Papers

Relational Prior-Data Fitted Networks (PFNs) such as RDB-PFN approximate Bayesian inference over multi-table relational databases by pretraining on millions of synthetic tasks. We investigate three intertwined questions about this paradigm. First, can a structurally different synthetic generator PluRel substitute for RDB-PFN's prior? Second, how much does the order in which synthetic data is presented to the PFN affect downstream performance? Third, how much relational reasoning can a PFN acquire from single-table synthetic pretraining alone, before any relational data is introduced? Using PluRel as the sole synthetic data source across all experiments, we find: (i) a progressive single-table curriculum that gradually widens schema complexity from 7 to 17 columns reaches 0.703 average ROC-AUC on the 23-task tabular benchmark using only approximately 13,300 synthetic tables (approximately 45x fewer single-table datasets than RDB-PFN's reported warm-up recipe), while the same data trained all-at-once collapses to 0.541 ROC-AUC; (ii) a relational curriculum trained from scratch on only approximately 5,500 PluRel databases reaches 0.638 average ROC-AUC on the 19-task RelBench/4DBInfer benchmark, recovering 88% of RDB-PFN's reported performance with approximately 220x less relational synthetic data; and (iii) the single-table curriculum model, evaluated directly on the relational benchmark without any relational adaptation, achieves 0.631, nearly matching the dedicated relational pipeline. Together, these findings suggest that curriculum design and synthetic data diversity may matter more for relational PFN pretraining than the specific relational generator or raw synthetic scale alone.

Differentially private (DP) training of text-conditioned generative models suffers a utility cliff at strong privacy. We revisit this problem through the geometry of rectified flows: along the straight interpolation between noise and data, the Bayes-optimal velocity is governed to leading order at the noise end by a few class-conditional moments, and increasingly sample-specific structure matters toward the data end. StraightDP exploits this heterogeneity end to end. A small budget share releases whitened class-conditional moments once, to be distilled into the weights or injected at sampling time. The rest is spent by pre-declared DP-SGD toward the data end, beyond the moments' reach. At $\varepsilon=1$ on MNIST, the released moments alone already attain $0.76$ downstream accuracy with prototype-like samples and an FID of $237$, and uniform DP-SGD attains $0.21$. The pipeline built on the release reaches $0.81$ accuracy at FID $56$ in a public latent space. Constraining per-token stream norms of the multimodal backbone leaves the pretraining loss unchanged yet improves downstream accuracy in the extreme-noise pixel-space regime, and its accuracy effect becomes monotonically more favorable as privacy strengthens. The released moments also port to frozen SD3-medium, where sampling-time injection beats DP-LoRA training at a fraction of the budget.

Accurate prediction of lithium-ion battery state of health (SOH) is essential for reliable energy storage operation. However, purely data-driven models may generalize poorly across cycling protocols and produce physically implausible behavior during long-term extrapolation. We developed a physics-informed differentiable degradation modeling framework (PiDDM) for battery SOH prediction. PiDDM incorporates empirical Arrhenius degradation kinetics associated with solid electrolyte interphase growth and loss of lithium inventory into the training objective, encouraging physically consistent capacity fade under diverse operating conditions. The framework was evaluated using a public dataset of 55 batteries cycled under six operating protocols. PiDDM achieved the lowest average prediction error among the evaluated models and substantially reduced mean squared error relative to a multilayer perceptron and a baseline physics-informed neural network. For extrapolation, the models were trained on the first 90% of each battery's cycle life and evaluated on the unseen final 10%. PiDDM captured accelerated end-of-life degradation while avoiding the nonphysical capacity regeneration produced by the baseline models. These results show that incorporating degradation physics into neural network training improves predictive accuracy and physical consistency, providing a promising approach for practical battery health monitoring.

Postoperative adverse events, including mortality and morbidity, remain a major global burden, many of which are preventable through early identification of high-risk patients and targeted perioperative care. Accurate risk stratification is therefore essential. With the growing availability of large-scale electronic health records (EHRs), machine learning (ML) provides a data-driven approach to model complex clinical patterns. However, existing studies vary widely in design, and methodological practices remain fragmented. This scoping review characterizes ML pipelines for surgical risk stratification and outcome prediction using EHR data. We reviewed 190 studies covering the ML workflow, including data preprocessing, algorithm selection, model evaluation, and explainability. Most studies relied on single-center private datasets with limited data modalities, while the scarcity of open-access surgical datasets constrained reproducibility and generalizability. Reporting of key preprocessing steps, including missing data handling, feature selection, and class imbalance, was often incomplete. Conventional ML models and simple neural networks predominated, whereas deep learning and multimodal approaches remained uncommon. Benchmark datasets and standardized evaluation protocols were largely absent, hindering cross-study comparisons. Only about one-third of studies incorporated explainability methods. This review identifies methodological gaps limiting clinically robust postoperative ML tools and provides a structured reference to support more rigorous, reproducible, and clinically meaningful ML development for perioperative care.

