Papers

Generalized linear mixed-effects models (GLMMs) are widely used to analyze grouped and hierarchical data. In a GLMM, each response is assumed to follow an exponential-family distribution where the natural parameter is given by a linear function of observed covariates and a latent group-specific random effect. Since exact marginalization over the random effects is typically intractable, model parameters are estimated by maximizing an approximate marginal likelihood. In this paper, we replace the linear function with neural networks. The result is a more flexible model, the neural generalized mixed-effects model (NGMM), which captures complex relationships between covariates and responses. To fit NGMM to data, we introduce an efficient optimization procedure that maximizes the approximate marginal likelihood and is differentiable with respect to network parameters. We show that the approximation error of our objective decays at a Gaussian-tail rate in a user-chosen parameter. On synthetic data, NGMM improves over GLMMs when covariate-response relationships are nonlinear, and on real-world datasets it outperforms prior methods. Finally, we analyze a large dataset of student proficiency to demonstrate how NGMM can be extended to more complex latent-variable models.

Reinforcement learning (RL) policies often fail under dynamics that differ from training, a gap not fully addressed by domain randomization or existing adversarial RL methods. Distributionally robust RL provides a formal remedy but still relies on surrogate adversaries to approximate intractable primal problems, leaving blind spots that potentially cause instability and over-conservatism. We propose a dual formulation that directly exposes the robustness-performance trade-off. At the trajectory level, a temperature parameter from the dual problem is approximated with an adversarial network, yielding efficient and stable worst-case rollouts within a divergence bound. At the model level, we employ Boltzmann reweighting over dynamics ensembles, focusing on more adverse environments to the current policy rather than uniform sampling. The two components act independently and complement each other: trajectory-level steering ensures robust rollouts, while model-level sampling provides policy-sensitive coverage of adverse dynamics. The resulting framework, robust adversarial policy optimization (RAPO) outperforms robust RL baselines, improving resilience to uncertainty and generalization to out-of-distribution dynamics while maintaining dual tractability.

Stability assessment is central to safety-critical systems governed by differential-algebraic equations (DAEs), whose dynamics are constrained by physical laws and admissibility conditions. These systems operate under stochastically varying environmental inputs, so stability must be reassessed as the context distribution shifts, yet repeated large-scale DAE simulation is prohibitive in high-dimensional or real-time settings. We propose a test-oriented learning framework that tests a trajectory-level chance constraint from deployment contexts alone. Rather than re-estimating physical parameters or re-solving the DAE, we learn a latent representation from baseline context-trajectory data that retains stability-relevant information and is regularized toward a tractable reference distribution, and calibrate a latent discrepancy test over the composite safety null. We establish exact validity for oracle calibration and asymptotic validity for its empirical implementation under class-conditional latent invariance, and show that the guarantee degrades gracefully when this invariance holds only approximately. On simulated dynamical systems and a power-system real-world example, our approach strikes a balance between validity and power, whereas other baseline methods each fail in at least one regime. An ablation that injects controlled violations of the invariance assumption shows that decisions stay correct while the violation is below the safety margin, as the theory predicts.

Data leakage remains a recurrent source of optimistic bias in biomedical machine learning studies. Standard row-wise cross-validation and globally estimated preprocessing steps are often inappropriate for data with repeated measurements, study-level heterogeneity, batch effects, or temporal dependencies. This paper describes bioLeak, an R package for constructing leakage-aware resampling workflows and for auditing fitted models for common leakage mechanisms. The package provides leakage-aware split construction, train-fold-only preprocessing, cross-validated model fitting, nested hyperparameter tuning, post hoc leakage audits, and HTML reporting. The implementation supports binary classification, multiclass classification, regression, and survival analysis, with task-specific metrics and S4 containers for splits, fits, audits, and inflation summaries. The simulation artifacts show how apparent performance changes under controlled leakage mechanisms, and the case study illustrates how guarded and leaky pipelines can yield materially different conclusions on multi-study transcriptomic data. The emphasis throughout is on software design, reproducible workflows, and interpretation of diagnostic output.

