to legal canons that guide judicial discretion). We evaluate our framework on a 5,000-scenario subset of the WildChat dataset and show that both interventions significantly improve judgment consistency across a panel of reasonable interpreters. Our approach offers a first step toward systematically managing interpretive ambiguity, an essential step for building more robust, law-following AI systems.

Image copy detection (ICD) aims to determine whether a query image is an edited copy of any image from a reference set. Currently, there are very limited public benchmarks for ICD, while all overlook a critical challenge in real-world applications, i.e., the distraction from hard negative queries. Specifically, some queries are not edited copies but are inherently similar to some reference images. These hard negative queries are easily false recognized as edited copies, significantly compromising the ICD accuracy. This observation motivates us to build the first ICD benchmark featuring this characteristic. Based on existing ICD datasets, this paper constructs a new dataset by additionally adding 100, 000 and 24, 252 hard negative pairs into the training and test set, respectively. Moreover, this paper further reveals a unique difficulty for solving the hard negative problem in ICD, i.e., there is a fundamental conflict between current metric learning and ICD. This conflict is: the metric learning adopts symmetric distance while the edited copy is an asymmetric (unidirectional) process, e.g., a partial crop is close to its holistic reference image and is an edited copy, while the latter cannot be the edited copy of the former (in spite the distance is equally small). This insight results in an Asymmetrical-Similarity Learning (ASL) method, which allows the similarity in two directions (the query <-> the reference image) to be different from each other. Experimental results show that ASL outperforms state-of-the-art methods by a clear margin, confirming that solving the symmetric-asymmetric conflict is critical for ICD. The NDEC dataset and code are available at https://github.com/WangWenhao0716/ASL.

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

We resolve an open problem of Hanneke on the subject of universally consistent online learning with non-i.i.d. processes and unbounded losses. The notion of an optimistically universal learning rule was defined by Hanneke in an effort to study learning theory under minimal assumptions. A given learning rule is said to be optimistically universal if it achieves a low long-run average loss whenever the data generating process makes this goal achievable by some learning rule. Hanneke posed as an open problem whether, for every unbounded loss, the family of processes admitting universal learning are precisely those having a finite number of distinct values almost surely. In this paper, we completely resolve this problem, showing that this is indeed the case. As a consequence, this also offers a dramatically simpler formulation of an optimistically universal learning rule for any unbounded loss: namely, the simple memorization rule already suffices. Our proof relies on constructing random measurable partitions of the instance space and could be of independent interest for solving other open questions. We extend the results to the non-realizable setting thereby providing an optimistically universal Bayes consistent learning rule.

Byzantine robustness has received significant attention recently given its importance for distributed and federated learning. In spite of this, we identify severe flaws in existing algorithms even when the data across the participants is identically distributed. First, we show realistic examples where current state of the art robust aggregation rules fail to converge even in the absence of any Byzantine attackers. Secondly, we prove that even if the aggregation rules may succeed in limiting the influence of the attackers in a single round, the attackers can couple their attacks across time eventually leading to divergence. To address these issues, we present two surprisingly simple strategies: a new robust iterative clipping procedure, and incorporating worker momentum to overcome time-coupled attacks. This is the first provably robust method for the standard stochastic optimization setting. Our code is open sourced at https://github.com/epfml/byzantine-robust-optimizer.

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is the compute-optimal scaling law, which reports the performance as a function of units of compute when choosing model sizes optimally. We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. This reproduces many observations about neural scaling laws. First, our model makes a prediction about why the scaling of performance with training time and with model size have different power law exponents. Consequently, the theory predicts an asymmetric compute-optimal scaling rule where the number of training steps are increased faster than model parameters, consistent with recent empirical observations. Second, it has been observed that early in training, networks converge to their infinite-width dynamics at a rate 1/width but at late time exhibit a rate width^{-c}, where c depends on the structure of the architecture and task. We show that our model exhibits this behavior. Lastly, our theory shows how the gap between training and test loss can gradually build up over time due to repeated reuse of data.

On-policy distillation (OPD) trains a student on its own trajectories with token-level teacher feedback and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its standard advantage weighted policy gradient suffers from three structural weaknesses, including high variance updates, vanishing gradients in zero-advantage regions, and exploration bottlenecks when corrective signals are insufficient. We therefore propose Asymmetric On-Policy Distillation (AOPD), which replaces ineffective negative reinforcement with localized divergence minimization in non-positive advantage regions while preserving positive reinforcement learning. Experiments on mathematical reasoning benchmarks show that AOPD consistently outperforms standard OPD, with average gains of 4.09 / 8.34 under strong / weak initialization, respectively. AOPD also maintains higher policy entropy during training and better capability retention during sequential tool-use adaptation.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly GRPO, has become the standard for eliciting LLM reasoning. However, its efficiency in exploration and difficulty adaptation remains an open challenge. In this work, we argue that these bottlenecks stem from an implicit advantage symmetry inherent in Group Relative Advantage Estimation (GRAE). This symmetry induces two critical limitations: (i) at the group level, strict symmetry in weights between correct and incorrect trajectories leaves unsampled action logits unchanged, thereby hindering exploration of novel correct solution. (ii) at the sample level, the algorithm implicitly prioritizes medium-difficulty samples, remaining agnostic to the non-stationary demands of difficulty focus. Through controlled experiments, we reveal that this symmetric property is sub-optimal, yielding two pivotal insights: (i) asymmetrically suppressing the advantages of correct trajectories encourages essential exploration. (ii) learning efficiency is maximized by a curriculum-like transition-prioritizing simpler samples initially before gradually shifting to complex ones. Motivated by these findings, we propose Asymmetric GRAE (A-GRAE), which dynamically modulates exploration incentives and sample-difficulty focus. Experiments across seven benchmarks demonstrate that A-GRAE consistently improves GRPO and its variants across both LLMs and MLLMs.

Machine learning models in modern mass-market applications are often updated over time. One of the foremost challenges faced is that, despite increasing overall performance, these updates may flip specific model predictions in unpredictable ways. In practice, researchers quantify the number of unstable predictions between models pre and post update -- i.e., predictive churn. In this paper, we study this effect through the lens of predictive multiplicity -- i.e., the prevalence of conflicting predictions over the set of near-optimal models (the Rashomon set). We show how traditional measures of predictive multiplicity can be used to examine expected churn over this set of prospective models -- i.e., the set of models that may be used to replace a baseline model in deployment. We present theoretical results on the expected churn between models within the Rashomon set from different perspectives. And we characterize expected churn over model updates via the Rashomon set, pairing our analysis with empirical results on real-world datasets -- showing how our approach can be used to better anticipate, reduce, and avoid churn in consumer-facing applications. Further, we show that our approach is useful even for models enhanced with uncertainty awareness.