While on-policy distillation (OPD) reduces exposure bias by training student language models on their own rollouts, early student errors in long-horizon agentic scenarios can lead to contexts unfamiliar to the teacher. To improve trajectory quality, recent work on agentic OPD introduces teacher intervention into training rollouts by switching the executor between the student and the teacher. However, existing methods determine how much teacher intervention is needed—but not when. To address this limitation, we propose DASH-OPD (Discrepancy-Aware Switching with Hysteresis for OPD), the first agentic OPD method to perform adaptive, bidirectional executor switching. At each turn, DASH-OPD measures teacher–student discrepancy using a mean log-likelihood ratio over action tokens. High student-to-teacher ratios on student turns serve as drift signals, while low teacher-to-student ratios on teacher turns serve as recovery signals. These signals are accumulated over multiple turns to form drift and recovery evidence, respectively. DASH-OPD switches executors when either type of evidence exceeds its corresponding switching threshold, introducing hysteresis that prevents rapid switching triggered by transient discrepancy fluctuations. Across three benchmarks and two student model scales, DASH-OPD outperforms five baselines in all 14 task-performance comparisons, while requiring the fewest interaction turns in nine of ten efficiency comparisons. Code, trained models, and training logs are available at https://github.com/Lucian1115/DASH-OPD

Federated learning of foundation models faces a fundamental resource-asymmetry challenge: the institutions holding the most valuable domain-specific data cannot host billion-parameter models. Existing heterogeneous federated approaches attempt to bridge this gap through parameter-efficient tuning, model pruning, or knowledge distillation, yet each trades away a critical property, whether full-model memory reduction, architectural self-containedness, or representational fidelity, leaving the core tension unresolved. We propose FedSLM, a parameter-centric framework for federated fine-tuning with heterogeneous compressed clients. FedSLM uses SVD-based decomposition to produce self-contained client models, whose low-rank subspaces form nested manifolds that are structurally compatible for aggregation. It then applies a two-stage protocol that synchronizes lightweight adapters within compression groups and fuses full-rank reconstructions across groups via structural alignment. Finally, a weak-to-strong elicitation step with auxiliary confidence loss transfers the aggregated knowledge to the full-scale server, while an explicit bias–variance trade-off mitigates compression artifacts. We provide theoretical guarantees for adapter-level aggregation, subspace-alignment bounds for cross-group fusion, and a characterization of how the confidence loss mitigates weak-supervision noise. Experiments on natural language and vision–language benchmarks show that FedSLM outperforms existing federated baselines under both IID and non-IID partitions, while client models operate at roughly 50% of the GPU memory required by the full model.

Police crash narratives contain information that may supplement structured crash databases, but manual review is labor-intensive and it remains unclear how well large language models (LLMs) reproduce official crash coding. This study benchmarked six frontier LLMs by comparing narrative-derived crash attribute codes with corresponding fields in the Arkansas fatal-crash database. The analysis linked 5,587 fatal-crash narratives with 5,889 structured crash records from Arkansas (2015-2025), yielding 4,194 matched crashes. Six LLMs were evaluated using an identical zero-shot prompt to code crash manner, non-motorist relation, intersection type, work-zone relation, roadway surface condition, and light condition. Performance was evaluated using agreement, macro-averaged F1 score, Cohen's kappa, coverage, selective agreement, and comparisons with always-majority, always-Unknown, and keyword-rule baselines. Repeated-measures analyses and a generalized estimating equations model assessed differences among models and attributes. GPT-5.5 High achieved the highest agreement among the evaluated LLMs, but the always-majority baseline produced higher raw agreement and the keyword-rule baseline achieved macro-averaged F1 score and Cohen's kappa comparable to the best-performing LLM. Agreement was highest for non-motorist relation and crash manner and lowest for light condition, roadway surface condition, and work-zone relation. Differences across crash attributes exceeded differences across models. These results provide a benchmark for evaluating LLM-based crash coding and show that deployment should be evaluated on an attribute-specific basis using transparent baselines and human review.