We study continuous-time online learning where data are generated by a diffusion process with unknown coefficients. The learner employs a two-layer neural network, continuously updating its parameters in a non-anticipative manner. The mean-field limit of the learning dynamics corresponds to a stochastic Wasserstein gradient flow adapted to the data filtration. We establish regret bounds for both the mean-field limit and finite-particle system. Our analysis leverages the logarithmic Sobolev inequality, Polyak-Lojasiewicz condition, Malliavin calculus, and uniform-in-time propagation of chaos. Under displacement convexity, we obtain a constant static regret bound. In the general non-convex setting, we derive explicit linear regret bounds characterizing the effects of data variation, entropic exploration, and quadratic regularization. Finally, our simulations demonstrate the outperformance of the online approach and the impact of network width and regularization parameters.

Hypergraph neural networks (HGNNs) have shown remarkable potential in modeling high-order relationships that naturally arise in many real-world data domains. However, existing HGNNs often suffer from shallow propagation, oversmoothing, and limited adaptability to complex hypergraph structures. In this paper, we propose Hypergraph Neural Diffusion (HND), a novel framework that unifies nonlinear diffusion equations with neural message passing on hypergraphs. HND is grounded in a continuous-time hypergraph diffusion equation, formulated via hypergraph gradient and divergence operators, and modulated by a learnable, structure-aware coefficient matrix over hyperedge-node pairs. This partial differential equation (PDE) based formulation provides a physically interpretable view of hypergraph learning, where feature propagation is understood as an anisotropic diffusion process governed by local inconsistency and adaptive diffusion coefficient. From this perspective, neural message passing becomes a discretized gradient flow that progressively minimizes a diffusion energy functional. We derive rigorous theoretical guarantees, including energy dissipation, solution boundedness via a discrete maximum principle, and stability under explicit and implicit numerical schemes. The HND framework supports a variety of integration strategies such as non-adaptive-step (like Runge-Kutta) and adaptive-step solvers, enabling the construction of deep, stable, and interpretable architectures. Extensive experiments on benchmark datasets demonstrate that HND achieves competitive performance. Our results highlight the power of PDE-inspired design in enhancing the stability, expressivity, and interpretability of hypergraph learning.

Selecting prototypical examples from a source distribution to represent a target data distribution is a fundamental problem in machine learning. Existing subset selection methods often rely on implicit importance scores, which can be skewed towards majority classes and lead to low-quality prototypes for minority classes. We present $\methodprop$, a novel subset selection framework that minimizes the optimal transport (OT) distance between a uniformly weighted prototypical distribution and the target distribution. While intuitive, this formulation leads to a cardinality-constrained maximization of a super-additive objective, which is generally intractable to approximate efficiently. To address this, we propose a principled reformulation of the OT marginal constraints, yielding a partial optimal transport-based submodular objective. We prove that this reformulation enables a greedy algorithm with a $(1-1/e)$ approximation guarantee relative to the original super-additive maximization problem. Empirically, we showcase that enforcing uniform prototype weights in UniPROT consistently improves minority-class representation in imbalanced classification benchmarks without compromising majority-class accuracy. In both finetuning and pretraining regimes for large language models under domain imbalance, UniPROT enforces uniform source contributions, yielding robust performance gains. Our results establish UniPROT as a scalable, theoretically grounded solution for uniform-weighted prototype selection. Our code is publicly available at GitHub\footnote{Code: https://github.com/efficiency-learning/UniPROT}

Transformer models have become foundational across a wide range of scientific and engineering domains due to their strong empirical performance. A key capability underlying their success is in-context learning (ICL): when presented with a short prompt from an unseen task, transformers can perform per-token and next-token predictions without any parameter updates. Recent theoretical efforts have begun to uncover the mechanisms behind this phenomenon, particularly in supervised regression settings. However, these analyses predominantly assume stationary task distributions, which overlook a broad class of real-world scenarios where the target function varies over time. In this work, we bridge this gap by providing a theoretical analysis of ICL under non-stationary regression problems. We study how the gated linear attention (GLA) mechanism adapts to evolving input-output relationships and rigorously characterize its advantages over standard linear attention in this dynamic setting. To model non-stationarity, we adopt a first-order autoregressive process and show that GLA achieves lower training and testing errors by adaptively modulating the influence of past inputs – effectively implementing a learnable recency bias. Our theoretical findings are further supported by empirical results, which validate the benefits of gating mechanisms in non-stationary ICL tasks.

