Papers

As an extension of the classical multi-armed bandit problem, multi-fidelity multi-armed bandits (MF-MAB) enable individual arms to be evaluated using diverse feedback sources that vary in both cost and accuracy. Prior stochastic models typically assume fixed low-to-high fidelity discrepancies, whereas modern proxy sources, such as learning-based simulators and Large Language Models (LLMs), can be improved using additional calibration. We investigate adaptive MF-MAB with improving proxy sources, and focus on the canonical two-fidelity case in which the low-fidelity source becomes more informative with repeated use. To capture this dynamic, we introduce a selected-average mismatch bound that converts dynamic low-fidelity observations into improvement-aware confidence bounds for the high-fidelity target. We propose the Threshold-Based Adaptive Continuation Companion (TACC), an optimistic algorithm that uses a bounded continuation rule to decide when low-fidelity sampling remains cost-effective and when to escalate. We prove an instance-dependent regret bound showing that, for detected intermediate arms, adaptive continuation replaces logarithmic high-fidelity confirmation with bounded low-fidelity continuation. Experiments on synthetic bandits and an LLM-as-a-judge policy-evaluation task examine when continuation improves cost-weighted regret.

Parameter-efficient adaptation of pretrained vision models is commonly performed through linear probes, prompts, low-rank updates, or lightweight residual modules. While effective, these methods usually treat adaptation as a discrete Euclidean perturbation of frozen representations, without explicitly modeling the geometry of the task-induced feature displacement. We propose MC-RFM, a mixed-curvature Riemannian flow-matching framework for few-shot adaptation of frozen visual backbones. The key idea is to represent adapted features on a product manifold combining a hyperbolic factor, which captures hierarchy-sensitive semantic structure, and a Euclidean factor, which preserves locally discriminative visual variation. Adaptation is formulated as a task-conditioned continuous transport from frozen features to support-set prototypes, trained with a flow-matching objective and coupled to a hybrid prototype-linear classifier. The method is lightweight, backbone-agnostic, and operates entirely on cached frozen features. Across seven visual recognition benchmarks, five frozen backbones, and 1/4/16-shot regimes, MC-RFM is the best-performing method in a majority of evaluated settings, with the strongest gains on Transformer backbones and fine-grained datasets. Ablations show that the mixed-curvature head, task conditioning, adaptive branch gating, prototype shrinkage, and discriminative supervision each contribute to performance. These results suggest that few-shot adaptation benefits not only from deciding which parameters to update, but also from modeling how representations should move through a geometry matched to the structure of the downstream task.

LLMs are increasingly used to make or support high-stakes decisions under uncertainty, where alignment depends not only on factual accuracy but on how models weigh tradeoffs between different outcomes. We present an empirical pipeline for estimating the implied preferences that an LLM's observed choices optimize: we elicit the model's probability distribution over unknowns along with the choice it would make for the decision task and then fit a discrete choice model to recover the cost function that best rationalizes the model's decisions. We show how this revealed-preference description allows rigorous evaluation of whether models behave in a consistently goal-directed way, whether they can verbalize a description of their objectives which matches their revealed decision policy, and whether prompting can reliably steer those policies to implement a user-specified cost function. We apply this evaluation across four medical diagnosis domains and multiple frontier and open-source models. We find that while many models have a nontrivial degree of internal coherence, they also have significant weaknesses in faithfully reporting or adopting preferences in response to user direction.