Multi-agent systems (MAS) are increasingly deployed to solve complex tasks. In case of incorrect or unsatisfactory outputs, users have to manually locate agent mistakes by inspecting agent trajectories (i.e., failure attribution) and provide feedback to refine the outputs (i.e., repair). Despite some recent work in MAS failure attribution, automated mechanisms to recover from such mistakes remain largely unexplored. To bridge this gap, we propose MARS, a search-based framework that formulates MAS repair as a Monte Carlo Tree Search (MCTS) process and navigates the vast space of potential repairs via diagnosis-guided expansion with taxonomy-augmented evaluation. Unlike standard MCTS, which evaluates a complete simulation via full rollout, MARS evaluates the agent trajectory using partial rollout to reduce token consumption. Furthermore, we introduce StateMAS, a large-scale MAS repair benchmark with 1,310 replayable multi-agent failure trajectories spanning four types of agent architectures and four LLM backbones. Experiments on StateMAS demonstrate that MARS consistently outperforms state-of-the-art methods, achieving an absolute improvement from 3.0% to 12.1% across all settings, while maintaining a comparable token consumption cost. The ablation study further confirms that taxonomy-augmented evaluation and diagnosis-guided expansion are critical to achieving these performance gains.

Standard model comparison is global, aggregating losses across the covariate space to declare a single winner. This can obscure heterogeneous performance, where different models are preferable in different regions. We introduce conformalized local model comparison, a split-sample framework for constructing calibrated local best-model maps. Given a model comparison score, such as the difference between two squared losses, the method uses three disjoint splits to fit competing models, estimate local centers and scales from out-of-sample scores, and conformally calibrate residual uncertainty. At a target point, the procedure declares a local winner only when a one-sided conformal bound excludes a tie, with the score's sign determining the favored model. We prove finite-sample marginal control for one-sided erroneous declarations on the realized future comparison score, establish pointwise consistency of the localized mean-score estimator away from tie boundaries, show that aggregate comparison can disagree sharply with the prevalence of local superiority, and derive a squared-loss bias–variance decomposition that clarifies how model structure affects local wins. Synthetic and real-data experiments show that the method recovers heterogeneous winner regions, abstains under uncertainty, and yields higher conditional gain than global selection.

State-of-the-art neural network verifiers use the branch-and-bound procedure as their core solving mechanism. We introduce an inprocessing framework for neural network verification driven by the lookahead procedure. Under this framework, lookahead derives new lemmas over the phases of unstable ReLUs, which are collected into an implication graph that is used to prune the search space and vivify boolean cuts. We instantiate the framework in two state-of-the-art verifiers, Marabou and $\alpha$-$\beta$-CROWN, and demonstrate that it improves performance in both, proving up to 34% more instances unsatisfiable.

Fractional scientific machine learning requires numerical operators that can be differentiated, batched, accelerated, and composed with neural networks. When the dominant linear fractional evolution is known through a Mittag-Leffler propagator, repeatedly reconstructing that response with a history solver or relearning it from data is unnecessary. We present DFSC, a PyTorch environment organized around the Mittag-Leffler Spectral Layer (MLSL). The layer separates known fractional propagation from data-driven corrections, so neural modules learn only unresolved dynamics while fractional orders and residual-network parameters are optimized jointly. Its adaptive algorithm increases special-function truncation depth or Lanczos dimension until successive differentiable evaluations satisfy a requested tolerance. In the negative-real alternating-series regime, DFSC additionally returns a certified first-omitted-term bound; outside that regime it explicitly labels estimates as empirical. DFSC supports dense, sparse, matrix-free, self-adjoint, generalized, and controlled complex operator paths; trainable fractional orders; direct inverse problems; residual neural composition; and CPU/GPU execution. The certified series bound covers all 59 eligible reference cases, with median bound/error effectivity 1.246 for resolved errors. Reusing a prepared batched Lanczos basis gives identical fixed-path values and reduces repeated-query time by 4.61–7.11 times on CPU and 13.07–16.22 times on an RTX 5070, excluding one-time preparation. A 27-case inverse matrix finds full-rank local curvature throughout, while remaining explicitly model-conditional. External solver and mixed real-data results support DFSC as an error-aware optional primitive for matched fractional structure, rather than a general replacement for fractional solvers or neural models.

