Papers

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.

Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence speed, data requirements, and solution accuracy. In complex fluid flows, these challenges are exacerbated by long-range spatial dependencies arising from distant boundary conditions, which typically necessitate extensive supervision data to achieve acceptable results. We propose the Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN), a framework designed to resolve such multiscale interactions with minimal supervision. By utilizing localized networks with a unified global loss, DDS-PINN captures global dependencies while maintaining local precision. The robustness of the approach is demonstrated across a suite of benchmarks, including a multiscale linear differential equation, the nonlinear Burgers' equation, and data-free Navier-Stokes simulations of flat-plate boundary layers. Finally, DDS-PINN is applied to the computationally challenging backward-facing step (BFS) problem; for laminar regimes (Re = 100), the model yields results comparable to computational fluid dynamics (CFD) without the need for any data, accurately predicting boundary layer thickness, separation, and reattachment lengths. For turbulent BFS flow at Re = 10,000, the framework achieves convergence to O(10^-4) using only 500 random supervision points (< 0.3 % of the total domain), outperforming established methods like Residual-based Attention-PINN in accuracy. This approach demonstrates strong potential for the super-resolution of complex turbulent flows from sparse experimental measurements.

This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions, given by the composition of convex and monotonic terms, so that the surrogate problem can be solved directly through parallel convex optimization. As a proof of concept, numerical experiments on a nonconvex path tracking problem confirm the approximation quality of the proposed method.

Numerical preprocessing remains a critical component of tabular deep learning, as the representation of continuous features can strongly affect downstream performance. We systematically study spline-based numerical encodings, including B-splines, M-splines, and integrated splines (I-splines), under uniform, quantile-based, target-aware, and learnable-knot placement. For the learnable variants, we adopt a differentiable knot parameterization that enables stable end-to-end optimization of knot locations jointly with the backbone. We evaluate these encodings on a diverse collection of public regression and classification datasets using MLP, ResNet, and FT-Transformer backbones, and compare them against common numerical preprocessing baselines. Our results show that the effectiveness of numerical encoding depends strongly on the task, encoding size, and backbone. For classification, piecewise-linear encoding (PLE) is the most robust choice overall, while spline-based encodings remain competitive. For regression, no single encoding dominates, with performance depending on the spline family and knot-placement strategy, and larger gains generally observed for MLP and ResNet than for FT-Transformer. Learnable-knot variants can be optimized stably but may substantially increase training cost. Overall, numerical encodings should therefore be assessed jointly in terms of predictive performance and computational overhead. The implementation is publicly available at https://github.com/mkumar73/tdl-numerical-encodings/.

Deep learning models for computer vision often suffer from poor generalization when deployed in real-world settings, especially when trained on synthetic data due to the well-known Sim2Real gap. Despite the growing popularity of style transfer as a data augmentation strategy for domain generalization, the literature contains unresolved contradictions regarding three key design axes: the diversity of the style pool, the role of texture complexity, and the choice of style source. We present a systematic empirical study that isolates and evaluates each of these factors for driving scene understanding, resolving inconsistencies in prior work. Our findings show that (i) expanding the style pool yields larger gains than repeated augmentation with few styles, (ii) texture complexity has no significant effect when the pool is sufficiently large, and (iii) diverse artistic styles outperform domain-aligned alternatives. Guided by these insights, we derive StyleMixDG (Style-Mixing for Domain Generalization), a lightweight, model-agnostic augmentation recipe that requires no architectural modifications or additional losses. Evaluated on the GTAV $\rightarrow$ {BDD100k, Cityscapes, Mapillary Vistas} benchmark, StyleMixDG demonstrates consistent improvements over strong baselines, confirming that the empirically identified design principles translate into practical gains. The code will be released on GitHub.

Autoregressive graph generators define likelihoods via a sequential construction process, but these likelihoods are only meaningful if they are consistent across all linearizations of the same graph. Segmented Eulerian Neighborhood Trails (SENT), a recent linearization method, converts graphs into sequences that can be perfectly decoded and efficiently processed by language models, but admit multiple equivalent linearizations of the same graph. We quantify violations in assigned negative log-likelihood (NLL) using the coefficient of variation across equivalent linearizations, which we call Linearization Uncertainty (LU). Training transformers under four linearization strategies on two datasets, we show that biased orderings achieve lower NLL on their native order but exhibit expected calibration error (ECE) two orders of magnitude higher under random permutation, indicating that these models have learned their training linearization rather than the underlying graph. On the molecular graph benchmark QM9, NLL for generated graphs is negatively correlated with molecular stability (AUC $=0.43$), while LU achieves AUC $=0.85$, suggesting that permutation-based evaluation provides a more reliable quality check for generated molecules. Code is available at https://github.com/lauritsf/linearization-uncertainty

Self-conditioning has been central to the success of continuous diffusion language models, as it allows models to correct previous errors. Yet its ability degrades precisely in the regime where diffusion is most attractive for deployment: few-step sampling for fast inference. In this study, we show that when models only have a few denoising steps, inaccurate self-conditioning induces a substantial approximation gap; this mistake compounds across denoising steps and ultimately dominate the sample quality. To address this, we propose a novel training framework that handles these errors during learning by perturbing the self-conditioning signal to match inference noise, improving robustness to prior estimation errors. In addition, we introduce a token-level noise-awareness mechanism that prevents training from saturation, hence improving optimization. Extensive experiments across conditional generation benchmarks demonstrate that our framework surpasses standard continuous diffusion models while providing up to 400x faster inference speed, and remains competitive against other one-step diffusion frameworks.