Large language models can generate useful code from natural language, but their outputs come without correctness guarantees. Verifiable code generation offers a path beyond testing by requiring models to produce not only executable code, but also formal specifications and machine-checkable proofs. Progress in this direction, however, is difficult to measure: existing benchmarks are often small, cover only part of the pipeline, lack ground-truth proofs or rigorous specification validation, or target verification settings far from mainstream software development. We present VeriContest, a benchmark of 1,006 competitive-programming problems from LeetCode and Codeforces for verifiable code generation in Rust with Verus. Each problem includes a natural language description, expert-validated formal specifications, judge-accepted Rust code, Verus-checked proofs, and positive and negative test suites. VeriContest is constructed through a three-phase pipeline that scales from manually verified seed problems to semi-automated expansion with human-in-the-loop review. To strengthen benchmark quality, we also use testing to validate postcondition completeness. VeriContest supports both isolated and compositional evaluation of specification, code, and proof generation, and end-to-end verified program synthesis. Evaluating ten state-of-the-art models reveals a sharp gap between ordinary coding and verifiable code generation: the strongest model reaches 97.51% on natural-language-to-code generation, but only 57.16% on specification generation, 13.82% on proof generation, and 6.76% end-to-end. These results identify proof and specification generation as the central bottlenecks for current models and establish VeriContest as a rigorous platform for evaluating and training future systems that generate code with machine-checkable correctness.

Independent Component Analysis (ICA) is a foundational tool for unsupervised representation learning, yet its high-dimensional theory remains largely limited to single-component recovery. We develop an asymptotically exact mean-field theory for multi-component online ICA, capturing the coupling induced by simultaneous learning and orthogonalization. In the high-dimensional limit, the joint empirical distribution of learned estimates and ground-truth components converges to a deterministic process, yielding a closed ODE system for the overlap matrix between learned directions and true components. This characterization reveals a genuinely multi-component, initialization-driven phase structure: a decoupled regime, where estimates align with distinct components and evolve nearly independently, and a competition regime, where overlapping initializations induce orthogonality-driven conflicts, slow reorientation, and delayed convergence. Our steady-state analysis gives explicit learnability boundaries and competition conditions linking step size, data moments, and initialization. These conditions show that larger higher-order moments and competition shrink the stable learning-rate window, increase convergence times, and predict a staircase phenomenon in which the number of recoverable components changes discretely with the learning rate. Experiments on synthetic data and hyperspectral remote sensing data validate the predicted trajectories and phase behavior.

The population dynamics of molecules, cells, and organisms are governed by a number of unknown forces. In the last decade, population dynamics have predominantly been modeled with Wasserstein gradient flows. However, since gradient flows minimize free energy, they fail to capture important dynamical properties, such as periodicity. In this work, we propose a change in perspective by considering dynamics that minimize a population-level action under a damped Wasserstein Lagrangian. By deriving the corresponding Hamiltonian equations of motion, we formalize Wasserstein Lagrangian Mechanics, a structured class of second-order dynamics that encompasses classical mechanics, quantum mechanics, and gradient flows. We then propose WLM as the first algorithm that learns these second-order dynamics from observed marginals, without specifying the Lagrangian. By directly learning the population mechanics, WLM can both forecast and interpolate unseen marginals, and outperforms existing gradient flow and flow matching methods across a wide range of dynamics, including vortex dynamics, embryonic development, and flocking.

The Gromov-Wasserstein (GW) problem provides a framework for aligning heterogeneous datasets by matching their intrinsic geometry, but its statistical and computational scaling remains an issue for high-dimensional problems. Slicing techniques offer an appealing route to scalability, but, unlike Wasserstein distances, GW problems do not generally admit closed-form solutions in one-dimension. We resolve this problem for the GW problem with inner product cost (IGW), propose a sliced IGW distance that enjoys a natural rotational invariance property, and comprehensively study its structural and computational properties. Numerical experiments validating our theory are presented, followed by applications to heterogeneous clustering of text data and language model representation comparison.

Neural scaling laws approximate a language model's loss as a power-law function of parameter count $N$ and token count $D$. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs at one or a few fixed tokens-per-parameter (TPP) ratios $k$, with $D = kN$. We show that this collinear design, combined with the empirically common near-equality of the exponents governing $N$ and $D$, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the $N$- and $D$-exponents. The scale coefficients become practically unidentifiable, with confidence intervals inflating by orders of magnitude, yielding a "sloppy" model whose extrapolations degrade sharply off the training ray. We prove this for four scaling-law formalisms and derive a closed-form TPP-diversity threshold that characterizes well-conditioned estimation to leading order. Empirically, in controlled experiments with 5M-77M-parameter models, non-collinear designs outperform collinear ones on held-out data with a 97.3% win rate across four laws and five corpora, and 98.7% in bfloat16. We further show the degeneracy is rooted in Jacobian geometry and is not an artifact of the loss function: any smooth objective whose Gauss-Newton weights are bounded above and away from zero inherits the same ill-conditioning.