Sparse identification of nonlinear dynamics (SINDy) and PDE functional identification (PDE-FIND) recover parsimonious ordinary and partial differential equations (ODEs and PDEs) from data. However, sparse and noisy temporal measurements can make derivative estimates unreliable. To address this problem, we evaluate Koopman-based upsampling techniques implemented with dynamic mode decomposition (DMD), extended DMD (EDMD), and optimized DMD. These methods learn finite-dimensional approximations of Koopman evolution on selected observables and are used to interpolate and denoise snapshots inside the observed time window before derivative estimation and sparse regression. The empirical benchmark comprises two ODE systems, Lorenz-63 and Van der Pol, and three periodic PDE systems, Burgers, Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP), and linear advection-diffusion, over sparse and noisy sampling regimes. Polynomial EDMD gives the strongest ODE results, especially in coefficient accuracy. The PDE results are system-dependent: low-rank DMD-assisted reconstructions improve Burgers and advection-diffusion discovery, while the raw baseline (without upsampling) remains competitive for the Fisher-KPP data. A comparison against linear and smoothing-spline interpolation techniques shows that the selected Koopman-based preprocessors provide overall performance gains over these non-dynamical alternatives. We also demonstrate that DMD-assisted upsampling can stabilize Pareto-based non-oracle support-size selection. Overall, Koopman-based upsampling is best viewed as a dynamics-aware preprocessing step that can reduce derivative-estimation error when its observable representation and low-rank structure are appropriate for the data.

Modern opaque AI models prize performance over interpretability, which makes testing difficult. However, formal statistical tests conducted on a model's embedding space can provide robust characterizations of semantic structure, concept separation, and knowledge graph alignment. Model developers would benefit from a model comparison technique that leverages human-curated knowledge structures to test alignment. The scale of the input space for even relatively simple tasks motivates the need for alignment checks that augment standard outcome reasoning. This work develops and demonstrates a topology-based multi-modal alignment test to make deployment, selection, and comparison of opaque models more interpretable. These methods also offer an intuitive connection to possibility theory and a unified decision theoretic framework from data to deployment.

Multimodal information can improve the accuracy of click-through rate (CTR) prediction and effectively alleviate item cold-start and long-tail problems. Recent studies commonly discretize pretrained multimodal embeddings into semantic identifiers (SIDs), allowing the model to learn task-specific semantic representations for recommendation. However, existing methods still provide limited gains due to two major limitations. First, codebook assignment fails to preserve semantic relevance and discards fine-grained continuous signals in the original embedding space. Second, the residual code paths are highly dependent on prefix codes, which limits the effective representational scalability of hierarchical identifiers. To address these issues, we propose PaletteID (PID), a prototype-based semantic identifier. Inspired by palette-based color composition, PID uses a compact set of representative prototype items as semantic anchors to bridge pretrained multimodal content space and recommendation models. Specifically, we first construct a prototype palette with Semantic Quality-Aware Determinantal Point Process (SQ-DPP), which jointly considers local content density and global semantic diversity. Then, for each target item, PID retrieves a sequence of semantically related prototypes and aggregates them into an informative PID representation, enabling rich and complementary semantic modeling. Extensive experiments on two public datasets demonstrate that PID consistently improves CTR prediction and yields larger gains for long-tail items. PID also produces more robust identifier assignments and provides more interpretable token semantics than existing residual SID methods.

High-fidelity radio fields are typically simulated for every scene–transmitter configuration or fitted separately to each scene, failing to exploit propagation structures shared across environments. We present Point2Radio, a foundation model that learns a transferable propagation prior from multiple environments. Given a material-aware point cloud and a transmitter (TX) setting, a common encoder produces a TX-conditioned scene representation that can be queried at arbitrary receiver (RX) locations. Task-specific query decoders map this representation to different radio quantities, e.g., three-dimensional (3D) path-gain (PG) fields and power angular spectra (PAS). At inference for a new scene, the model uses only a material-aware point cloud and transceiver queries, running in milliseconds on a single GPU without meshes or explicit path tracing. We evaluate PG prediction on a scene-disjoint split of a 337-scene corpus containing 86,272 TX-conditioned fields. Point2Radio achieves 0.871 dB mean absolute error (MAE), reducing error by 76.7% relative to a same-split UNet-style baseline. The same encoder also supports PAS prediction via a task-specific decoder. Experiments further show that light target-scene fine-tuning improves adaptation to a specific environment.

