Papers

Matrix-structured parameters frequently appear in many artificial intelligence models such as large language models. More recently, an efficient Muon optimizer is designed for matrix parameters of large-scale models, and shows markedly faster convergence than the vector-wise algorithms. Although some works have begun to study convergence properties (i.e., optimization error) of the Muon optimizer, its generalization properties (i.e., generalization error) is still not established. Thus, in this paper, we study generalization error of the Muon optimizer based on algorithmic stability and mathematical induction, and prove that the Muon has a generalization error of $O\big(\frac{1}{N\kappa^{T}}\big)$, where $N$ is training sample size, and $T$ denotes iteration number, and $\kappa>0$ denotes minimum difference between singular values of gradient estimate. To enhance generalization of the Muon, we propose an effective mixed Muon (MiMuon) optimizer by cautiously using orthogonalization of gradient, which is a hybrid of Muon and momentum-based SGD optimizers. Then we prove that our MiMuon optimizer has a lower generalization error of $O\big(\frac{1}{N}\big)$ than $O\big(\frac{1}{N\kappa^{T}}\big)$ of Muon optimizer, since $\kappa$ generally is very small. Meanwhile, we also studied the convergence properties of our MiMuon algorithm, and prove that our MiMuon algorithm has the same convergence rate of $O(\frac{1}{T^{1/4}})$ as the Muon algorithm. Some numerical experimental results on training large models including Qwen3-0.6B and YOLO26m demonstrate efficiency of the MiMuon optimizer.

Validating interpretable surrogate models for ensemble learners requires measuring agreement between the ensemble's internal representation and its surrogate approximation, rather than mere association. Correlation-based approaches are scale-invariant and fail to detect systematic discrepancies in co-occurrence structure. We propose a statistical framework grounded in the agreement-association distinction, centered on the normalized Loss of Interpretability (nLoI). Rooted in the Cressie-Read power divergence family with lambda equal to 2, the nLoI admits a closed-form decomposition into within-node and between-node components, providing a unique diagnostic capability to identify precisely where and why reconstruction fails. The framework incorporates four complementary measures capturing distinct structural facets of approximation quality. A unified permutation testing procedure delivers valid inference for all measures within a single resampling pass. Theoretical properties, including boundedness and symmetry, are established for each metric. Monte Carlo simulations and empirical evaluations confirm exact Type I error control and demonstrate that these measures detect reconstruction fidelity gradients invisible to correlation-based alternatives. The framework is developed and illustrated in the context of Explainable Ensemble Trees (E2Tree), and empirical evaluation on three benchmark datasets illustrates the practical utility of the framework.

We investigate the asymptotic properties of the Lévy Adaptive B-spline (LABS) regression model, a Bayesian nonparametric method that incorporates B-spline kernels into the Lévy Adaptive Regression Kernel (LARK) model. LABS applies splines of varying degrees with independently defined knots, yielding a flexible model class capable of adapting to irregular and locally structured features of the true function. Within the nonparametric regression framework with univariate random design and Gaussian errors, we establish that the LABS posterior contracts around the true function in Besov classes at nearly minimax-optimal rates, up to a logarithmic factor, while adapting automatically to unknown smoothness. This study contributes to filling a gap in the literature, where theoretical results on posterior contraction of the LARK model in Besov spaces remain scarce. Simulation experiments on standard test functions in Besov spaces, including Blocks, Bumps, HeaviSine, and Doppler, complement the theoretical results and demonstrate the practical utility of LABS.

Integrated Gradients (IG) is a widely adopted feature attribution method that satisfies desirable axiomatic properties. However, the choice of integration path significantly affects the quality of attributions, and the standard straight-line path introduces all input features simultaneously, often accumulating noisy gradients along the way. To address this limitation, we propose Spectral Integrated Gradients, which constructs integration paths based on singular value decomposition (SVD) of the baseline-to-input difference. By progressively activating singular components from largest to smallest, SIG introduces global structure before fine-grained details, naturally following a coarse-to-fine progression. Through extensive evaluation across diverse image classification datasets, we demonstrate that SIG produces cleaner attribution maps with reduced noise and achieves improved quantitative performance compared to existing path-based attribution methods. Our code is available at https://github.com/leekwoon/sig/.