Multivariate time series forecasting often struggles to capture long-range dependencies due to fixed lookback windows. Retrieval-augmented forecasting addresses this by retrieving historical segments from memory, but existing approaches rely on a channel-agnostic strategy that applies the same references to all variables. This neglects inter-variable heterogeneity, where different channels exhibit distinct periodicities and spectral profiles. We propose CRAFT (Channel-wise retrieval-augmented forecasting), a novel framework that performs retrieval independently for each channel. To ensure efficiency, CRAFT adopts a two-stage pipeline: a sparse relation graph constructed in the time domain prunes irrelevant candidates, and spectral similarity in the frequency domain ranks references, emphasizing dominant periodic components while suppressing noise. Experiments on seven public benchmarks demonstrate that CRAFT outperforms state-of-the-art forecasting baselines, achieving superior accuracy with practical inference efficiency.

Active noise cancellation (ANC) is widely deployed on consumer headphones and earbuds to suppress environmental noise. However, existing ANC systems require an error microphone at the user's ear canal to measure residual sound, preventing deployment on emerging open-ear wearable devices such as smart glasses and VR headsets, which leave the ear unoccluded. Here we present an ANC system for open-ear wearables that suppresses environmental noise using only microphones and miniaturized open-ear speakers embedded within the frame of the wearables, removing the need for an in-ear error microphone. Our low-latency computational pipeline uses a neural network to estimate the noise at the ear from an array of eight microphones distributed around the wearable's frame and generates an anti-noise signal in real-time. This mapping generalizes to unseen users and acoustic environments without prior acoustic measurement. We develop a custom glasses prototype and evaluate across eleven unseen users and eight unseen environments under mobility in the 100 to 1000 Hz frequency range, where environmental noise is concentrated. We achieve a mean noise reduction of 9.6 dB without any calibration, and 11.2 dB with a brief user-specific calibration. Further, we demonstrate that our approach extends to the broader class of open-ear wearables including VR headsets and headbands.

We propose an active learning algorithm for linear system identification with optimal centered noise excitation. Notably, our algorithm, based on ordinary least squares and semidefinite programming, attains the minimal sample complexity while allowing for efficient computation of an estimate of a system matrix. More specifically, we first establish lower bounds of the sample complexity for any active learning algorithm to attain the prescribed accuracy and confidence levels. Next, we derive a sample complexity upper bound of the proposed algorithm, which matches the lower bound for any algorithm up to universal factors. Our tight bounds are easy to interpret and explicitly show their dependence on the system parameters such as the state dimension.

Protecting the intellectual property of open-weight large language models (LLMs) requires verifying whether a suspect model is derived from a victim model despite common laundering operations such as fine-tuning (including PPO/DPO), pruning/compression, and model merging. We propose AttnDiff, a data-efficient white-box framework that extracts fingerprints from models via intrinsic information-routing behavior. AttnDiff probes minimally edited prompt pairs that induce controlled semantic conflicts, captures differential attention patterns, summarizes them with compact spectral descriptors, and compares models using CKA. Across Llama-2/3 and Qwen2.5 (3B–14B) and additional open-source families, it yields high similarity for related derivatives while separating unrelated model families (e.g., $>0.98$ vs.\ $<0.22$ with $M=60$ probes). With 5–60 multi-domain probes, it supports practical provenance verification and accountability.

Immune checkpoint inhibitors (ICIs) have transformed cancer therapy; yet substantial proportion of patients exhibit intrinsic or acquired resistance, making accurate pre-treatment response prediction a critical unmet need. Transcriptomics-based biomarkers derived from bulk and single-cell RNA sequencing (scRNA-seq) offer a promising avenue for capturing tumour-immune interactions, yet the cross-cohort generalisability of existing prediction models remains unclear.We systematically benchmark nine state-of-the-art transcriptomic ICI response predictors, five bulk RNA-seq-based models (COMPASS, IRNet, NetBio, IKCScore, and TNBC-ICI) and four scRNA-seq-based models (PRECISE, DeepGeneX, Tres and scCURE), using publicly available independent datasets unseen during model development. Overall, predictive performance was modest: bulk RNA-seq models performed at or near chance level across most cohorts, while scRNA-seq models showed only marginal improvements. Pathway-level analyses revealed sparse and inconsistent biomarker signals across models. Although scRNA-seq-based predictors converged on immune-related programs such as allograft rejection, bulk RNA-seq-based models exhibited little reproducible overlap. PRECISE and NetBio identified the most coherent immune-related themes, whereas IRNet predominantly captured metabolic pathways weakly aligned with ICI biology. Together, these findings demonstrate the limited cross-cohort robustness and biological consistency of current transcriptomic ICI prediction models, underscoring the need for improved domain adaptation, standardised preprocessing, and biologically grounded model design.