Accurate assessment of spheno-occipital synchondrosis (SOS) maturation is a key indicator of craniofacial growth and a critical determinant for orthodontic and surgical timing. However, SOS staging from cone-beam CT (CBCT) relies on subtle, continuously evolving morphological cues, leading to high inter-observer variability and poor reproducibility, especially at transitional fusion stages. We frame SOS assessment as a fine-grained visual recognition problem and propose a progressive representation-learning framework that explicitly mirrors how expert clinicians reason about synchondral fusion: from coarse anatomical structure to increasingly subtle patterns of closure. Rather than training a full-capacity network end-to-end, we sequentially grow the model by activating deeper blocks over time, allowing early layers to first encode stable cranial base morphology before higher-level layers specialize in discriminating adjacent maturation stages. This yields a curriculum over network depth that aligns deep feature learning with the biological continuum of SOS fusion. Extensive experiments across convolutional and transformer-based architectures show that this expert-inspired training strategy produces more stable optimization and consistently higher accuracy than standard training, particularly for ambiguous intermediate stages. Importantly, these gains are achieved without changing network architectures or loss functions, demonstrating that training dynamics alone can substantially improve anatomical representation learning. The proposed framework establishes a principled link between expert dental intuition and deep visual representations, enabling robust, data-efficient SOS staging from CBCT and offering a general strategy for modeling other continuous biological processes in medical imaging.

Rapid growth in artificial intelligence (AI) workloads is driving up data center power densities, increasing the need for advanced thermal management. Direct-to-chip liquid cooling can remove heat efficiently at the source, but many cold plate channel layouts remain heuristic and are not optimized for the strongly non-uniform temperature distribution of modern heterogeneous packages. This work presents a generative design framework for synthesizing cooling channel geometries for the NVIDIA GB200 Grace Blackwell Superchip. A physics-based finite-difference thermal model provides rapid steady-state temperature predictions and supplies spatial thermal feedback to a constrained reaction-diffusion process that generates novel channel topologies while enforcing inlet/outlet and component constraints. By iterating channel generation and thermal evaluation in a closed loop, the method naturally redistributes cooling capacity toward high-power regions and suppresses hot-spot formation. Compared with a baseline parallel channel design, the resulting channels achieve more than a 5 degree Celsius reduction in average temperature and over 35 degree Celsius reduction in maximum temperature. Overall, the results demonstrate that coupling generative algorithms with lightweight physics-based modeling can significantly enhance direct-to-chip liquid cooling performance, supporting more sustainable scaling of AI computing.

Deep neural networks remain highly vulnerable to adversarial perturbations, limiting their reliability in security- and safety-critical applications. To address this challenge, we introduce QShield, a modular hybrid quantum-classical neural network (HQCNN) architecture designed to enhance the adversarial robustness of classical deep learning models. QShield integrates a conventional convolutional neural network (CNN) backbone for feature extraction with a quantum processing module that encodes the extracted features into quantum states, applies structured entanglement operations under realistic noise models, and outputs a hybrid prediction through a dynamically weighted fusion mechanism implemented via a lightweight multilayer perceptron (MLP). We systematically evaluate both classical and hybrid quantum-classical models on the MNIST, OrganAMNIST, and CIFAR-10 datasets, using a comprehensive set of robustness, efficiency, and computational performance metrics. Our results demonstrate that classical models are highly vulnerable to adversarial attacks, whereas the proposed hybrid models with entanglement patterns maintain high predictive accuracy while substantially reducing attack success rates across a wide range of adversarial attacks. Furthermore, the proposed hybrid architecture significantly increased the computational cost required to generate adversarial examples, thereby introducing an additional layer of defense. These findings indicate that the proposed modular hybrid architecture achieves a practical balance between predictive accuracy and adversarial robustness, positioning it as a promising approach for secure and reliable machine learning in sensitive and safety-critical applications.