Dental aerosol procedures produce sub-50 micrometre nuclei that can remain airborne for long periods in enclosed clinics, creating pathways for airborne pathogen transmission. Reynolds-Averaged Navier-Stokes (RANS) simulations with Euler-Lagrange particle tracking capture this transport accurately but require very long run times per scenario, which precludes real-time clinical decision support in 3D. We present the Eulerian-Lagrangian Graph Interaction Network (ELGIN), a physics-informed graph surrogate that jointly predicts carrier-flow dynamics on the OpenFOAM polyhedral mesh and the per-parcel motion of the polydisperse spray cloud. ELGIN couples a multi-head Graph Transformer with Jacobi-preconditioned learnable pressure projection and a turbulence-closure head to a sigmoid-gated Lagrangian Interaction Network through differentiable inverse-distance mesh-parcel coupling, and advances parcels with a symplectic Stormer-Verlet integrator. A four-stage physics-informed curriculum stabilises 260-step autoregressive rollouts without gradient explosion. A parameter sweep with foam-extend 4.1 OpenFOAM reactingParcelFoam across clinically relevant ventilation rates and handpiece spray speeds provides CFD ground truth. This article reports a single-case demonstration in which both ELGIN and a Lagrangian-only baseline (M0) are trained and evaluated on Sweep_Case_03 of a twenty-case sweep; full 16/2/2 retraining is in progress and will replace all reported metrics. On this case, ELGIN tracks the foam-extend particle cloud much more closely than M0: mean parcel displacement error falls from 19.56% to 16.20% of room width and cloud radius-of-gyration error from 9.85% to 6.58%. A 26-second rollout completes in ~64 s on a 4 GB GPU, approximately 37x faster than the foam-extend reference pipeline, toward per-appointment infection-risk screening once the multi-case checkpoint is in place.

We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully censored feedback, we introduce an action-dependent feedback model inspired by real limit order books: when a trade occurs, the trader's valuation remains hidden, whereas when no trade occurs, informative feedback about supply and demand is revealed. We show that this additional information fundamentally changes the learnability of the problem. In the stochastic setting with i.i.d. market prices, we propose an elimination-based algorithm that achieves $O(\sqrt T)$ regret with high probability, without requiring any smoothness assumptions on the distribution of trader valuations. We then extend this result to a broad class of mean-reverting price processes by considering both local, autoregressive dynamics and a weaker global drift condition based on cumulative deviations from the mean. Under either assumption, we establish high-probability $O(\sqrt T)$ regret bounds, relying on a new concentration inequality of independent interest. Finally, in the adversarial setting with oblivious prices, we design an explore-then-perturb algorithm that guarantees $O(T^{2/3})$ regret in expectation. Our results quantify the value of observing the order book in online market making and demonstrate that even limited, action-dependent feedback can substantially improve regret guarantees compared to standard bandit feedback models.

HiLiftAeroML is, to our knowledge, the first open high-fidelity computational fluid dynamics dataset dedicated to high-lift aircraft aerodynamics. It contains 1,800 simulations spanning 180 variants of the NASA Common Research Model high-lift configuration and ten angles of attack from $4^\circ$ to $22^\circ$. Each case was generated with a GPU-accelerated explicit wall-modeled large-eddy simulation approach on solution-adapted grids of 300–500 million cells, covering attached, separated, and post-stall flow conditions. Comparisons with wind-tunnel measurements for reference landing configurations show good agreement in integrated loads and sectional pressures, with grid adaptation substantially improving drag and pitching-moment predictions. The CC-BY-4.0 release includes geometries, time-averaged surface and volume fields, integrated loads, validation material, and deterministic benchmark splits. Initial GeoTransolver and Transolver baselines, evaluated on the complete native surface and volume support of every held-out case rather than on a sampled subset, reconstruct the fields well for several interpolation and held-out-geometry tests, while high-angle separated flow, limited-data training, and out-of-distribution flow-regime shifts remain substantially harder. The dataset and baselines provide a common resource for developing and assessing data-driven models for realistic high-lift aerodynamics.