Inductive biases influence the behavior and performance of sequential models. In this work, we study an underexplored inductive bias in sequential modeling: continuity in time. We ask a simple question: do models motivated by continuous-time formulations, such as state-space models, actually behave continuously in time, and does this translate into better performance on tasks with continuous temporal structure? To answer this, we formalize model continuity as convergence under temporal refinement, where a model is continuous if its predictions approach an underlying continuous trajectory as the temporal discretization is refined. We show that S4 exhibits stable continuous behavior, whereas S6 (the core of Mamba) can be more sensitive to input amplitude and selective dynamics, despite being derived from a continuous dynamical system. To study whether this distinction matters for learning, we also need a corresponding notion of task continuity. We therefore introduce a metric to quantify the continuity of datasets directly from their temporal structure. Across benchmarks, we find a clear empirical alignment between task continuity, model continuity, and model performance. Beyond an inductive bias, continuity also has practical consequences: we show that it enables a simple temporal subsampling strategy that improves both efficiency and performance.

Current LLM agents lack principled mechanisms for managing persistent memory across long interaction horizons. We present a biologically-grounded memory architecture comprising six cognitive mechanisms: (1) sleep-phase consolidation, (2) interference-based forgetting, (3) engram maturation, (4) reconsolidation upon retrieval, (5) entity knowledge graphs, and (6) hybrid multi-cue retrieval. Each mechanism addresses a specific failure mode of naive memory accumulation. We introduce a synthetic calibration methodology that derives all pipeline thresholds without benchmark data exposure, eliminating a common source of evaluation leakage. We evaluate on two benchmarks. First, a VSCode issue-tracking dataset (13K issues, 120K events) where deduplication-based consolidation achieves 97.2% retention precision with 58% store reduction (+21.8 pp over baseline). Second, the LongMemEval personal-chat benchmark where we conduct the first streaming M-tier evaluation (475 sessions, ~540K unique turns). At a 200K-token context budget, our pipeline matches raw retrieval accuracy (70.1% vs. 71.2%, overlapping 95% CI) while exposing a tunable accuracy/store-size operating curve. At S-tier scale (50 sessions), dedup-based consolidation yields a +13.3 pp improvement in preference recall.

Modern deep learning treats neural networks primarily as endpoint functions from inputs to outputs. Inspired by the shift from force to geometry in physics, we ask whether a network should instead be understood through the geometry of its internal propagation. We define a neural propagation field as the collection of hidden-state trajectories and local Jacobian operators across depth. Endpoint losses constrain only the boundary behavior of this field, leaving its interior geometry underdetermined. We show that endpoint-equivalent models can differ by orders of magnitude in trajectory and Jacobian structure, and introduce observable field metrics such as path sensitivity, solver consistency, and trajectory/Jacobian retention. In controlled teacher-flow and PDE systems, endpoint fitting fails to recover the underlying propagation law. In real multi-path tasks, field-aware objectives improve unseen-path generalization, OOD robustness, and calibration when aligned with the observation structure, but can collapse when over-constrained. In continual learning, field-preservation regularization complements replay and distillation: on Split CIFAR-100, DER++ with field preservation improves average accuracy, backward transfer, and field-retention metrics. These results identify propagation-field quality as a measurable and trainable property of neural networks beyond endpoint performance.