Medium- to long-horizon equity allocation is challenging due to weak predictive structure, non-stationary market regimes, and the degradation of signals under realistic trading constraints. Conventional approaches often rely on single predictors or loosely coupled pipelines, which limit robustness under distributional shift. This paper proposes EvoNash-MARL, a closed-loop framework that integrates reinforcement learning with population-based policy optimization and execution-aware selection to improve robustness in medium- to long-horizon allocation. The framework combines multi-agent policy populations, game-theoretic aggregation, and constraint-aware validation within a unified walk-forward design. Under a 120-window walk-forward protocol, the final configuration achieves the highest robust score among internal baselines. On out-of-sample data from 2014 to 2024, it delivers a 19.6% annualized return, compared to 11.7% for SPY, and remains stable under extended evaluation through 2026. While the framework demonstrates consistent performance under realistic constraints and across market settings, strong global statistical significance is not established under White's Reality Check (WRC) and SPA-lite tests. The results therefore provide evidence of improved robustness rather than definitive proof of superior market timing performance.

In large language models performing long-form reasoning, the KV cache grows rapidly with decode length, creating bottlenecks in memory and inference stability. Existing reasoning-oriented KV compression has mostly followed an eviction-centered view: estimate token importance more accurately, then discard lower-ranked entries. Our analysis suggests that scorer refinement alone often fails to substantially reorganize the actual keep-set and may therefore not be the main lever for preserving reasoning behavior. We instead frame reasoning KV compression as a behavior-preserving structured consolidation problem. CASK partitions the decode-time reasoning trace into a protected core that anchors answer formation and intermediate state, and mergeable scratch with high redundancy. The core is preserved, while selective consolidation is applied only to the scratch. To address prompt-heavy regimes where the prefix can exhaust the budget before decode-stage compression becomes active, CASK further uses a two-stage design: prefix eviction followed by decode-stage consolidation. On the H100 reasoning gate, CASK shows higher full-KV continuation fidelity than TriAttention at matched budgets on both AIME24 and AIME25, with recurring cask@384 > triattention@512 crossings. In prompt-heavy replay, multi_news and vcsum act as decode-active witnesses, while qmsum and gov_report expose the prefix_budget_exhausted boundary. The overall evidence supports a simple conclusion: effective reasoning KV compression depends less on more elaborate scorer engineering than on combining core preservation with selective scratch consolidation to lower the usable budget frontier.

Large language models (LLMs) have shown great performance on complex reasoning tasks but often require generating long intermediate thoughts before reaching a final answer. During generation, LLMs rely on a key-value (KV) cache for autoregressive decoding. However, the memory footprint of the KV cache grows with output length. Prior work on KV cache optimization mostly focus on compressing the long input context, while retaining the full KV cache for decoding. For tasks requiring long output generation, this leads to increased computational and memory costs. In this paper, we introduce ZoomR, a novel approach that enables LLMs to adaptively compress verbose reasoning thoughts into summaries and uses a dynamic KV cache selection policy that leverages these summaries while also strategically "zooming in" on fine-grained details. By using summary keys as a coarse-grained index during decoding, ZoomR uses the query to retrieve details for only the most important thoughts. This hierarchical strategy significantly reduces memory usage by avoiding full-cache attention at each step. Experiments across math and reasoning tasks show that our approach achieves competitive performance compared to baselines, while reducing inference memory requirements by more than $4\times$. These results demonstrate that a multi-granularity KV selection enables more memory efficient decoding, especially for long output generation.

Graph pre-training can facilitate knowledge transfer across graph datasets, but severe structural and feature shifts may cause negative transfer and adaptation-induced overwriting of reusable knowledge. We propose DIB-OD, a heterogeneous graph adaptation framework that combines a Decoupled Information Bottleneck with Online Distillation. A multiview teacher first learns a compressed, task-relevant representation, which is distilled into a transferable core branch and a complementary residual branch. Mutual-information objectives and HSIC-based dependence regularization discourage information overlap between the branches, while a confidence-aware semantic regularizer and a frozen teacher anchor reliable pretrained information during target-domain adaptation. Experiments on seven graph-classification datasets spanning chemical, biological, and social-network domains show consistent improvements over representative baselines, particularly under challenging cross-type transfer.

