Papers

Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving reasoning in large language models (LLMs), yet the underlying geometry of the resulting parameter trajectories remains underexplored. In this work, we demonstrate that RLVR weight trajectories are extremely low-rank and highly predictable. Specifically, we find that the majority of downstream performance gains are captured by a rank-1 approximation of the parameter deltas, where the magnitude of this projection evolves near-linearly with training steps. Motivated by this, we propose a simple and compute-efficient method RELEX (REinforcement Learning EXtrapolation), which estimates the rank-1 subspace from a short observation window and extrapolates future checkpoints via linear regression, with no learned model required. Across three models (i.e., Qwen2.5-Math-1.5B, Qwen3-4B-Base, and Qwen3-8B-Base), RELEX produces checkpoints that match or exceed RLVR performance on both in-domain and out-of-domain benchmarks, requiring as few as 15% steps of full RLVR training. Remarkably, RELEX is able to extrapolate far beyond the observation window at no training cost, predicting checkpoints up to 10-20$\times$ beyond the observed prefix with continued improvement (e.g., observe only the first 50 steps and extrapolate to 1000 steps). Our ablation analysis confirms the minimalist sufficiency of RELEX: neither increasing the subspace rank nor employing non-linear modeling yields further gains in extrapolation. Finally, we show that RELEX's success stems from a "denoising" effect: by projecting updates onto the rank-1 subspace, the model discards stochastic optimization noise that would otherwise degrade performance during extrapolation. Our code is available at https://github.com/weizhepei/RELEX.

Reinforcement learning from verifiable rewards (RLVR) has emerged as a central technique for improving the reasoning capabilities of large language models. Despite its effectiveness, how response-level rewards translate into token-level probability changes remains poorly understood. We introduce a discriminator view of RLVR updates, showing that the policy-gradient update direction implicitly acts as a linear discriminator over token-gradient vectors and thereby determines which token probabilities are increased or decreased during learning. Under standard sequence-level RLVR, this discriminator is constructed from positive- and negative-side centroids formed by advantage-weighted averaging of token-gradient vectors. However, such centroid construction can be dominated by shared high-frequency patterns, such as formatting tokens, diluting sparse yet discriminative directions that better distinguish high-reward responses from low-reward ones. To address this limitation, we propose $\textbf{DelTA}$, a discriminative token credit assignment method that estimates token coefficients to amplify side-specific token-gradient directions and downweight shared or weakly discriminative ones. These coefficients reweight a self-normalized RLVR surrogate, making the effective side-wise centroids more contrastive and thereby reshaping the RLVR update direction. On seven mathematical benchmarks, DelTA outperforms the strongest same-scale baselines by 3.26 and 2.62 average points on Qwen3-8B-Base and Qwen3-14B-Base, respectively. Additional results on code generation, a different backbone, and out-of-domain evaluations further demonstrate the generalization ability of DelTA.

Global Navigation Satellite Systems (GNSS) are widely used to provide position, velocity, and timing (PVT) information for various applications, including transportation, location-based communication services, and intelligent agriculture. In urban canyons, high-rise buildings and narrow streets can cause signal obstruction, non-line-of-sight (NLOS) reception, and multipath effects that introduce errors in GNSS pseudorange measurements. Although multi-constellations GNSS effectively increase the number of available satellites, the inclusion of degraded signals can lead to severe positioning errors. This study proposes a machine learning framework for the weighted least squares (WLS) algorithm incorporating activation functions to enhance positioning accuracy. Several signal quality indicators are employed as training features for ensemble learning algorithms to identify poor quality signals by providing quality scores. Then, activation functions are employed to transform the machine learning predicted scores to appropriate weights for WLS positioning. To evaluate the performance of our approach, experiments are conducted using real-world datasets from Hong Kong and Tokyo urban areas. Comparative analysis of activation functions reveals that sigmoid functions consistently yield the greatest improvements with different machine learning algorithms and GNSS constellation configurations. The proposed algorithm demonstrates substantial reductions in positioning errors for both single- and multiconstellation scenarios. Furthermore, our results indicate that the proposed algorithm exhibits strong geographical transferability. The proposed algorithm maintains comparable level of performance when trained on data from other regions with similar levels of urbanization.