While LLM-based agents excel at planning and executing long action sequences, their execution often remains inconsistent across trials, limiting reliability. Consolidating agent consistency requires distilling trial-error trajectories into reusable skills that preserve task-relevant invariants while discarding trajectory-specific noise. However, in multimodal settings, the key challenge is not only that useful invariants are distributed across vision and language information, but that different modalities support different kinds of reusable skill content: while some skills are verbalizable and interpretable, others reside in perceptual evidence beyond text. Text-only skills may lose perceptual cues, whereas storing text and perception naively introduces redundancy and noise. Existing inference-time methods, such as self-consistency, improve reliability through costly multi-sample decoding, while internalization strategies lack a way to separate verbalizable skill content from residual perceptual information. To address this, we introduce Conditional Multimodal Information Bottleneck (CMIB), a method for multimodal skill construction. CMIB begins with a joint bottleneck over multimodal skills and derives an exact sequential decomposition: (1) a text-stage bottleneck distilling interpretable skill cards, and (2) a conditional multimodal bottleneck compressing only residual information in perception that remains predictive beyond text. Unlike naive two-stream formulations, CMIB explicitly conditions the multimodal latent on the text skill, thus structurally reducing cross-modal redundancy and enabling independent control over textual and perceptual compression. We instantiate CMIB with a variational objective that makes its conditional decomposition tractable to optimize, yielding reusable multimodal skills that improve execution stability without incurring multi-sample inference overhead.

Post-disaster situational awareness relies heavily on understanding both the extent and the volume of floodwaters. While 2D semantic segmentation provides accurate flood masking, it lacks the vertical dimension required to assess navigability and structural risk. This paper presents a geometric "Water Surface Elevation" approach for estimating flood depth from monocular aerial imagery. Our pipeline utilizes Mask2Former, a state-of-the-art transformer-based segmentation model, to generate precise 2D flood masks. These masks are fused with Digital Elevation Models (DEMs) to identify the water-land boundary, calculate a global water surface elevation ($Z_{water}$), and compute per-pixel depth based on the principle of local hydrostatic equilibrium. We evaluate this workflow using the FloodNet and CRASAR-U-DROIDS datasets, demonstrating how high-performance segmentation can be leveraged to extract 3D volumetric data from 2D imagery without the latency of hydrodynamic simulations.

LLM-based evolution has emerged as a promising way to improve agents by refining non-parametric artifacts, but its wall-clock cost remains a major bottleneck. We identify that this cost comes from synchronized stage execution and imbalance inside each LLM-heavy stage. We present FlashEvolve, an efficient framework that replaces synchronized execution with asynchronous workers and queues, allowing different stages and steps to overlap. To handle data staleness introduced by asynchrony, FlashEvolve tracks artifact versions and applies different policies to update, discard, or patch stale artifacts. Unlike weight-space staleness in asynchronous RL, language-space staleness is inspectable and repairable: a stale artifact is not just delayed work, but readable evidence that the LLM can reflect on, revise, and turn into useful evolution signal. FlashEvolve further improves throughput and token efficiency with speculative stage completion and adaptive workflow control. On GEPA workloads, FlashEvolve improves proposal throughput by $3.5\times$ on local vLLM and $4.9\times$ on API serving over synchronous GEPA. The same design also applies to ACE and Meta-Harness.

Learning from scarce labeled data with a larger pool of unlabeled samples, known as semi-supervised few-shot learning (SS-FSL), remains critical for applications involving tabular data in domains like medicine, finance, and science. The existing SS-FSL methods often rely on self-supervised learning (SSL) frameworks developed for vision or language, which assume the availability of a natural form of data augmentations. For tabular data, defining meaningful augmentations is non-trivial and can easily distort semantics, limiting the effectiveness of conventional SSL. In this work, we rethink SSL for tabular data and propose Separated-at-Birth Alignment (SeBA), a joint-embedding framework for SS-FSL that eliminates the dependence on augmentations. Our core idea is to separate the data into two independent, but complementary views and align the representations of one view to mirror the nearest-neighbor correspondence of the data in the second view. Our experimental evaluation supported by a theoretical analysis justifies that SeBA generates an output space, which improves the feature-label relationship. An experimental study conducted in various benchmark datasets demonstrates that SeBA achieves the state-of-the-art performance in the majority of cases, opening a new avenue for SS-FSL paradigm in the domain of tabular data.