We propose an operational, quantitative definition of intelligence for arbitrary physical systems. The intelligence density of a system is the ratio of the logarithm of its independent outputs to its total description length. A system memorizes if its description length grows with its output count; it knows if its description length remains fixed while its output count diverges. The criterion for knowing is generalization. A system knows its domain if a single finite mechanism can produce correct outputs across an unbounded range of inputs, rather than storing each answer individually. The definition places intelligence on a substrate-independent continuum from logic gates to brains. We then argue that meaning over a domain is a selection and ordering of functions that produces correct outputs where correctness is specifiable. We also define a measure of contextuality of an output as the inverse of its conditional Kolmogorov complexity given the context of prior outputs, which unifies correctness and independence into a single condition. Together, these refute Searle's third premise, that syntax is insufficient for semantics, over any domain where correctness is specifiable.

In modern financial markets, decision-makers increasingly rely on quantitative methods to navigate complex trade-offs among multiple, often conflicting objectives. This paper addresses constrained multi-objective optimization (MOO) with an application to portfolio optimization for minimizing risk and maximizing return. To address existing gaps, we propose a novel reinforcement learning (RL)-guided non-dominated sorting genetic algorithm II (NSGA-II) enhanced with gray relational coefficients (GRC), termed RL-NSGA-II-GRC, which combines an RL agent controller and GRC-based selection to improve convergence and diversity of Pareto fronts. The agent adapts evolutionary parameters online using metrics of hypervolume, feasibility, and diversity, while the GRC tournament operator ranks parents via a unified score considering dominance rank, crowding distance, and proximity to ideal reference. We evaluate the framework on the Kursawe and CONSTR benchmarks and a NASDAQ portfolio application. On the benchmarks, RL-NSGA-II-GRC achieves convergence improvements of about 5.8% and 4.4% over NSGA-II, while preserving well-distributed non-dominated solutions. In the portfolio application, it produces a smooth, densely populated efficient frontier supporting identification of the maximum Sharpe ratio portfolio (annualized Sharpe =1.92) and utility-optimal portfolios for different risk-aversion levels. The main contributions are three-fold: 1) we propose an RL-NSGA-II-GRC method integrating an RL agent into the evolutionary framework to adaptively control parameters via generational feedback; 2) we design a GRC-enhanced binary tournament operator providing a comprehensive indicator to guide the search toward the Pareto front; 3) we demonstrate, on benchmark MOO and a NASDAQ case study, that the method delivers improved convergence and well-populated frontiers supporting actionable insights.

Despite the promise of AI to assist complex decisions, practitioners still lack ways to detect likely failures and inspect the consequences of model edits before committing them. We present RuleEdit, an interactive, rule-guided human-AI model editing system that (i) surfaces likely failures through interpretable mismatch signals from rule tables and (ii) supports user-authored rule feedback with prospective previews of projected performance changes and embedding shifts. We instantiate RuleEdit in stroke rehabilitation assessment and evaluate it with health professionals and students. Rule-guided failure detection significantly increased Human + AI performance by 14.16% ($p<0.001$) while improving rejection of incorrect AI and reducing both over- and under- reliance as well as ChangedToWrong decisions. In addition, presenting prospective embedding previews improved participants' feedback for model adaptation, increasing post-update local performance gains from 11.50% to 36.38% after incorporating users' rule-based feedback ($p<0.001$). Our findings show that mismatch-based failure cues and prospective impact previews can support failure-aware human-AI model editing, while also revealing a local-global tradeoff: edits that help a specific case can degrade performance when transferred globally. We discuss implications of designing failure-aware and controllable human-AI systems.