This paper presents a learning-augmented trajectory planning framework for cooperative unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) handover missions. While centralized trajectory optimization ensures dynamic feasibility and task optimality, its high computational cost limits real-time applicability. We propose a neural surrogate planner utilizing decoupled encoder-decoder long short-term memory (LSTM) networks to generate coordinated handover trajectory predictions from the task specifications. These predictions serve as informed warm starts for the downstream centralized optimizer, thereby accelerating convergence to dynamically feasible solutions. Benchmark evaluations demonstrate that the learning-augmented planning framework achieves more than a threefold speedup and 100% optimization success rate compared to cold start optimization. The results indicate that combining data-driven inference with model-based refinement enables fast and reliable trajectory generation for heterogeneous multi-robot systems.

As Large Language Models (LLMs) advance toward practical deployment, the Microscaling FP4 (MXFP4) format has emerged as a cornerstone for next-generation low-bit inference, owing to its ability to balance high dynamic range with hardware efficiency. However, directly applying MXFP4 to LLM activation quantization inevitably leads to significant accuracy degradation. In this paper, we theoretically analyze the error structure of MXFP4 activation quantization, revealing that the root cause of this performance drop lies in two structural imbalances between activation distributions and the MXFP4 block floating-point format: (1) extreme inter-block variance imbalance and (2) intra-block codebook utilization imbalance. To address these challenges, we propose TORQ (Two-level Orthogonal Rotation for MXFP4 Quantization), a training-free Post-Training Quantization (PTQ) framework designed to reshape the geometric properties of the activation space through optimal coordinate transformations. At the macroscopic level, TORQ leverages the Schur-Horn theorem to redistribute activation energy via inter-block orthogonal rotation, preventing high-variance blocks from driving up shared scaling factors and thereby preserving the precision of small-magnitude elements. At the microscopic level, TORQ employs maximum-entropy-guided intra-block rotation to alleviate codebook collapse and maximize the MXFP4 codebook's information capacity. Experiments on mainstream LLMs such as LLaMA3 and Qwen3 show that TORQ significantly improves the accuracy of MXFP4 activation quantization compared to existing methods: on Qwen3-32B, the perplexity on WikiText is reduced to 8.43 (vs. 7.61 for BF16), and the average accuracy increases from 38.40% with direct RTN to 73.63% (vs. 74.82% for BF16), substantially narrowing the gap between 4-bit floating-point quantization and full-precision inference.

We study post-hoc Learning to Defer (L2D) through the lens of ideal distributions: divergence-regularized reweightings of the data distribution under which a model attains low loss. We define deferral via the density-ratio between a model's and an expert's ideals. Using the reduction from density-ratio estimation to class-probability estimation, we derive the DR CPE losses for post-hoc L2D scorers. Deferral decisions are then made by thresholding the scorer, allowing deferral rates to be adjusted without retraining. For KL-based ideal distributions, our deferral rules recovers Chow's rule under the original distribution and a connection to an expert-tilted Bayes posterior – which incorporates the expert's performance – depending on if the ideal distributions are joint or marginal distributions. Experimentally, our approach is competitive compared to common baselines and more robust across dataset settings. More broadly, our results cast post-hoc L2D as density-ratio learning between ideal distributions, bridging Chow-style rules, expert comparison, and elucidating connections to related learning settings including anomaly detection.