Many learning problems require representations that reconcile direct input, nearby structure, and broader context. In implicit neural layers, these influences are usually absorbed into a single fixed-point update, making it hard to identify what enters from the stimulus, what propagates locally, what comes from global context, and what is produced by solver dynamics. Here we introduce SILVA Networks, Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields. SILVA separates stimulus, local interaction, global interaction, damping, and readout inside one fixed-point architecture. The same template is instantiated for images, molecules, citation networks, and long-range graph benchmarks through domain-specific definitions of nodes, neighborhoods, and global summaries. Experiments and ablations show task-dependent roles for these terms: local interactions are load-bearing in the graph tasks, MNIST gains little from recurrence at the tested capacity, and the clearest global benefit appears in a long-range node-classification benchmark. SILVA therefore provides an implicit representation whose internal interaction dynamics can be trained, ablated, visualized, and diagnosed.

Graph Foundation Models (GFMs) have recently emerged as a promising paradigm for enabling knowledge transfer across diverse domains. Unlike traditional graph learning methods that are typically designed for in-domain settings, GFMs aim to learn transferable knowledge that can generalize to unseen graph domains. However, unlike language or visual data, graphs lack intrinsic and unified representation units, such as tokens in language and patches in vision, making it challenging to identify transferable knowledge units for building graph foundation models. Existing graph foundation models mainly focus on mitigating domain discrepancies through feature alignment and structure alignment, while overlooking the exploration of transferable knowledge units underlying graph data. Moreover, these methods generally rely on fixed propagation mechanisms during message passing, overlooking the heterogeneity in propagation patterns, as different edges may exhibit distinct propagation patterns for different feature dimensions. To address these limitations, we propose a Propagation-aware Graph Foundation Model (ProGFM), which regards the propagation relationships between edges and feature dimensions as transferable knowledge units. Through a propagation relationship prototype bank, ProGFM learns cross-domain transferable propagation knowledge, enabling adaptive information aggregation in unseen graph domains. Extensive experiments across various cross-domain transfer scenarios demonstrate that ProGFM possesses strong cross-domain knowledge transfer capability and exhibits superior generalization performance compared with existing methods.

Machine learning of Hamiltonian dynamics has driven growing interest in Hamiltonian neural networks (HNNs), which encode Hamilton's equations of motion into the learning architecture. Despite this progress, it remains unknown whether such networks can predict dynamical regimes absent from their training data, in particular the broad chaotic sea that emerges beyond the observed parameter interval. We address this question using a parameter-aware random-feature Hamiltonian neural network (RF-HNN). Trained using data from only a small number of control-parameter values at which invariant tori dominate, the RF-HNN predicts autonomous long-time dynamics at unseen parameter values where mixed phase space develops and chaotic regions expand, with no data from that regime used in training or model selection. The method is demonstrated across four two-degree-of-freedom Hamiltonian families, including the Hénon-Heiles system. Using Poincaré-section geometry and finite-time Lyapunov exponents, we show that the RF-HNN reproduces the breakup of regular structures and the emergence and growth of chaotic regions, whereas conventionally trained HNNs with the same Hamiltonian structure remain too regular. These results show that what decides parameter extrapolation is not Hamiltonian structure alone but how the fitted Hamiltonian continues in the control parameter. To our knowledge, this is the first demonstration that a learned Hamiltonian can qualitatively extrapolate from predominantly regular dynamics into a broad chaotic sea absent from training.

Contrastive learning is widely used for user modeling in large-scale recommender systems, where standard in-batch negatives implicitly assume universal exposure that any user can be shown any item. On local community platforms such as Karrot, however, exposure is geographically constrained; many user-item pairs are impossible by design yet still treated as negatives during training, diluting the contrastive learning signal. We address this impossible negatives problem and propose Region-Constrained Batch Sampling (RCBS), a simple yet effective batching method that constructs region-homogeneous mini-batches so that users are contrasted primarily against items they could feasibly see. By replacing impossible negatives with feasible ones, RCBS naturally introduces harder and more informative negatives under realistic exposure constraints. With offline evaluations and online A/B tests, we show that RCBS consistently improves user representation quality and consequently enhances home feed ranking, retrieval, and display ads ranking. The resulting user embeddings have been deployed in production across various applications.