We introduce LAWS (Learning from Actual Workloads Symbolically), a self-certifying inference caching architecture that builds a growing library of certified expert functions from deployment observations. Each expert covers a region of input space defined by a node in the Probabilistic Language Trie (PLT) of the base model and carries a formal error bound holding uniformly over all inputs. The central result is a self-certification theorem: for any input x, the LAWS approximation error is bounded by epsilon_fit + 2*Lambda(W)*C_E, where Lambda(W) is the model Lipschitz constant, C_E is the maximum embedding diameter, and epsilon_fit is the expert training error – all checkable at deployment time without ground truth. We prove that LAWS generalizes both Mixture-of-Experts and KV prefix caching as special cases and is strictly more expressive than any fixed-K MoE or finite cache. Further results include a monotone hit rate theorem (any-match routing ensures coverage only increases), an expert library growth rate of O(2^H log N) where H is workload entropy, a fleet learning convergence theorem with Omega(K) speedup for K-unit fleets, and an over-the-air update bandwidth bound. We conjecture that LAWS is acquisition-optimal among stationary online caching algorithms and that the effective Lipschitz constant on the training distribution grows polynomially rather than exponentially in depth. Applications are developed for LLM inference, robotic control, and multi-agent edge deployment.

The use of artificial intelligence in supply chain forecasting has attracted many scientific studies for several decades. However, the process of selecting an appropriate forecasting solution becomes a daunting task. This complexity arises due to the distinct features inherent to each dataset. Research to tackle this issue has been performed since the eighties but recent development of demand forecasting has opened new perspectives. This research aims to enhance automatic forecasting model selection by proposing a novel architecture that acts as a double deep reinforcement learning agent, selecting automatically a forecasting model from the forecasting committee at the time of prediction. Moreover, a novel early-stopping approach based on average reward convergence has been introduced to expedite training time. To evaluate the model's performance, an empirical study was conducted utilizing grocery sales datasets and snack demands datasets. The experimental results demonstrate the robustness of the proposed approach when compared to state-of-the-art methods.

This study presents a controlled parametric framework for analyzing energy storage planning under uncertainty in a multi-stage model predictive control setting. The framework enables a broad and systematic exploration through parametrized generation of synthetic datasets in the context of energy price arbitrage. It facilitates the study of the joint effects of battery characteristics, signal structure, forecast uncertainty, and planning horizon on revenue performance in energy storage optimization, which are rarely considered together. The analysis is driven by two objectives. First, it characterizes how these interacting factors influence operational revenue and its sensitivity to planning horizon selection, including economic losses caused by deviations from optimal horizons. This provides guidance on expected horizon ranges and their impact on revenue and computational cost. Second, it enables a compact parametrization of the relationships between battery properties, data characteristics, forecast uncertainty, and horizon-dependent performance, providing a basis for future modelling of optimal planning horizon length. Results show that the framework captures consistent structural dependencies across configurations and provides meaningful guidance for horizon selection under uncertainty. In particular, increasing forecast uncertainty systematically reduces the optimal planning horizon across battery types, reflecting the diminishing value of long-term information under increasingly unreliable forecasts. Comparison with real market data shows that the parametrization reproduces the main qualitative trends of optimal horizon behavior, suggesting its potential as a lightweight surrogate for more complex simulation-based analysis.

Understanding communication behavior in modern system-on-chip (SoC) designs is critical for functional verification, performance analysis, and post-silicon debugging. Communication traces capture message exchanges among system components and provide valuable insights into system behavior. However, deriving concise communication specifications from such traces remains challenging due to interleaved instances of communication flows, and ambiguous causal relationships among messages. Existing mining approaches often struggle with scalability and ambiguity when traces contain complex interleaving of message patterns across multiple components. These conditions often lead to an explosion in the number of candidate flows and inaccurate extraction of communication behaviors. This paper presents AutoFlows++, a design-architecture-guided hierarchical framework for mining message flows from communication traces of complex SoC designs. AutoFlows++ operates in two stages: local mining followed by global mining. In the local mining stage, simple communication patterns are extracted from traces observed at individual communication interfaces between components. In the global mining stage, these local patterns are composed to identify higher-level message flows that characterize communication behavior across multiple components. Experimental results on both synthetic traces and traces generated from SoC models in GEM5 demonstrate that AutoFlows++ significantly improves flow extraction accuracy compared with prior approaches, highlighting its effectiveness for practical SoC validation tasks.