Randomized experiments are the standard for measuring causal effects that guide decisions, but are costly. Simulators calibrated to historical data offer a cheaper alternative, but their policies can become suboptimal under drift, a change in dynamics after calibration. We study if, when, and how to collect data for recalibrating the simulator. We consider a system with multiple units running in parallel and managed by a single operator. The real-world system is a partially observed process with a latent variable, while the simulator models it as a fully observed Markovian process, and thus is misspecified. Two data collection strategies exploit the current policy: (i) never recalibrating and (ii) recalibrating from on-policy data (passive adaptation). Two others collect off-policy data by trying actions outside the current policy: (iii) continuous exploration across all units and (iv) randomized experimentation on a sample of units over a predefined window. We investigate these strategies theoretically and in a vending-machine simulation. Experiments can improve on passive adaptation when drift is invisible in on-policy data or recalibration lags behind continuing drift. Experimentation is preferable to exploration when trying a worse action is expensive and the dynamics may not have changed.

Statistical decision algorithms are increasingly deployed in domains where ground-truth labels are hard to obtain, such as hiring, university admissions, and content moderation. In these settings, models are typically trained on historical human evaluations – for example, using past hiring decisions as a proxy for true applicant quality. However, if past evaluations unjustly favor certain groups, models trained on these labels may inherit those biases. To address this problem, we propose basing predictions on rubric embeddings, a representation framework that replaces standard black-box embeddings with features derived from expert-defined criteria that align with the underlying construct of interest. By anchoring predictions to semantically meaningful dimensions, this approach guards against biased proxy signals. We provide both theoretical and empirical evidence that rubric embeddings mitigate label bias under plausible conditions. Empirically, we evaluate our method on a novel dataset of applications to a large master's program. We find that models trained on rubric embeddings reduce group disparities while improving measures of cohort quality. Our results suggest that basing predictions on interpretable, domain-grounded representations offers a practical approach to learning in the presence of biased labels.

Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function classes, such as continuous functions on compact subsets of $\mathbb{R}^d$, $L^p$ spaces, or Sobolev spaces. Over the past four decades, these qualitative universality results have evolved into a rich quantitative theory addressing approximation rates, parameter efficiency, and the role of architectural features such as depth and width. This survey presents several glimpses into this theory. We review classical density results for single-hidden-layer networks, as well as quantitative bounds that relate approximation error to network size and smoothness assumptions on target functions. Particular emphasis is placed on depth–width trade-offs and on results demonstrating that deeper architectures can achieve superior parameter efficiency for structured function classes. In addition to standard feedforward neural networks, we also review recent developments on Kolmogorov–Arnold Networks (KANs), which offer an alternative architectural paradigm and whose approximation-theoretic properties have begun to attract significant theoretical attention.

Modern LLMs typically require multistage training pipelines to achieve strong downstream performance, with post-training serving as the main interface for adapting open-weight models. We introduce torchtune, a PyTorch-native library designed to streamline the post-training lifecycle of LLMs, enabling efficient fine-tuning, experimentation, and deployment-oriented workflows. Unlike many existing fine-tuning frameworks, which often optimize for ease of use, specialized recipes, or hardware efficiency at the cost of transparency and extensibility, torchtune emphasizes modularity, hackability, and direct access to the underlying PyTorch components. In this paper, we present the design principles behind torchtune, describe how they are reflected in its model builders, training recipes, and distributed training stack, and evaluate the library across representative post-training settings. We compare against popular fine-tuning frameworks, including Axolotl and Unsloth, and show that torchtune provides strong performance and memory efficiency across many settings while remaining flexible enough for rapid research iteration. These results position torchtune as a practical foundation for reproducible LLMs post-training research.