Prompt tuning adapts vision–language models with few trainable parameters, but existing approaches trade off efficiency and adaptation: static textual prompts can overfit source classes, image-conditioned prompts add per-instance computation, and multimodal tuning modifies the visual branch. We propose VDA (Visual Distribution Anchoring), a training-free target adaptation framework that augments a frozen semantic classifier with class-level visual prototypes estimated offline from an unlabeled target pool. We first ask whether prototypes can be synthesized from class names. A text-to-centroid mapper reconstructs held-out source prototypes but fails under dataset shift because class names specify semantic identity, not target-domain appearance. An oracle analysis confirms that true target prototypes are highly discriminative. VDA therefore uses frozen semantic and domain-template classifiers to partition unlabeled target images into class-correlated groups. Confidence-ranked image features form normalized prototypes, fused with the semantic classifier using one global weight. Adaptation requires no target labels, target-side optimization, uniform class-prior assumption, iterative refinement, or test-query access, and yields a fixed, cacheable classifier. Controlled experiments show that class-specific partitioning drives gains and that visually local pseudo-label errors can remain useful despite being class-incorrect. Across ten ImageNet-to-target transfers, the same frozen design improves zero-shot CLIP, TCP, and MaPLe by 3.22, 3.39, and 3.35 points, respectively, improving nine of ten targets in every setting. Its visual correction further improves leakage-free PromptKD by 2.79 points, complementing zero-shot, source-prompted, multimodal-prompted, and target-distilled classifiers.

Adversarial training is one of the most effective defenses against adversarial attacks, yet the computational cost remains prohibitive at modern scales, especially for large language models (LLMs). While existing mitigation strategies, e.g., latent adversarial training (LAT), have been developed, they still incur a high computational cost. In this work, focusing on LLM-based classifiers, we investigate computation-efficient strategies to speed up LAT from two complementary perspectives: (1) Defense-side optimization: We explore representation fine-tuning (ReFT) within LAT, and reveal a potential issue if there is a mismatch on which tokens to apply ReFT and the attack. (2) Attack-side optimization: When computing adversarial attacks in each LAT iteration, we extract only the relevant circuits from the LLM to construct a lightweight surrogate model, avoiding the computation in the forward-backward passes through the full model during the attack generation. For both perspectives, we provide theoretical justifications and numerical evidence to illustrate the effectiveness of the proposed strategies. Compared to standard LAT with full fine-tuning, our method on average reduces per-step adversarial-training FLOPs by 29.6% while requiring only 0.0118% trainable parameters, at a moderate cost in robustness.

Branch and Bound (BaB) aims to achieve complete verification of neural networks by adaptively partitioning the problem and applying off-the-shelf verifiers to subproblems. Its problem-splitting history can be represented as a tree, where each subproblem corresponds to a child node. A key problem of BaB lies in searching for the verdict boundaries across all the paths that divide the verified and unverified subproblems. We observe that the existing BaB approach tackles this problem by solving each expensive subproblem sequentially along the tree path as its depth increases, requiring costly bounds propagation at every visited BaB tree node (i.e., subproblem), which is inefficient. To address this issue, we propose effective search approaches that leverage the monotonicity of each path to efficiently and precisely locate the verdict boundary by simultaneously splitting multiple activation functions (e.g., ReLU), rather than processing them one at a time as in the classical approach. Our approach performs an effective exponential search along each path, allowing us to skip many boundary-unrelated subproblems when identifying the verdict boundary. The enhanced version further improves this process by estimating the boundary's position using quantitative information obtained from subproblem solving. We perform experimental evaluation on commonly-used benchmarks to assess our proposed techniques, and compare them with recent BaB-based approaches.

Large language models (LLMs) are increasingly used to solve complex problems by searching over program space, offering a general paradigm for scientific problems that can be naturally represented and solved as programs. Despite recent progress, identifying effective optimization directions for a candidate program remains challenging. By analogy with automatic differentiation, existing methods typically guide the search using a textual “gradient”: a first-order update direction expressed as textual edits. Such gradients are inferred either from previously evaluated programs or from LLM-generated feedback on the implicit program-score mapping. However, these estimates become increasingly unreliable as the program–score mapping grows more complex, limiting their practical utility. We argue that explicit gradients are not essential for effective program optimization. Leveraging their prior knowledge, LLMs can propose plausible atomic edits directly from the current program, thereby enabling a zeroth-order optimization strategy. However, zeroth-order search suffers from a weakest-link effect: when a bundle of edits is accepted or rejected as a whole, a single harmful edit can negate the benefits of all remaining edits. To address this issue, we introduce HERO, a program optimizer that prompts an LLM to generate diverse, non-overlapping atomic edits and then systematically selects and composes them into coherent program improvements using evaluator scores. We evaluate HERO across algorithmic problems, strategy games, the design of LLM-based agentic systems, and robotic path planning. Across these domains, HERO consistently discovers higher-scoring programs and converges substantially faster than prior LLM-based optimizers, while consuming fewer tokens.