Irregular Medical Time Series play a critical role in the clinical domain to better understand the patient's condition. However, inherent irregularity arising from heterogeneous sampling rates, asynchronous observations, and variable gaps poses key challenges for reliable modeling. Existing methods often distort temporal sampling irregularity and missingness patterns while failing to capture variable decay irregularity, resulting in suboptimal representations. To address these limitations, we introduce DBGL, Decay-Aware Bipartite Graph Learning for Irregular Medical Time Series. DBGL first introduces a patient-variable bipartite graph that simultaneously captures irregular sampling patterns without artificial alignment and adaptively models variable relationships for temporal sampling irregularity modeling, enhancing representation learning. To model variable decay irregularity, DBGL designs a novel node-specific temporal decay encoding mechanism that captures each variable's decay rates based on sampling interval, yielding a more accurate and faithful representation of irregular temporal dynamics. We evaluate the performance of DBGL on four publicly available datasets, and the results show that DBGL outperforms all baselines.

Low-rank adaptation (LoRA) is a widely used strategy for efficient fine-tuning of large language models (LLMs), but its strictly linear structure fundamentally limits expressive capacity. The bilinear formulation of weight updates captures only first-order dependencies between low-rank factors, restricting the modeling of nonlinear and higher-order parameter interactions. In this paper, we propose Polynomial Expansion Rank Adaptation (PERA), a novel method that introduces structured polynomial expansion directly into the low-rank factor space. By expanding each low-rank factor to synthesize high-order interaction terms before composition, PERA transforms the adaptation space into a polynomial manifold capable of modeling richer nonlinear coupling without increasing rank or inference cost. We provide theoretical analysis demonstrating that PERA offers enhanced expressive capacity and more effective feature utilization compare to existing linear adaptation approaches. Empirically, PERA consistently outperforms state-of-the-art methods across diverse benchmarks. Notably, our experiments show that incorporating high-order nonlinear components particularly square terms is crucial for enhancing expressive capacity and maintaining strong and robust performance under various rank settings. Our code is available at https://github.com/zhangwenhao6/PERA

Language models are increasingly used to simulate people: survey respondents, negotiators, stakeholders in policy exercises. In that role a model should reproduce how people plausibly behave, hesitating, conceding late, and settling for imperfect deals, rather than playing the best move. We call this the sampler role, in contrast to the solver role of finding the best move, and we test how the reasoning modes providers ship to strengthen models as solvers affect it. Our testbed is multi-party negotiation: five agents bargain over a regulation for fifteen turns, and unresolved issues are decided by an authority. Agents without a structured memory of the negotiation almost never reach agreement, whether reasoning is on or off: 314 of 315 such runs end with the authority deciding. What reasoning changes is how the failure looks. With reasoning enabled, one model family negotiates visibly, with varied moves, concessions in most runs, and a different path every time, yet still ends without agreement in fifteen runs of fifteen. Diversity checks would pass a model whose endings never change. Two further results show the task permits agreement: when agents write their own short running notes on the negotiation, agreement becomes the norm, while the same notes supplied ready-made change nothing; and hand-coded agents following textbook concession strategies agree in most runs under identical rules. Simulation pipelines should therefore vet models as samplers, on the distributions of outcomes they produce. Fidelity as a sampler must be tested on its own: solver strength is no guide to it, and switching on reasoning leaves it where it was.

While critical for alignment, Supervised Fine-Tuning (SFT) incurs the risk of catastrophic forgetting, yet the layer-wise emergence of instruction-following capabilities remains elusive. We investigate this mechanism via a comprehensive analysis utilizing information-theoretic, geometric, and optimization metrics across model scales (1B-32B). Our experiments reveal a distinct depth-dependent pattern: middle layers (20%-80%) are stable, whereas final layers exhibit high sensitivity. Leveraging this insight, we propose Mid-Block Efficient Tuning, which selectively updates these critical intermediate layers. Empirically, our method outperforms standard LoRA up to 10.2% on GSM8K (OLMo2-7B) with reduced parameter overhead, demonstrating that effective alignment is architecturally localized rather than distributed. The code is publicly available at https://anonymous.4open.science/r/base_sft.