Deep neural networks (DNNs) are suffering from ethical issues such as individual discrimination. In response, extensive NN repair techniques have been developed to adjust models and mitigate such undesired behaviors. However, existing fairness repair methods are typically data-centric, which often lack provable guarantees and generalization to unseen samples. To overcome these limitations, we propose ProF, a novel fairness repair framework with provable guarantees. The key intuition of ProF is to leverage interval bound propagation (a widely used NN verification technique) to soundly capture model outputs over the whole set $S(\mathbf{x})$ around a biased sample $\mathbf{x}$. The derived bounds are utilized to guide fairness repair which encourages the model to produce consistent outputs on $S(\mathbf{x})$. Specifically, we integrate fairness constraints and model modifications into a unified constraint-solving formulation, which can be transformed to a Mixed-Integer Linear Programming (MILP) problem solvable by off-the-shelf solvers. The solution to the MILP problem effectively induces a repaired model with guaranteed fairness over the whole set $S(\mathbf{x})$. We evaluate ProF on four widely used benchmark datasets and demonstrate that it achieves provable fairness repair, with generalization of up to 95.93% on full datasets and 93.16% on the entire input space. Notably, ProF can be easily configured to support multiple sensitive attributes and more practical fairness definitions, while providing provable repair guarantees and delivering around 90% fairness improvement. Our code is available at https://github.com/nninjn/ProF.

Progress in LLMs is increasingly measured through standardized benchmarks, where state-of-the-art improvements are often separated by fractions of a percentage point. At the same time, the computational cost of evaluating modern LLMs has driven widespread adoption of specialized inference backends, software systems that execute trained models efficiently at inference time. While critical for scalability, system-level optimizations, such as custom CUDA kernels and reduced-precision arithmetic, can alter token probabilities and introduce non-determinism, possibly cascading into divergent generation. In this work, we first survey the inference landscape, identifying 200 distinct engines, and analyze 35,000 ML publications, finding that the specific inference stack is rarely reported despite this widespread diversity. We then present a systematic empirical study of how inference backends affect LLM benchmark results. Holding model weights, decoding parameters, and hardware constant, we evaluate five widely used inference engines, including vLLM, SGLang, and llama$.$cpp, across multiple open-weight models and established benchmarks. We show that the choice of backend alone can shift benchmark scores by up to 16.6 percentage points and induce high rates of output disagreement. By isolating backend optimizations and tracing the execution pipeline, we find this divergence is driven by system-level optimizations like prefix caching and CUDA graphs, custom kernels, and engine-specific defaults in logit processing. Our findings identify the inference backend as a previously unreported but consequential hyperparameter in the evaluation of LLM and advocate standardized reporting of inference stacks to improve the reproducibility and interpretability of benchmark comparisons.

Text-to-image diffusion models can synthesize high-quality images, yet the outcome is notoriously sensitive to the random seed: different initial seeds often yield large variations in image quality and prompt-image alignment. We revisit this "seed effect" and show that attention dynamics over prompt core tokens, the content-bearing words, measured during the first few denoising steps, strongly predict final generation quality. Building on this observation, we introduce Attention-Based Seed Selection (ABSS), a training-free, plug-and-play method that ranks seeds for a given prompt by leveraging cross-attention to core tokens during the denoising process. ABSS requires no finetuning and does not alter the initial noise; it scores and ranks all candidate seeds, keeps only the top-k for full generation, and discards the rest, without relying on a fixed accept/reject threshold. Operating purely at inference time, ABSS can serve as a lightweight pre-selection add-on for existing seed-optimization pipelines, enabling additional gains. Across three benchmarks, extensive experiments show that ABSS enables consistent improvements in text-image alignment and visual quality for Stable Diffusion variants, as corroborated by human preference and alignment metrics.

As AI-generated text enters the real-world at scale, institutions increasingly use commercial AI-text detectors, especially in education and academic-integrity workflows. We report a surprising empirical finding about such systems: when evaluated by GPTZero and Pangram, generated text from base models is often judged overwhelmingly human, whereas text generated by their instruction-tuned counterparts is not. Building on this observation, we propose Humanization by Iterative Paraphrasing (HIP), a detector-agnostic pipeline that minimally fine-tunes a base model into a paraphraser and applies it iteratively. Compared with the baselines we test, HIP yields a stronger trade-off between semantic preservation and detector evasion on commercial detectors. Across Llama-3 and Qwen-3 families, spanning model sizes from 0.6B to 70B, HIP consistently improves detector human-likeness. Our findings suggest that current detectors are tracking artifacts of instruction tuning and local context more than any invariant notion of machine-generated text. This, in turn, calls for detector designs that model these factors more explicitly.