Despite its many benefits, widespread access to individuals' personal data also causes severe privacy concerns for consumers, companies, and policymakers. This study proposes a novel framework that adapts the Shapley-value-based feature attribution approach to the problem domain of data privacy by capturing the two crucial dimensions of data privacy—disclosure risk and data utility. Our proposed framework takes a holistic view of data masking through a fair feature attribution approach based on Shapley values. Different from the existing literature that mostly focuses on the risk-utility tradeoff at the dataset level, the proposed framework addresses the tradeoff at the feature level. Furthermore, the proposed framework is agnostic to data masking methods, statistical and machine learning methods, and data utility and disclosure risk evaluation metrics. Experimental results show that our proposed method can effectively reduce disclosure risk while preserving data utility.

Synthetic tabular data is increasingly used in privacy-preserving data sharing, data augmentation, and to mitigate downstream classifier bias. State-of-the-art tabular diffusion models such as TabDDPM and TabSyn achieve excellent distributional fidelity but offer no mechanism for fairness; conversely, fairness-aware tabular generators (DECAF, FairTGAN, FairTabDDPM) impose explicit fairness penalties at training time, yielding modest fairness gains at substantial cost to either sample quality or downstream utility. We introduce FairDiffuseVQVAE, a two-stage architecture that decouples fidelity from fairness: a vector-quantized autoencoder with a row-level discriminator (Stage~1, no fairness terms) is followed by a DiffuseVAE-style continuous diffusion refiner that conditions on both the Stage-1 reconstruction and the protected attribute via classifier-free guidance (Stage~2). Fairness emerges as a property of the sampling distribution – uniform sampling of the protected attribute at inference time enforces demographic parity by construction, rather than from competing loss terms. On the Adult, Bank and COMPAS datasets, FairDiffuseVQVAE achieves the highest mean Demographic Parity Ratio ($0.702$, $+47\%$ over FairTabDDPM) and Equalized Odds Ratio ($0.686$, $+100\%$). It also attains the lowest mean pair-wise correlation error ($0.034$) of any published method, while explicitly trading $\sim$$15$ AUC points for these fairness gains.

Structure-preserving neural networks are essential for the long-term prediction of Hamiltonian systems from data. Many important Hamiltonian systems in mechanics and control admit symmetry reduction to Lie–Poisson systems, including rigid bodies, underwater vehicles, fluids, plasmas, and optimal control problems. A fundamental challenge in learning such systems is that their dynamics evolve in momentum variables that are typically unobservable, while available data consist only of observable quantities such as configurations and velocities. In optimal control applications, the situation is further complicated because the latent variables contain unobservable co-states and the Hamiltonian may be degenerate, preventing the existence of a corresponding Lagrangian and rendering the encoder-decoder approaches inapplicable. We introduce Latent Lie–Poisson Neural Networks (LLPNNs), a structure-preserving framework for learning Lie–Poisson dynamics directly from observable data. The proposed approach exploits three geometric ingredients: (i) learning either a Hamiltonian decoder or a pseudo-Lagrangian encoder on the active variables, (ii) constructing latent trajectories through a universal Noether invariant arising from Lie–Poisson symmetry reduction, and (iii) reconstructing observable and latent dynamics through Lie–Poisson flows combined with Magnus-based Lie-group updates. The resulting method preserves the geometric structure and is applicable to both regular and degenerate Hamiltonian systems. We demonstrate the method on three examples: a generalized rigid body on SO(3), Kirchhoff's underwater vehicle on SE(3), and an optimal-control problem for interacting vehicles on $SE(2)^N$. Numerical experiments show excellent long-term predictive accuracy, strong robustness to noise, and competitive performance using only modest datasets and lightweight neural-network architectures.

Dynamic matching markets require decisions about whom to match and when: matching now yields value but removes participants who may create better future opportunities. We develop a value-based reinforcement-learning framework for this problem on finite, evolving weighted graphs. We study an infinite-horizon continuous-time model with stochastic arrivals, node-type transitions, edge realizations, and exogenous exits. We prove an event-time reduction: without loss of optimality, the planner acts immediately after each exogenous event and then waits for the next one. We further show that the optimal edge-wise $Q$-function is characterized by a single continuation-value function on post-decision residual graphs, reducing the learned object from state-action values to graph values. Exact action selection still requires combinatorial matching optimization; we approximate the value with a graph neural network, train it by temporal-difference learning, and use it in a forward-greedy matching heuristic. In a binary-type benchmark, the learned policy substantially outperforms immediate and threshold-greedy rules by preserving common nodes for rare arrivals of valuable matches while forming lower-value matches only in thick pools. In a kidney paired donation benchmark, it performs similarly to immediate greedy when exits are unpredictable, recovers the logic of patient matching when warnings are reliable, and outperforms the better of Immediate Greedy and Patient Greedy across intermediate warning probabilities. These results show that residual-graph value learning yields state-dependent dynamic matching policies that adapt to realized connectivity and exit information.