We revisit a neural negative binomial model for weekly earthquake counts on a 3 x 3 degree grid over the Tian Shan and Pamir, and ask which of its conclusions survive a careful evaluation. At the completeness magnitude of 4.5, the 144-week test period holds 2448 cell-weeks; six cell-weeks, in five distinct weeks, have three or more events. Two conclusions survive. First, Poisson forecasts, temporal ETAS included, understate the probability of such a busy week: ETAS expects 0.72 where six occurred, a shortfall by a factor of 8.3 (p = 0.00009, exact test). One dispersion parameter removes it (ETAS with dispersion expects 4.45, p = 0.58); simulating aftershock chains within the week also reproduces the tail but overshoots the total count by about a quarter. Second, the network's advantage over a linear model disappears once that model has an intercept per cell: the remaining gain is 3.4% of deviance, not significant (p = 0.57 over five test years), and it comes from one cell-week out of the 4420 scored; without it the network is 0.7% worse. A blind test on 2024 to September 2026, with every model fitted on data through 2023, confirms the tail result: Poisson forecasts are rejected (p from 3 x 10^-8 to 0.001), dispersion models are not (p between 0.25 and 0.84), except the NB GLM, whose level blew up out of sample and which is rejected at p = 0.003. Out of sample, model families differ in how they extrapolate beyond the training range, not in the per-cell term. We also measure the evaluation traps met on the way: a biased reference level, a single seed (five of six effects in v1's results table change sign), too few bootstrap resamples, and a threshold below completeness, which shrinks the ETAS shortfall from 8.3 to 2.8 times. This version replaces preprint v1; Section 7 lists the corrections.

Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better represented by probability distributions than real vectors. Concretely, when node features are Gaussians, characterized by a mean and a covariance matrix, naively concatenating their parameters into a single vector and applying standard message passing discards the geometric and algebraic structure that governs means and covariances. We propose Gaussian Sheaf Neural Networks (GSNNs), a principled framework that incorporates these inductive biases into graph-based learning. Building on the theory of cellular sheaves, we derive a new Laplacian operator that generalizes the sheaf Laplacian to this setting and preserves its key properties. We complement our theoretical contributions with experiments on synthetic and real-world data that illustrate the practical relevance of GSNNs.

Tactile-based reinforcement learning (RL) is currently hindered by fragmented research and a focus on over-saturated orientation tasks. We introduce v2 of the Robot Tactile Olympiad (roto 2.0), a GPU-parallelised benchmark designed to standardise tactile-based RL across four distinct robotic morphologies (16-DOF to 24-DOF). Unlike prior benchmarks, roto focuses on end-to-end "blind" manipulation, utilising only proprioception and tactile sensing without state information or distillation. We demonstrate a significant performance leap, with our blind agents achieving 13 Baoding ball rotations in 10 seconds, an order of magnitude faster than current state-of-the-art speeds. By open-sourcing our environments and robustly tuned baselines, we reduce the barrier to entry and enable researchers to prioritise fundamental algorithmic challenges over tedious RL tuning. Website: https://elle-miller.github.io/roto/

We study the task of agnostic learning of multiclass linear classifiers under the Gaussian distribution. Given labeled examples $(x, y)$ from a distribution over $\mathbb{R}^d \times [k]$, with Gaussian $x$-marginal, the goal is to output a hypothesis whose error is comparable to that of the best $k$-class linear classifier. While the binary case $k=2$ has a well-developed algorithmic theory, much less is known for $k \ge 3$. Even for $k=3$, prior robust algorithms incur exponential dependence on the inverse of the desired accuracy in both complexity and representation size. In this work, we develop new structural results for multiclass linear classifiers and use them to design fully polynomial-time robust learners with dimension-independent error guarantees. Our first result shows that the standard multiclass perceptron algorithm requires super-polynomially many samples and updates, even with clean labels and Gaussian marginals, revealing a basic obstruction absent in the binary case. Our main positive result is a pairwise improper-learning framework which yields an efficient learner with error $\widetilde O(k^{3/2}\sqrt{\mathrm{opt}})+\epsilon$ for general $k$. Additionally, we develop a sharper localization-based framework which leads to error $O(\mathrm{opt})+\epsilon$ for $k=3$, and error $\mathrm{poly}(k)\mathrm{opt}+\epsilon$ for geometrically regular $k$-class linear classifiers.