Many works make the eye-catching claim that Transformers are Turing-complete. However, the literature often conflates two distinct settings: (i) a fixed Transformer system setting, in which a fixed autoregressive Transformer is coupled with a fixed context-management method to process inputs of different lengths step by step, and (ii) a scaling-family setting, in which a family of different models (with increasing context-window length or numerical precision) is used to handle different input lengths. Existing proofs of Transformer Turing-completeness are frequently established in setting (ii), whereas real-world LLM deployment and the standard notion of Turing-completeness correspond more naturally to setting (i). In this paper, we first formalize the fixed-system setting, thereby providing a concrete characterization of how real-world LLMs operate. We then argue that results proved in the scaling-family setting provide theoretically meaningful resource bounds but do not establish Turing-completeness, thereby clarifying a common misinterpretation of existing results. Finally, we show that different context-management methods can yield sharply different computational power, and we advocate the position that context management is a central component that critically determines the computational power of real-world autoregressive Transformers.

Reinforcement learning for legged locomotion has matured into a stack of multi-component reward functions and physics-engine benchmarks whose morphologies are uniformly derived from real commercial hardware. Game NPCs, however, are bound by stylistic constraints absent from sim-to-real robotics and routinely take the form of creatures with no real-robot counterpart. We introduce ARC-RL, a suite of four MuJoCo continuous-control environments featuring robotic morphologies inspired by the bestiary of ARC Raiders: the 18-DoF tall hexapod Queen, the 12-DoF armoured hexapod Bastion, the 18-DoF compact hexapod Tick, and the 12-DoF quadruped Leaper. All four robots share a unified observation template, action convention, simulation cadence, and a single closed-form multi-component reward function whose only per-morphology variation lives in a small set of weights and parameters. The reward fuses a velocity-tracking tent, a healthy survive bonus, a phase-locked gait-compliance bonus/cost pair, action regularisers, three safety penalties, and a posture anchor; no motion-capture data enters the reward at any point. We additionally provide hand-crafted Central Pattern Generator demonstrators per morphology, which serve both as fixed expert references and as sources of prior data for offline-to-online training. On this playground, we conduct a controlled empirical study comparing standard online algorithms (SAC, SPEQ, SOPE-EO) and methods augmented with prior data (SACfD, SPEQ-O2O, SOPE), and characterise how each paradigm copes with the playground's morphological diversity and animation-style stylistic constraints. Source code is available at https://github.com/CarloRomeo427/ARC_RL.git.

Using recent works of one of the authors (VSB) on collapse in generative models and two time scale dynamics in stochastic gradient descent in high dimensions, we give a system theoretic explanation of the memorization phenomenon in generative models. This relies purely on the dynamic aspects of the training phase. Specifically, we use a result of Austin [2016] to motivate a stylized model for the loss function for stochastic gradient descent (SGD) wherein the loss function has a strong dependence on some variables and weak dependence on the rest in a precise sense. This naturally leads to two distinct time scales in the constant step size SGD that is commonly used in machine learning. This fact has been used to explain the double descent phenomenon in SGD in Borkar [2026]. In conjunction with a mathematical model for collapse phenomenon in SGD developed in Borkar [2025a], we analyze the constant step size SGD using the recent results of Azizian et al. [2024] in order to explain the phenomenon of memorization wherein a generative model that is concurrently being tuned yields the same or similar outputs for significant stretches of time. This gives a novel perspective on the aforementioned phenomena reported in machine learning literature and their interrelationships, using a dynamical systems viewpoint.

Discrete diffusion language models (DDLMs) generate text by iteratively denoising categorical token sequences, while recent drifting methods for continuous generators suggest that part of this sampling-time correction can instead be absorbed into training through an anti-symmetric fixed-point objective. We study how to transfer this principle to DDLMs, where the main challenge is the interface with discrete text: hard token samples are non-differentiable, and categorical predictions do not directly provide continuous samples to drift. We formulate TokenDrift, a drifting objective that lifts categorical predictions to soft-token features, applies anti-symmetric drifting in a frozen semantic space, and backpropagates the resulting stop-gradient feature target to DDLM logits. In controlled continual-training experiments with masked and uniform-state diffusion backbones, TokenDrift improves fixed-NFE generation quality over matched continuation baselines, reducing Gen.-PPL at 4 NFEs by 89% on MDLM and 86% on DUO. These results suggest that drifting can provide a practical refinement objective for DDLMs.