We describe an approach for estimating the statistical risk of deep networks that contain a mix of learned and known operators. Building on the maximal training error bounds previously established for known operator learning, we derive a deep risk estimator that connects the expected error of a layered network to the size of the training sample. The estimator decomposes the total risk into a sum over learned layers; every known operator contributes zero to this sum, while every learned layer adds an approximation term inspired by Barron's classic work and an estimation term that decreases with the number of training samples. We are able to show that the bound shrinks whenever a learned layer is replaced by a known operator and that the corresponding sample requirement scales with the number of trainable parameters of the layer that is replaced. As an application, we use computed tomography as an example and compare an operator-aware filtered backprojection network with a fully connected substitute that collapses the entire reconstruction pipeline into a single learned dense matrix. The predicted parameter ratio coincides with the structural sparsity that the analytic decomposition into a circulant filter and a sparse backprojection exposes. We confirm the predicted scaling on CPU at small image scale and on GPU at medium image scale, all on the same scaling law. Beyond CT reconstruction, the estimator applies to physics-informed neural networks that hardcode a known physical operation in its architecture, and we expect the result to be of interest for a broad community working on operator-aware deep learning. Calibrating the per-layer constants on each sweep yields a bound that tracks the empirical test MSE within a factor of two at every training-set size, so the estimator can be inverted to predict how many training samples are required to reach a target error.

Unlike standard expected-return Reinforcement Learning (RL), Distributional RL (DRL) models the full return distribution, making it better-suited for uncertainty-aware and risk-sensitive decision-making. Conditional Flow Matching (CFM) critics have recently attracted attention for modelling continuous, multi-modal return distributions. Despite this interest, there remains a substantial metric mismatch: DRL theory relies on the distributional Bellman operator being contractive in the $p$-Wasserstein distance, yet existing CFM critics are trained with arbitrary source-target couplings, so their flow-matching losses are not Wasserstein-aligned surrogates for matching Bellman target return distributions. In this work, we address this mismatch by proposing FlowIQN, a CFM critic that sorts source and Bellman target samples within each mini-batch to approximate the monotone optimal transport coupling, replacing arbitrary pairings with quantile-aligned flow paths. We prove that the loss of our quantile-coupled CFM critic yields a Wasserstein-aligned approximate projection compatible with the foundations of DRL. To our knowledge, FlowIQN is the first flow-matching distributional critic with an explicit Wasserstein-aligned projection guarantee. We further extend FlowIQN with shortcut models for efficient inference. Empirical results show that FlowIQN improves Wasserstein return-distribution accuracy over other CFM critics. It also yields competitive performance on offline RL benchmarks across multiple policy extraction methods, providing a theoretically grounded CFM critic that is readily compatible with DRL pipelines. Code: https://github.com/ori-goals/flowIQN.

Safety alignment in language models operates through two mechanistically distinct systems: refusal neurons that gate whether harmful knowledge is expressed, and concept neurons that encode the harmful knowledge itself. By targeting a single neuron in each system, we demonstrate both directions of failure – bypassing safety on explicit harmful requests via suppression, and inducing harmful content from innocent prompts via amplification – across seven models spanning two families and 1.7B to 70B parameters, without any training or prompt engineering. Our findings suggest that safety alignment is not robustly distributed across model weights but is mediated by individual neurons that are each causally sufficient to gate refusal behavior – suppressing any one of the identified refusal neurons bypasses safety alignment across diverse harmful requests.

Temporally contrastive representation learning induces a latent structure capable of reducing long-horizon planning to inference in a low-dimensional linear system. However, existing contrastive planning work learns a single latent geometry which cannot distinguish multiple valid behaviors trading task efficiency against risk exposure for the same start-goal query. We introduce MoMo, a preference-conditioned contrastive planner allowing a scalar user preference to continuously modulate plan conservativeness at inference time, without retraining. MoMo learns a joint conditioning of the representation geometry and latent prediction operator via Feature-Wise Linear Modulation and low-rank neural modulation, respectively. We show that our formulation preserves the probability density ratio encoded in the representation space that is required for inference-driven contrastive planning, further retaining its inference-time efficiency. Across six environments, MoMo smoothly adapts plan safety according to user preferences, yielding improved temporal and preferential consistency over state augmentation baselines.