One-shot magnitude pruning can cause severe accuracy collapse in the high-sparsity regime, even when the pruning mask preserves the largest weights. We argue that this failure reflects a granularity mismatch in post-pruning repair. Under global magnitude pruning, nearly collapsed channels can coexist with channels that retain informative activation variance within the same layer. Existing layer-wise activation repair methods apply a single correction to the whole layer, and can therefore over-amplify damaged channels while trying to restore the layer-level signal. We propose Adaptive Signal Resuscitation (ASR), a training-free channel-wise repair method that matches the granularity of repair to the granularity of damage. ASR estimates a variance-matching correction for each output channel and stabilizes it with a data-driven shrinkage rule, suppressing unreliable corrections for channels with weak post-pruning signal while preserving corrections for healthier channels. Applied before BatchNorm recalibration, ASR requires only forward passes on a small calibration set and no retraining. Across three datasets, four convolutional architectures, and both unstructured and structured sparsity settings, ASR generally improves over layer-wise repair, with the clearest gains in high-sparsity regimes. On ResNet-50 at 90% sparsity, ASR recovers 55.6% top-1 accuracy on CIFAR-10, compared with 41.0% for layer-wise repair and 28.0% for BatchNorm-only recalibration. Ablations show that naive channel-wise variance matching is insufficient, and that shrinkage stabilizes post-pruning repair.

As LLMs continue to scale up, improving training efficiency heavily relies on effective data utilization. Data selection mitigates this issue by allocating the limited training budget to high-value examples that optimally facilitate the model's target behavior. Most existing approaches define target behavior via a set of target examples and score candidate training data based on their estimated influence on these samples. However, such methods uniformly treat all target examples as equally important, ignoring the varying relevance of individual examples to model optimization. Specifically, target examples that align closely with the model's inherent behavior deliver stronger supervisory signals, whereas discrepant examples yield only weak and ineffective local guidance. We propose PRISM, a Preference-aware Influence function based Data Selection Method. It leverages model preference to assign weights to target examples and builds a preference-aware target direction. PRISM evaluates candidate training samples according to their influence on this direction, and prioritizes data budget allocation to samples that effectively drive the model to match expected target behavior. Theoretical analysis verifies that weighted preference construction generates a superior first-order gradient direction for boosting target preference, compared with uniform aggregation strategies. Extensive experiments covering diverse model architectures and parameter scales demonstrate that PRISM achieves better performance in efficient fine-tuning and safety-aligned supervised fine-tuning rectification. The results validate that accurate characterization of target behavior serves as the core of cost-effective data selection.

Reaction condition recommendation sits immediately after retrosynthetic disconnection selection, and in practice, chemists require both accurate predictions and the precedents that justify them. We present HiRes (Hierarchical Reaction Representations), a retrieval-augmented condition recommendation system whose learned reaction space serves as both a classifier feature and an inspectable precedent memory. The model combines a graph encoder, transformation-aware cross-attention, multi-stream reaction fusion, and a k-NN retrieval layer. HiRes achieves state-of-the-art performance among primary-slot USPTO-Condition models, reaching Catalyst, Solvent, and Reagent top-1 accuracies (Acc@1) of 0.929, 0.534, and 0.530 respectively. It ties the best reported baseline on Catalyst while outperforming models such as REACON on Solvent and Reagent. Furthermore, paired bootstrap analysis demonstrates that integrating retrieval with learned condition heads provides statistically significant gains for solvent and reagent selection over purely parametric approaches. Ultimately, HiRes bridges the gap between predictive accuracy and chemical interpretability, offering a single representation that supplies both competitive recommendations and the concrete chemical precedents necessary for practical synthesis planning.