Machine learning for tabular data remains constrained by poor schema generalization, a challenge rooted in the lack of semantic understanding of structured variables. This challenge is particularly acute in domains like clinical medicine, where electronic health record (EHR) schemas vary significantly. To solve this problem, we propose Schema-Adaptive Tabular Representation Learning, a novel method that leverages large language models (LLMs) to create transferable tabular embeddings. By transforming structured variables into semantic natural language statements and encoding them with a pretrained LLM, our approach enables zero-shot alignment across unseen schemas without manual feature engineering or retraining. We integrate our encoder into a multimodal framework for dementia diagnosis, combining tabular and MRI data. Experiments on NACC and ADNI datasets demonstrate state-of-the-art performance and successful zero-shot transfer to unseen schemas, significantly outperforming clinical baselines, including board-certified neurologists, in retrospective diagnostic tasks. These results validate our LLM-driven approach as a scalable, robust solution for heterogeneous real-world data, offering a pathway to extend LLM-based reasoning to structured domains.

The computational demands of deep learning motivate the investigation of alternative approaches to computation. One alternative is physical neural networks~(PNNs), in which learning and inference are performed directly via physical processes. Stochastic PNNs arise when the underlying neurons are realized by the dynamics of a stochastic activation switch. Here we propose novel electronic and photonic stochastic neurons. The electronic realization is implemented by single-electron tunneling through a quantum dot. The photonic realization is implemented via a single-photon source driving one of two modes coupled via a controllable beam-splitter-like interaction. In the electronic case, the charge state of the quantum dot forms the basis for the stochastic neuron, whereas in the photonic case the occupation of the undriven mode serves as the basis for the stochastic neuron. Training of stochastic PNNs is performed with models of stochastic neurons, as well as with coherently-driven, single-photon detector stochastic neurons previously introduced. Several training strategies for MNIST handwritten digit classification have been investigated using single-hidden-layer stochastic PNNs, including varying the number of trials in each layer to control forward pass stochasticity and employing either true probability or empirical outputs in the backward pass to evaluate their influence on gradient estimation. We show that when empirical outputs are used in the backward pass, the network achieves more than 97% test accuracy with few trials per layer. Despite the simplicity of the model architecture, high test accuracy is maintained in the presence of a high degree of noise and model uncertainty. The results demonstrate the potential of embracing stochastic PNNs for deep learning.

Diffusion models generate samples by iteratively querying learned score estimates. A rapidly growing literature focuses on accelerating sampling by minimizing the number of score evaluations, yet the information-theoretic limits of such acceleration remain unclear. In this work, we establish the first score query lower bounds for diffusion sampling. We prove that for $d$-dimensional distributions, given access to score estimates with polynomial accuracy $\varepsilon=d^{-O(1)}$ (in any $L^p$ sense), any sampling algorithm requires $\widetilde{\Omega}(\sqrt{d})$ adaptive score queries. In particular, our proof shows that, within any polynomial total-query budget, successful sampling requires searching over $\widetilde{\Omega}(\sqrt{d})$ distinct noise levels, providing a formal explanation for why multiscale noise schedules are necessary in practice.

Federated learning (FL) performance is highly sensitive to heterogeneity across clients, yet practitioners lack reliable methods to anticipate how a federation will behave before training. We propose readiness indices, derived from Task2Vec embeddings, that quantifies the alignment of a federation prior to training and correlates with its eventual performance. Our approach computes unsupervised metrics – such as cohesion, dispersion, and density – directly from client embeddings. We evaluate these indices across diverse datasets (CIFAR-10, FEMNIST, PathMNIST, BloodMNIST) and client counts (10–20), under Dirichlet heterogeneity levels spanning $\alpha \in \{0.05,\dots,5.0\}$ and FedAVG aggregation strategy. Correlation analyses show consistent and significant Pearson and Spearman coefficients between some of the Task2Vec-based readiness and final performance, with values often exceeding 0.9 across dataset$\times$client configurations, validating this approach as a robust proxy for FL outcomes. These findings establish Task2Vec-based readiness as a principled, pre-training diagnostic for FL that may offer both predictive insight and actionable guidance for client selection in heterogeneous federations.