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly conservative decisions, whereas small sets risk excluding the true outcome. Recent data-driven approaches, particularly conformal prediction, offer finite-sample validity guarantees but remain largely task-agnostic, ignoring the downstream decision structure. In this paper, we propose a decision-aware conformal framework that learns uncertainty sets tailored to robust optimization objectives. Our approach parameterizes a flexible family of polyhedral sets via data-driven hyperplanes and learns their geometry by directly minimizing the induced robust loss, while preserving statistical validity through conformal calibration. To correct for data-dependent selection, we incorporate a re-calibration step on an independent dataset to restore coverage. The resulting sets capture directional and anisotropic uncertainty aligned with the decision objective while remaining computationally tractable. We provide finite-sample coverage guarantees and bounds on the sub-optimality gap to an oracle decision. This work bridges the gap between statistical validity and decision optimality, providing a principled framework for data-driven robust optimization.

We study the long-context limit of softmax self-attention with a fixed query and a random context of $n$ i.i.d. keys on the sphere with the intrinsic dimension of the key distribution held fixed, viewing the inverse temperature $\beta_n$ as the scaling parameter that decides whether attention degenerates into uniform averaging or collapses onto the single closest key. We show that the critical scale at which selectivity emerges is determined by the local exponent of the distance-to-query distribution near zero rather than by global features of the context, and scales like $\beta_n^\ast \asymp n^{2/(d-1)}$ for uniform keys on $\mathbb{S}^{d-1}$. Furthermore, we characterize the limiting laws of the ordered attention weights and of the attention output across all regimes of $\beta_n$: a subcritical regime in which the output reduces to a local average around $q$ with explicit deterministic bias and Gaussian fluctuations; a critical regime in which a finite collection of nearest keys retains macroscopic mass without single-key collapse; and a supercritical regime in which all mass concentrates on the closest key. Of notable interest is the subcritical case with identity value matrix where the attention map approximately implements a backward heat equation.

We introduce MathConstraint, a hard, adaptive benchmark for evaluating the combinatorial reasoning capabilities of LLMs. We combine constraint satisfaction problems with rigorous solver-based verification and design an adaptive generator to create instances that remain challenging as the LLMs improve in their reasoning capabilities. Unlike existing benchmarks that quickly saturate on fixed datasets or use LLM-as-a-judge for checking solutions,MathConstraint uses parameterized problem types that enable scalable generation of arbitrarily difficult and automatically verifiable instances. We release MathConstraint-Easy ($266$ instances), on which frontier models achieve between $72.6\%$ (gemini-3.1-flash-lite) and $87.6\%$ (gpt-5.5) accuracy, and MathConstraint ($329$ instances) on which the same models drop to between $18.5\%$ (claude-4.6-sonnet) and $66.9\%$ (gpt-5.5) accuracy, demonstrating the resilience of our benchmark generator against rapid progress in LLM reasoning capabilities. We evaluate 12 frontier and open-weight models with and without access to a sandboxed Python environment that includes generic SAT/SMT solvers. Tool access roughly doubles frontier accuracy on MathConstraint (mean $+28$pp; up to $+52$pp for claude-4.6-sonnet). Further, halving the tool-call budget from $8$ to $4$ rounds erases up to $37$ points – a sensitivity that most single-budget benchmarks miss. We release the generator, dataset, and evaluation harness as a robust environment for studying combinatorial reasoning and tool-use behavior under adversarially-tunable difficulty.

Deep learning and large public datasets have recently catalyzed the proliferation of AI models for processing brain recordings. However, systematically evaluating these models remains a challenge: not only do the preprocessing pipelines, training and finetuning approaches largely vary across studies, but their downstream evaluation is often limited to small sets of tasks and/or datasets. Here, we present NeuralBench: a unified framework for benchmarking AI models of brain activity. We accompany this framework with NeuralBench-EEG v1.0 – a large EEG benchmark that includes 36 electroencephalography (EEG) tasks and 14 deep learning architectures, and is evaluated on 94 datasets accessed through a standardized interface. This first EEG-focused release already highlights two main findings. First, current foundation models only marginally outperform task-specific models. Second, a large set of tasks (e.g. cognitive decoding, clinical predictions) remain highly challenging, even for the best models. Critically, NeuralBench is designed for the integration of new tasks, datasets, models, and neuroimaging modalities, as illustrated by preliminary extensions to MEG and fMRI datasets and models. Through this white paper, we invite the community to expand this open-source framework and work together toward a unified benchmarking standard for neuroimaging models.