In sixth-generation (6G) ultra-dense networks, aggressive frequency reuse amplifies inter-cell interference (ICI), making multi-cell orthogonal frequency-division multiple access (OFDMA) scheduling and power control strongly coupled across neighboring cells. We study distributed downlink resource management – joint subcarrier scheduling and power allocation – under interference coupling and long-term per-user quality-of-service (QoS) minimum-rate constraints. By using virtual-queue deficit weights to enforce long-term QoS, we develop FedCritic, a serverless federated multi-agent actor-critic framework with decentralized execution. Unlike centralized training with decentralized execution (CTDE) approaches that require centralized critic learning and joint trajectory aggregation, FedCritic federates the critic through lightweight gossip-based parameter averaging over the interference graph, enabling stable value estimation without a central coordinator while keeping policies local. Simulations in an interference-rich reuse-1 setting show that FedCritic improves mean signal-to-interference-plus-noise ratio (SINR) and cell-edge rate, increases network-wide average sum-rate and fairness relative to non-coordinated and CTDE baselines, and achieves more stable training with lower coordination overhead.

We read twelve well-known LLM agent benchmark papers and recorded, dimension by dimension, what each paper actually says about how its evaluation was run. The motivation came from a familiar frustration: two papers will report results on the same benchmark with the same model name and disagree, and you cannot tell why – the scaffold, the sampling settings, the subset, or the evaluator version. In many cases the published artifact does not let you answer. This paper is an implementation report on the attempt. We designed a small audit schema (five fields: benchmark identity, harness specification, inference settings, cost reporting, failure breakdown), wrote a scoring codebook with the boundary cases we hit during pilot scoring, applied it to twelve canonical papers (eight agent, four classical static), and recorded what we saw. We score the disclosure of an agent run, not its correctness, and make no claim that disclosure implies a trustworthy result. The mean audit score across the eight agent-benchmark papers is 0.38 (out of 1.0), and across the four classical static benchmarks 0.66; the largest gap is on cost (none of the eight agent benchmark papers disclose inference cost in any form) and on harness specification (none fully disclose a content-addressed container image of the evaluation environment). We release the schema as a JSON Schema file, the codebook as a Markdown document, and the raw scoring sheet as a CSV. The scoring was performed by a single auditor in one pass; a multi-rater audit is the natural next step, and we discuss what we think it would change.

Generative neural networks learn how to produce highly realistic images from a large, but finite number of examples - or do they simply memorise their training set? To settle this question, Kadkhodaie, Guth, Simoncelli and Mallat (ICLR '24) trained diffusion models independently on disjoint subsets of a dataset and showed that they converge to nearly the same density when the number of training images is large enough. This result raises two basic questions: how much data do you need for convergence, and what does convergence capture about learning the data distribution? Here, we address these questions by providing an exact analytical characterisation of the transition from memorisation to generalisation in linear generative models. We find that these models memorise at small load, while convergence emerges continuously when the number of samples is linear in the input dimension. Strikingly, we find that convergence is insensitive to recovery of the principal latent factors of the data, which are recovered in a sharp transition. After extending our approach to data with power-law spectra, we find the same distinction between convergence and latent recovery in our experiments with convolutional denoisers and in the data of Kadkhodaie et al. We thus show that generalisation in generative models decomposes into at least two distinct objectives: matching the bulk of the data distribution and recovering the principal latent factors. These objectives correspond to two different distances between true and learnt data distribution, and only the first one is captured by convergence.

The proliferation of emerging applications, such as autonomous driving and immersive experiences, demands cellular networks that are not only faster, but fundamentally more resilient and autonomous. This paper presents a BlueSky vision on how Artificial Intelligence will be natively integrated into 6G, shifting the paradigm from \underline{Network for AI} to \underline{AI for Network}. We envision that, unlike 5G's reliance on scattered, ad-hoc models each trained for a single task, native AI in the 6G era will be anchored by a foundation model and and orchestrated via collaborative multi-agent systems, framing network management as a unified, multi-modal, multi-task optimization problem. Built on this vision, we outline two transformative directions. The first focuses on developing a 6G foundation model as a unified backbone, with task-specific knowledge distilled into compact models suited for diverse edge deployments. The second advances multi-agent systems designed to autonomously diagnose, maintain, and recover networks with minimal human intervention. These directions chart a roadmap for 6G to evolve into an intelligent, self-sustaining communication infrastructure.

Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper develops a theoretical framework for understanding the regularity of transport maps and the generalization properties of one-step Wasserstein-guided generative models for PDE-induced probability measures. We consider normalized target densities associated with linear elliptic and parabolic equations on bounded domains, as well as diffusion and Fokker–Planck equations on the torus. Under standard structural assumptions, we prove that these target measures satisfy doubling conditions. By combining this fact with regularity theory for optimal transport between doubling measures, we show that the optimal transport map from a uniform source measure to the target measure is Hölder continuous. This regularity yields an approximation-theoretic justification for one-step generative models that learn PDE-induced distributions via a single pushforward map. As a representative instance, we study DeepParticle and derive excess-risk bounds characterizing the discrepancy between the learned map and the population-optimal map. We also establish a robustness estimate under target shift and illustrate the theory with experiments which support the derived rates.

Recent advances in Image Restoration (IR) have been largely driven by generative methods such as Diffusion Models and Flow Matching, which excel in synthesizing realistic textures while suffering from slow multi-step inference and compromised pixel fidelity. In contrast, classical regression-based IR methods excel precisely in these aspects, offering single-step efficiency and high pixel-level reconstruction fidelity. To bridge this gap, we propose DiSI, a unified framework that Disentangles the underlying Stochastic Interpolant process into independent generation and regression components. This decoupling endows DiSI with remarkable versatility, enabling a continuous and controllable transition from a pure regression process to a fully generative one. Technically, we instantiate this framework with two specific sampling trajectories, accompanied by a unified sampler for high-quality, few-step inference on arbitrary trajectories. Furthermore, we design a dual-branch U-Net style transformer network in pixel space, using a dedicated branch to enhance conditional guidance while ensuring high throughput. Extensive experiments demonstrate that DiSI efficiently achieves competitive results on various IR tasks, while uniquely offering the inference-time flexibility to control the distortion-perception trade-off within a single model.

Data scaling is fundamental to modern deep learning, and grows increasingly critical as autonomous driving shifts to end-to-end learning. Real-world driving data is expensive to annotate and scene-biased, making real-synthetic co-training with near-infinite synthetic data a promising direction. However, naively incorporating all available synthetic data is inefficient and leads to distribution shifts, and optimizing data mixture under practical training budgets remains a critical yet under-explored problem. In this sense, we claim that the mixture of training data requires clear guidance in terms of scene types and quantities. Particularly in this work, we conceptualize the data mixture approximately as a dynamic optimization process that iteratively adjusts the training data mixture to maximize model performance, guided by closed-loop evaluation feedback, and propose AutoScale, a fully automated closed-loop data engine unifying scene representation, data mixture optimization and retrieval, as well as model training and evaluation. Specifically, we propose Graph Regularized AutoEncoder (Graph-RAE) for driving scene representations, introduce Cluster-aware Gradient Ascent (Cluster-GA) for cluster-wise importance estimation and reweighting, and perform cluster-guided vector retrieval to select high-value samples. Experiments on NavSim demonstrate that AutoScale outperforms vanilla co-training and cross-domain baselines, achieving better performance with fewer synthetic samples under constrained budgets.

The growing use of fast-switching power electronics has made partial discharge (PD) analysis under switching-voltage excitation increasingly important, yet more challenging than under sinusoidal conditions due to activity concentrated at voltage transitions. This work presents an Amplitude-Width-Area (AWA) pattern representation for source-oriented PD analysis under switching-voltage excitation. In the proposed method, time domain PD pulses are characterized using pulse amplitude, width, and area, and mapped into a visual pattern where amplitude and area define the coordinate axes and width is encoded by color. The generated AWA patterns are used to distinguish six single and mixed PD source conditions: corona, internal, surface, corona+internal, corona+surface, and internal+surface. To evaluate the classification capability of the proposed representation, a Random Forest baseline and two Convolutional Neural Network (CNN) models, InceptionV3 and ResNet-18, are compared. The AWA patterns show distinguishable source-dependent distributions, and CNN-based classification achieves testing accuracy above 96%, compared with 73.33% for Random Forest. The results indicate that AWA patterns provide a visual representation of PD pulses suitable for multi-class PD source classification under switching-voltage excitation.