Safe exploration remains a fundamental challenge in reinforcement learning (RL), limiting the deployment of RL agents in the real world. We propose Sampling-Based Safe Reinforcement Learning (SBSRL), a model-based RL algorithm that maintains safety throughout the learning process by enforcing constraints jointly across a finite set of dynamics samples. This formulation approximates an intractable worst-case optimization over uncertain dynamics and enables practical safety guarantees in continuous domains. We further introduce an exploration strategy based on constraining epistemic uncertainty, eliminating the need for explicit exploration bonuses. Under regularity conditions, we derive high-probability guarantees of safety throughout learning and a finite-time sample complexity bound for recovering a near-optimal policy. Empirically, SBSRL achieves safe and efficient exploration both in simulation and in real robotic hardware, and readily extends to practical deep-ensemble implementations that scale to high-dimensional continuous control problems.

Self-supervised learning (SSL) assumes that solving pretext tasks on unlabeled data yields representations that transfer effectively across downstream applications via linear probing or fine-tuning. While this paradigm has driven major progress in vision and language, its benefits for time series remain under-investigated and often confounded by inconsistent experimental controls. To address this gap, we benchmark seven representative methods from five key SSL paradigms across anomaly detection, classification, and forecasting under parameter- and data-matched budgets. We find that transfer efficacy depends heavily on the downstream task. SSL yields substantial gains in anomaly detection and provides effective initializations for classification under fine-tuning, but offers limited to no advantage over non-pre-trained controls in forecasting. Furthermore, linear probing does not reliably predict fine-tuning performance, synthetic pre-training is often competitive with real-world corpora, and scaling encoder depth degrades forecasting accuracy. We synthesize these empirical results into practical evaluation and development guidelines for time-series SSL.

We study the max-margin solutions reached by mirror flow in deep neural networks with homogeneous activation functions. Extending classical results on gradient flow, we derive a novel balance equation for mirror flow from convex duality, enabling a characterization of the horizon function governing the induced margin. We further establish max-margin characterizations together with convergence rates and norm growth estimates. Finally, we support our theory through experiments on synthetic datasets and standard vision tasks. Concretely, we show that: (1) distinct non-homogeneous mirror maps can induce the same max-margin solution; (2) convergence can be extremely slow, including exponentially slow regimes; and (3) although all considered mirror maps exhibit feature learning, they can produce markedly different representations, ranging from sparse to dense neuron activations. Together, these results provide a unified perspective on sparse and dense feature learning in homogeneous neural networks, highlighting how mirror maps shape both optimization dynamics and the geometry of the learned classifiers.

Test-time reinforcement learning (TTRL) reports substantial accuracy gains on mathematical reasoning benchmarks using majority vote as a pseudo-label signal. We argue these gains are systematically misinterpreted: most reflect sharpening of already-solvable problems rather than genuine learning, while problems corrupted from correct to incorrect outnumber truly learned ones, and this damage is irreversible once majority vote locks onto a wrong answer. Per-problem tracking reveals that correct-answer signals in low-ability problems are briefly active before being permanently suppressed, a phenomenon we term the Correct-Answer Extinction Window, with Flip Rate (FR) as its leading indicator. We thus propose TTRL-Guard, a lightweight framework with three mechanisms targeting the extinction window: Flip-Rate-Aware Reward Scaling (FRS) down-weights at-risk updates as FR declines, Minority-Preserving Sampling (MPS) retains gradient signal from minority correct answers, and Risk-Conditioned Sparse Updatings (RCSU) suspends updates on polarized problems. Experiments across three models and four benchmarks show that TTRL-Guard achieves the best average pass@1 on Qwen2.5-7B-Instruct and Qwen3-4B, improves relatively over TTRL by +54% on AIME 2025.