We develop a unified Lyapunov-integral quadratic constraint (IQC) framework for establishing uniform stability of first-order accelerated optimization algorithms in the $\beta$-smooth and $\gamma$-strongly convex regime. Classical analyses of uniform stability, such as the work of Hardt, Recht, and Singer for stochastic gradient descent (SGD), rely on direct coupling arguments and case-by-case control of iterate differences under random sampling. Extending such arguments to accelerated methods, such as Nesterov Accelerated Gradient (NAG), is complicated by the presence of higher-order state dynamics induced by momentum. We first extend this classical approach with the use of Lyapunov functions to provide a uniform stability bound for smooth quadratic NAG, and supplement this result with small-scale numerical experiments. We then extend this framework by modeling first-order accelerated optimizers as Lur'e-type feedback interconnections between a linear dynamical system and a (non-linear) gradient operator. $\beta$-Smoothness and $\gamma$-strong convexity are encoded a sector IQC inequality. Under this representation, uniform stability is certified via the existence of a quadratic Lyapunov function satisfying a finite-dimensional linear matrix inequality (LMI) in the form of a feasibility problem, which can be solved via semi-definite programming (SDP). We instantiate this framework for NAG and show how classical uniform stability bounds can be recovered via this framework. These results underscore a structural connection between optimization dynamics and robust control theory, providing a modular methodology for reliable and reproducible numerical certification of uniform stability and generalization behavior of first-order methods via convex optimization tools that is adaptable to increasingly complex optimization algorithms.

We introduce the Sinkhorn treatment effect, an entropic optimal transport measure of divergence between counterfactual distributions. Unlike classical quantities such as the average treatment effect, this measure captures differences across entire distributions. We analyze this divergence as a statistical functional and show it can be written as a smooth transformation of counterfactual mean embeddings with an appropriate kernel. This characterization allows us to establish first-order pathwise differentiability in general, and second-order pathwise differentiability under the null hypothesis of equal counterfactual distributions. Leveraging this smoothness, we construct debiased estimators and use them to obtain asymptotically valid tests for distributional treatment effects with a fixed entropic regularization parameter. Because the power of the test depends on this unknown parameter, we further propose an aggregated test that combines evidence across a grid of regularization choices. Experiments on simulated and image data demonstrate the practical advantages of our estimator and testing procedure.

Automated ICD-10 coding from clinical discharge summaries requires models that are both accurate on long-tailed multi-label classification tasks and interpretable to clinicians. Concept Bottleneck Models (CBMs) offer a principled framework for interpretability by routing predictions through human-interpretable concepts, but this transparency often comes at a cost: compressing rich clinical text representations into a narrow concept layer can restrict gradient flow and limit predictive capacity. We present ShifaMind, a concept-grounded architecture built around a Multiplicative Concept Bottleneck (MCB), which changes the form, rather than the width, of the bottleneck. Instead of projecting through a narrow concept layer, ShifaMind uses a learned multiplicative gate over a concept-grounded representation while retaining a scalar concept interface for inspection. On MIMIC-IV top-50 ICD-10 coding, ShifaMind achieves performance competitive with LAAT, the strongest baseline, across F1, AUC, and ranking metrics, while outperforming five additional ICD-coding baselines and providing concept-mediated explanations. Its substantial gains over a capacity-matched Vanilla CBM in both predictive performance and interpretability-oriented metrics highlight the importance of the bottleneck design.