Solving partial differential equations with neural operators significantly reduces computational costs but remains bottlenecked by high training data requirements. Active learning offers a natural framework to mitigate this by selectively acquiring the most informative samples in an iterative manner. We introduce physics-based acquisition - a novel physics-informed active learning algorithm that leverages the partial differential equation residual to guide data selection. We validate the method by presenting numerical experiments for the 1D Burgers equation and the 2D compressible Navier-Stokes equations. We show that, in our experiments, physics-based acquisition consistently outperforms random acquisition and matches the state of the art in data efficiency. At the same time, it has the unique advantage of injecting a physics inductive bias into the training process, ensuring that simulation cost is spent where the model's physical understanding is weakest.

Diagnosing failures in LLM agents remains largely manual. Practitioners inspect a small subset of execution traces, form ad-hoc hypotheses, and iterate. This process misses patterns that only emerge across trace populations and does not scale to production corpora where individual traces span tens of thousands of tokens. We formalize the problem of corpus-level trace diagnostics. Given a corpus of execution traces, the goal is to produce grounded natural-language insights that characterize systematic behavioral patterns across trace groups, each linked to supporting evidence. We present the Insights Generator (IG), a multi-agent system that answers diagnostic questions by proposing and testing hypotheses across the trace corpus to produce an evidence-backed insights report. We evaluate IG across qualitative and objective dimensions, spanning rubric-based report assessment and downstream performance improvements achieved by implementing IG insights. Human experts using IG reports improve scaffold performance by 30.4 pp over the unmodified baseline scaffold, and coding agents leveraging IG-derived insights show consistent and stable gains. Across benchmarks, IG's scout-investigator architecture produces findings comparable in detection coverage to competing approaches, while domain experts rated IG reports as leading depth and evidence quality.

We study functional bilevel optimization with conditional moments, where plug-in hypergradients can inherit first-order errors from nonparametrically learned conditional expectations. We introduce OBiGrad, an orthogonalized hypergradient estimator whose bias is a product of nuisance errors. Under our regression and complexity conditions, projected gradient descent with the direct plug-in hypergradient yields expected stationarity error $O(T^{-1/2}+n^{-1/2}+n^{-\nu/b})$ for the best iterate, whereas OBiGrad achieves $O(T^{-1/2}+n^{-1/2}+n^{-2\nu/b})$, where $b=\nu(2+p)+\gamma$ combines the approximation and complexity exponents. Consequently, when $\nu(2-p)\ge\gamma$, OBiGrad attains the parametric statistical rate $O(T^{-1/2}+n^{-1/2})$, improving the sufficient sample-size bound relative to the direct plug-in bound for a fixed iteration budget. We illustrate these gains on instrumental-variable and fitted-Q-regression problems, examining stationary-point estimation, returned population stationarity, and regularization sensitivity.

Linear attention has emerged as a cornerstone for efficient long-context architectures, as evidenced by its integration into state-of-the-art open-source models including Qwen3.5/3.6, Kimi Linear/K3, and RWKV-7. Models that incorporate linear attention layers with the so-called Delta-Rule involve the inversion of triangular matrices as a core sub-routine. This operation often forms a performance bottleneck, and, due to its high-sensitivity to numerical errors, it can significantly deteriorate end-to-end model accuracy if it is not carefully implemented. This work provides a systematic analysis of both direct and iterative triangular inversion algorithms, targeting methods that are rich in matrix products, and, therefore, have the potential to efficiently utilize modern hardware. To that end, our analysis covers a broad spectrum of mathematical and practical aspects, with a heavy focus on numerical stability, computational complexity, and, ultimately, hardware efficiency and practical considerations. We provide a rigorous experimental evaluation to verify these properties in practical scenarios, and in low-precision floating-point representations, highlighting the strengths and limitations of each method. Performance benchmarks on NPUs reveal up to $4.3\times$ speed-up against the state-of-the-art implementations of SGLang for triangular matrix inversion, leading to significant performance improvements on the entire layer level, while maintaining end-to-end model accuracy.