When a model produces a correct solution under reinforcement learning with verifiable rewards (RLVR), every token receives the same reward signal regardless of whether it was a decisive reasoning step or a grammatical filler. A natural fix is to condition the model on the correct answer as a teacher, identifying tokens it would have generated differently had it known the answer. Prior work shows this either corrupts training by leaking the answer into the gradient, or produces a weak signal that cannot distinguish decisive steps from filler, since both look equally surprising relative to the model's baseline. We propose Contrastive Evidence Policy Optimization (CEPO), which asks a sharper question at every token: not just "does the correct answer favor this token?" but "does the correct answer favor it while the wrong answer disfavors it?" A token satisfying both is a genuine reasoning step; one satisfying neither is filler. The wrong-answer teacher is constructed from rejected rollouts already in the training batch, incurring no additional sampling cost. We prove CEPO inherits all structural safety guarantees of the prior state of the art while strictly sharpening credit at decisive tokens, with the improvement vanishing exactly at filler positions. Empirically, CEPO achieves 43.43% and 60.56% average accuracy across five multimodal mathematical reasoning benchmarks at 2B and 4B scale, respectively, versus 41.17% and 57.43% for GRPO under identical training budgets. Distribution-matching self-distillation methods (OPSD, SDPO) fall below the untrained baseline, empirically confirming the information leakage our theory predicts. Our code is available at https://github.com/ahmedheakl/CEPO.

Reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant paradigm for advanced reasoning in Large Language Models (LLMs), but rollout samples are expensive to obtain, making sample efficiency a critical bottleneck. A natural remedy is to reuse each rollout batch for multiple gradient updates, a standard practice in classical RL. Yet in RLVR, this amplifies policy shift, leading to severe performance degradation. Detecting the onset of degradation early enough to stop reuse remains an open and challenging problem. We close this gap by identifying the Disproportionate Weight Divergence (DWD) phenomenon: performance degradation is synchronized with a sharp surge in the lm\_head weight change, while intermediate layers remain stable. Empirically, we verify that DWD emerges consistently across diverse LLMs and tasks. Theoretically, we prove that (i) harmful gradients concentrate at the lm\_head while intermediate layers are structurally attenuated, and (ii) the lm\_head gradient norm lower-bounds the policy divergence. These results establish the lm\_head gradient norm as a principled, real-time signal of catastrophic policy shift. Guided by this insight, we propose Dynamic Gradient Gating (DGG), a lightweight intervention that monitors the lm\_head gradient norm in real time and intercepts harmful gradients before they corrupt the optimizer. DGG consistently matches or exceeds the standard single-use baseline, achieving up to $2.93\times$ sample efficiency and $2.14\times$ wall-clock speedup across math, ALFWorld, WebShop, and search-augmented QA tasks.

Continual Model Merging (CMM) enables rapid customization of foundation models by sequentially incorporating task-adapted models without repeated retraining. However, existing merging rules usually update the deployed model through fixed algebraic or projection-based operations, providing limited control over how much previously accumulated knowledge should be retained relative to the incoming task model. This limitation leads to unstable retention and performance degradation in long task streams, and becomes more pronounced when tasks have heterogeneous utilities. We propose ODE-driven Merging (ODE-M), a controllable framework that formulates each continual merge as a trajectory in parameter space rather than a one-step endpoint update. Motivated by mode connectivity, ODE-M constructs a barrier-aware trajectory using a rectified time-dependent velocity field, where lightweight first-order feedback from a small calibration set suppresses loss-increasing motion while preserving progress toward the incoming model. The next merged model is then obtained by selecting an operating point along this trajectory through a utility-aware time schedule, providing an explicit mechanism for balancing retained historical knowledge and incoming task expertise. Extensive experiments on standard CMM benchmarks show that ODE-M consistently improves over strong continual merging baselines across CLIP ViT backbones, stream lengths, and heterogeneous task-utility settings.