We study how to allocate inference-time compute for competitive programming under fixed budgets. Evaluating 216 Codeforces problems across Divisions 1-3, we compare agent-based reasoning with repeated independent sampling (k-shot) as a function of both cost and number of model calls. Across models and difficulty levels, k-shot consistently achieves a better accuracy-cost and accuracy-query tradeoff. This gap persists despite prompt caching in agent frameworks, indicating lower per-call effectiveness. Our results show that, for self-contained algorithmic tasks, independent exploration can outperform deeper agentic reasoning under realistic resource constraints. We also provide a budget-allocation analysis when the inference budget is fixed, and prove that a cost-optimal solver minimizes the principled metric log failure likelihood per dollar.

In this paper, we study in-context kernel ridge regression (KRR) with Gaussian kernels and show, both theoretically and empirically, that a standard softmax-attention transformer can approximate the KRR predictor during its forward pass. Under bounded-data assumptions, we construct a single-head transformer whose forward pass approximately implements preconditioned Richardson iteration on the associated kernel system. The construction uses $O(\log(1/\epsilon))$ blocks and MLP width $O(\sqrt{N/\epsilon})$ to achieve $\epsilon$-accurate prediction for prompts of length $N$. Our construction reveals a functional decomposition within the transformer architecture: softmax attention produces a row-normalized Gaussian-kernel operator needed for cross-token interactions, while MLP layers act locally to approximate the intra-token scalar arithmetic required by the update. Empirically, we train GPT-2-style transformers on Gaussian-process regression tasks and observe that they progressively align with the exact Gaussian KRR estimator across depth in terms of both prediction error and induced weights, with ablations further supporting this trend. Comparisons with classical KRR solvers also show that deeper layers align with later solver iterates. Together, we empirically demonstrate that the pretrained transformers exhibit progressive refinement toward exact Gaussian KRR across depth, and theoretically establish inexact preconditioned Richardson iteration as a concrete mechanism for approximating this predictor within an explicitly constructed softmax-attention transformer.

Local LLM-based coding agents increasingly work in settings where correctness is earned through execution feedback, persistent state, and bounded repair, not through a single fluent answer. Static retrieval, long-context prompting, self-refinement, execution-feedback repair, and reinforcement learning over model weights each address part of this setting, but they do not jointly provide validation-grounded episodic memory, adaptive retrieval-action selection, delayed credit assignment, and structural skill reuse around a frozen local model. We introduce PYTHALAB-MERA, a lightweight external controller for local validation-conditioned code generation. The frozen language model proposes complete source files; the controller decides which memory records and AST-derived skills should enter the next prompt, validates each candidate through a fail-fast pipeline, converts validation outcomes into bounded shaped rewards, and propagates delayed credit through TD(lambda)-style eligibility traces. We evaluate the implementation as a local CLI artifact on reinforcement-learning coding tasks with strict validation gates. In the measured hard RL setting with three tasks, three repetitions, and a three-attempt budget, PYTHALAB-MERA passed 8/9 strict validations; the self-refinement baseline and the investigated GRACE extension each passed 0/9. These results support a deliberately bounded claim: in this recorded setting, the external memory-and-retrieval controller improved validation success. They do not establish general-purpose code synthesis, state-of-the-art performance, formal program correctness, or formal safety.

Large language models show promise for automated CUDA programming, however even the strongest coding models (e.g., Claude-Opus-4.6) may still fall short of expert-level, architecture-aware optimization. We introduce CUDAHercules, a benchmark that evaluates generated CUDA against end-to-end human-expert SOTA systems. It spans single kernels, module-level operators, full applications, and unsolved challenge tasks across Ampere, Hopper, and Blackwell GPUs, with end-to-end tasks gated by domain-specific semantic validators. Evaluating models such as Claude-Opus-4.6 and GPT-5.4 shows a large gap between runnable CUDA and expert CUDA engineering: models often compile and pass tests, but rarely recover the optimization strategies needed to match expert performance. Application semantics further reduce success, and iterative or tool-augmented feedback can improve correctness while drifting toward slow fallback implementations. These results show that automated CUDA programming remains far from fully solved and requires stronger hardware reasoning, better tool use, and training objectives that connect code understanding to hardware architecture-grounded intelligence.