What can representational similarity matrices (RSMs) tell us about a neural code? As the popularity of these summary statistics grows, so too does the need for a more complete characterization of their properties. Here, we show that symmetries in network inputs can confound RSM-based analyses. Stimulus symmetries render many representations functionally equivalent, but these different configurations can lead to different RSMs. These different RSMs reflect qualitatively different representational geometries, ranging from disentangled to maximally-mixed codes. We show that stochastic gradient descent or energetic regularization can generate sparse, drifting codes, leading in turn to drifting RSMs. Moreover, we demonstrate that these phenomena are present in networks trained to encode image data, where the symmetry is latent. Our results illustrate the challenges inherent in comparing nonlinear neural codes, when functionally-equivalent representations are not related by a simple rotation.

Federated Learning (FL) enables collaborative model training without centralizing data. However, real-world deployments must simultaneously address statistical heterogeneity across client data (non-IID), system heterogeneity in device capabilities, and communication efficiency. Existing FL approaches mitigate these challenges through improved aggregation, personalization, or knowledge distillation, but they almost universally assume a fixed client architecture, limiting adaptability to heterogeneous data complexity and hardware constraints. This architectural constraint often leads to suboptimal trade-offs between accuracy and efficiency in real-world FL systems. This work introduces FedKDNAS, a distillation-driven FL framework that combines client-side neural architecture selection with distillation of server-coordinated knowledge. Each client autonomously selects a lightweight model under accuracy-resource constraints. It then trains it locally using a hybrid objective combining supervised learning and knowledge distillation and shares only predictions on a public reference set. The server then aggregates and smooths these predictions, optionally combining them with a teacher model, to produce stable distillation targets for the next round. Extensive evaluation on six datasets against six representative FL baselines (FedAvg, Ditto, FedMD, FedDF, FedDistill, Local-KD) demonstrates that FedKDNAS consistently achieves superior Pareto efficiency, improving accuracy by up to 15% under non-IID conditions, reducing client CPU usage by approximately 28%, and decreasing communication overhead by up to 44 times while maintaining lightweight logit-based communication.

Large language models (LLMs) are highly sensitive to the prompts used to specify task objectives and behavioral constraints. Many recent prompt optimization methods iteratively rewrite prompts using LLM-generated feedback, but the resulting prompts often become longer, accumulate narrow sample-specific rules, and generalize poorly beyond the training distribution. We study this failure mode as prompt distributional overfitting and argue that it reflects a lack of representation control in discrete text-space optimization. We formalize this view through representational inefficiency, a dual-factor measure that decomposes prompt inefficiency into capacity cost and scope narrowness, attributing distributional prompt overfitting to their coupled growth during optimization. We propose TextReg, a regularization framework that realizes a soft-penalty objective through regularized textual gradients, combining Dual-Evidence Gradient Purification, Semantic Edit Regularization, and Regularization-Guided Prompt Update. Across multiple reasoning benchmarks, TextReg substantially improves out-of-distribution (OOD) generalization, with accuracy gains of up to +11.8% over TextGrad and +16.5% over REVOLVE.

The aggregation of conflicting client updates remains a fundamental bottleneck in federated learning (FL) under heterogeneous data distributions. Naive averaging can produce a global update that improves the global objective while conflicting with specific clients, causing degradation for those clients. In this work, we propose CRAFT (Conflict-Resolved Aggregation for Federated Training), a new aggregation framework that treats the global update as a geometric correction problem. We formulate aggregation as finding the update closest to a reference direction while satisfying conflict-free alignment constraints. We derive a closed-form expression for the constrained optimization problem, avoiding the computational overhead of iterative solvers. Furthermore, we use a layer-wise adaptation to address conflicts at varying feature granularities. We provide a theoretical analysis showing that CRAFT promotes a common-descent structure and mitigates conflicts through its projection geometry. Extensive experiments on heterogeneous benchmarks demonstrate that CRAFT improves the accuracy of the global model while reducing performance disparity across clients compared with state-of-the-art baselines. The source code for CRAFT is available at https://github.com/tum-pbs/CRAFT.