We investigate data filtering for large model pretraining via new scaling studies that target the high compute, data-scarce regime. In spite of an apparently common belief that filtering data to include only high-quality information is essential, our experiments suggest that with enough compute, the best data filter is no data filter. We find that sufficiently trained large parameter models not only tolerate low-quality and distractor data, but in fact benefit from nominally “poor” data.

Recent Continuous Thought Machine architecture decouples internal computation from external inputs via neural dynamics, but relies on multi-layer perceptrons without stability guarantees. We propose to model neural dynamics using asymmetric Excitatory-Inhibitory (E-I) networks, which can be stabilized via principles from network theory and can be expressed as energy-based systems optimized through a game-theoretic loss. Building on this perspective, we introduce Temporal Inhibitory-Excitatory Dynamic Engine (TIDE), a neuro-inspired architecture that computes internal representations through neural dynamics stabilized by incorporating the Wilson-Cowan dynamics and lateral inhibition. TIDE balances biological realism by, for instance, using Hierarchical Receptive Fields and enforcing Dale's principle to ensure a realistic $80:20$ E-I balance ratio with an end-to-end trainable architecture. The aim of this paper is to introduce a new architecture that brings neuro-inspired learning to the forefront. We present proofs of convergence, stability, and complexity bounds, along with empirical ablation studies. Overall, TIDE surpasses CTM with under $50\%$ of the training time and improves $\texttt{top-1}$ accuracy by an average of $+1.65\%$ on ImageNet under various perturbations.

Deep learning models for medical image classification are susceptible to subgroup performance disparities across demographic attributes such as age, gender, and race. We identify a latent representational mechanism underlying these disparities: in transfer-learned models, the dominant penultimate-layer activation channel under positive predictions is co-activated by both disease-positive samples and privileged demographic groups (male, older patients), producing over-diagnosis; conversely, the dominant channel under negative predictions is co-activated by disadvantaged groups (female, younger patients), producing systematic under-diagnosis. To address this, we propose Neuron Incidence Redistribution (NIR), a lightweight regularization method that penalizes the variance of predicted-probability-weighted mean activations across penultimate-layer neurons, requiring no demographic labels at training time. On HAM10000, TPR disparity drops from 10.81% to 0.93% across age groups and from 12.04% to 0.74% across gender, with a marginal AUC improvement of 0.51 points. On Harvard OCT-RNFL, NIR reduces FPR disparity for race (from 15.68% to 10.66%) and age (from 12.69% to 1.80%), demonstrating that distributing latent disease evidence across the full penultimate layer is a principled and effective strategy for improving demographic fairness in medical AI.

The remarkable success of the Adam in training neural networks has naturally led to the widespread use of its descent-ascent counterpart, Adam-DA, for solving zero-sum games. Despite its popularity in practice, a rigorous theoretical understanding of Adam-DA still lags behind. In this paper, we derive ordinary differential equations (ODEs) that serve as continuous-time limits of the Adam-DA. These ODEs closely approximate the discrete-time dynamics of Adam-DA, providing a tractable analytical framework for understanding its behavior in zero-sum games. Using this ODE approach, we investigate two fundamental aspects of Adam-DA: local convergence and implicit gradient regularization. Our analysis reveals that the roles of the first- and second-order momentum parameters in zero-sum games are exactly the opposite of their well-documented effects in minimization problems. We validate these predictions through GAN experiments across multiple architectures and datasets, demonstrating the practical implications of this reversed momentum effect.

Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise, transforming it into a simple prior, and then use denoising score matching, a consequence of Tweedie's formula, to learn the score function and generate clean samples from noise. However, non-Gaussian diffusion models with state-dependent diffusion coefficient have been largely underexplored, as have the corresponding Tweedie's formulae. In this work, we extend Tweedie's formula to important non-Gaussian processes, including geometric Brownian motion (GBM), squared Bessel (BESQ) processes, and Cox-Ingersoll-Ross (CIR) processes, thereby yielding the corresponding denoising score-matching objectives. We then apply the derived formulae to image and financial time series generation using GBM- and CIR-based diffusion models, and to empirical Bayes estimation under the BESQ setting. The reported experimental results demonstrate the potential of non-Gaussian models.