Multistep credit assignment is critical for sample-efficient reinforcement learning, yet managing off-policy bias in Q-learning remains a fundamental challenge. For 30 years, practitioners have been limited to a binary choice: eliminate the bias at the cost of severely truncated eligibility traces (Watkins' Q($\lambda$)), or ignore the bias to learn faster while injecting detrimental errors into the value estimates (Peng's Q($\lambda$)). Modern off-policy estimators fail to resolve this tension, as importance-sampling ratios collapse under Q-learning's greedy target policy. We introduce Gated Q-learning, a novel algorithmic framework that ends this dilemma by smoothly interpolating between the two historical extremes. Rather than relying on importance sampling, our approach employs a continuous, state-action-dependent gating mechanism to selectively attenuate eligibility traces in an exploration-aware manner. We provide a rigorous theoretical foundation for this mechanism, proving that the expected operator remains a contraction mapping and deriving its exact fixed point. Empirical evaluations verify that intermediate gating safely enables longer credit-assignment horizons, yielding faster initial learning than either extreme. Gated Q-learning offers a simple alternative to importance sampling while enabling customization of the effective multistep horizon and the amount of off-policy bias in Q-learning agents.

Reflection, the ability to revisit and revise prior reasoning, is central to how humans improve their answers. Large language models (LLMs) are increasingly prompted to "reflect," yet whether this resembles human revision remains unclear. We introduce the Human-LLM Reflection Framework (HRF), a controlled two-pass protocol comparing human and LLM revision under identical conditions across self-, peer-, and cross-agent settings. Using an information-theoretic analysis based on per-iteration cross-entropy reduction, we find two failure modes of LLM reflection. On objective tasks with finite answer spaces, reflection yields near-zero information gain (Delta I approx 0), behaving as neutral re-generation indistinguishable from re-sampling. On subjective tasks, it yields significant negative gain (Delta I < 0), moving predictions away from the target. Human revision, by contrast, yields positive gain in both settings. Cross-agent experiments localize the failure to the revision step, not input quality: LLMs degrade even high-quality human responses. Diagnostic analyses (revision conditioned on first-pass correctness, and oracle-guided revision against a random-reshuffle baseline) show that which sub-step dominates varies by task and by model rather than reducing to a single mechanism: self-error detection is present on objective multiple-choice tasks but weak on subjective ones, and recovery under an oracle error signal exceeds the baseline for some models and falls below it for others. The unifying account is structural: without external information, self-conditioned revision cannot reduce uncertainty about the target, so LLM reflection is better understood as conditioned re-generation than as genuine error-driven revision.

Variance-based global sensitivity analysis (GSA) plays a key role in uncertainty quantification by identifying the contributions of uncertain inputs to the variability of the model response. The repeated model evaluations required for these tasks are often prohibitively expensive; surrogate models provide an efficient alternative by constructing inexpensive approximations of the underlying system response. Constructing surrogate models that combine scalability and interpretability for systems with high-dimensional stochastic inputs and functional responses remains challenging, particularly when sensitivity estimates are required across spatial or temporal domains. Polynomial chaos expansion (PCE) provides an effective framework for uncertainty propagation and sensitivity analysis due to its orthogonal structure and direct relationship with variance-based sensitivity measures. However, PCE suffers from the curse of dimensionality, whose computational burden is amplified for problems with functional responses. In this work, we introduce the Structured Neural Chaos (sNC) expansion as a surrogate modeling framework for variance-based GSA, inspired by the interpretability and orthogonal structure of PCE. The proposed framework retains the interpretability of structured decompositions while leveraging the expressive power of neural networks. The sNC expansion mirrors a truncated functional ANOVA decomposition, where each interaction component admits a separable low-rank approximation whose basis functions and coefficients are parameterized by neural networks. The expansion is constructed sequentially, adaptively identifying the dominant modes within each ANOVA subspace and determining the effective complexity of the representation. The resulting structure enables the extraction of statistical and sensitivity quantities directly from the coefficients of the sNC expansion at negligible cost.