This work investigates the adaptation of the AlphaZero reinforcement learning algorithm to Tablut, an asymmetric historical board game featuring unequal piece counts and distinct player objectives (king capture versus king escape). While the original AlphaZero architecture successfully leverages a single policy and value head for symmetric games, applying it to asymmetric environments forces the network to learn two conflicting evaluation functions, which can hinder learning efficiency and performance. To address this, the core architecture is modified to use separate policy and value heads for each player role, while maintaining a shared residual trunk to learn common board features. During training, the asymmetric structure introduced training instabilities, notably catastrophic forgetting between the attacker and defender roles. These issues were mitigated by applying C4 data augmentation, increasing the replay buffer size, and having the model play 25 percent of training games against randomly sampled past checkpoints. Over 100 self-play iterations, the modified model demonstrated steady improvement, achieving a BayesElo rating of 1235 relative to a randomly initialized baseline. Training metrics also showed a significant decrease in policy entropy and average remaining pieces, reflecting increasingly focused and decisive play. Ultimately, the experiments confirm that AlphaZero's self-play framework can transfer to highly asymmetric games, provided that distinct policy/value heads and robust stabilization techniques are employed.

We study language models as evolving model organisms and ask when autoregressive next-token learning selects for world-tracking representations. For any encoding of latent world states, the Bayes-optimal next-token cross-entropy decomposes into the irreducible conditional entropy plus a Jensen–Shannon excess term. That excess vanishes if and only if the encoding preserves the training ecology's equivalence classes. This yields a precise notion of ecological veridicality for language models and identifies the minimum-complexity zero-excess solution as the quotient partition by training equivalence. We then determine when this fixed-encoding analysis applies to transformer families: frozen dense and frozen Mixture-of-Experts transformers satisfy it, in-context learning does not enlarge the model's separation set, and per-task adaptation breaks the premise. The framework predicts two characteristic failure modes: simplicity pressure preferentially removes low-gain distinctions, and training-optimal models can still incur positive excess on deployment ecologies that refine the training ecology. A conditional dynamic extension shows how inter-model selection and post-training can recover such gap distinctions under explicit heredity, variation, and selection assumptions. Exact finite-ecology checks and controlled microgpt experiments validate the static decomposition, split-merge threshold, off-ecology failure pattern, and two-ecology rescue mechanism in a regime where the relevant quantities are directly observable. The goal is not to model frontier systems at scale, but to use small language models as laboratory organisms for theory about representational selection.

As language models shift from single-shot answer generation toward multi-step reasoning that retrieves and consumes evidence mid-inference, evaluating the role of individual retrieved items becomes more important. Existing RAG evaluation typically targets final-answer quality, citation faithfulness, or answer-level attribution, but none of these directly targets the intervention-based, per-evidence-item utility view we study here. We introduce CUE-R, a lightweight intervention-based framework for measuring per-evidence-item operational utility in single-shot RAG using shallow observable retrieval-use traces. CUE-R perturbs individual evidence items via REMOVE, REPLACE, and DUPLICATE operators, then measures changes along three utility axes (correctness, proxy-based grounding faithfulness, and confidence error) plus a trace-divergence signal. We also outline an operational evidence-role taxonomy for interpreting intervention outcomes. Experiments on HotpotQA and 2WikiMultihopQA with Qwen-3 8B and GPT-5.2 reveal a consistent pattern: REMOVE and REPLACE substantially harm correctness and grounding while producing large trace shifts, whereas DUPLICATE is often answer-redundant yet not fully behaviorally neutral. A zero-retrieval control confirms that these effects arise from degradation of meaningful retrieval. A two-support ablation further shows that multi-hop evidence items can interact non-additively: removing both supports harms performance far more than either single removal. Our results suggest that answer-only evaluation misses important evidence effects and that intervention-based utility analysis is a practical complement for RAG evaluation.

Multimodal representation learning is commonly built on a shared-private decomposition, treating latent information as either common to all modalities or specific to one. This binary view is often inadequate: many factors are shared by only subsets of modalities, and ignoring such partial sharing can over-align unrelated signals and obscure complementary information. We propose Hierarchical Contrastive Learning (HCL), a framework that learns globally shared, partially shared, and modality-specific representations within a unified model. HCL combines a hierarchical latent-variable formulation with structural sparsity and a structure-aware contrastive objective that aligns only modalities that genuinely share a latent factor. Under uncorrelated latent variables, we prove identifiability of the hierarchical decomposition, establish recovery guarantees for the loading matrices, and derive parameter estimation and excess-risk bounds for downstream prediction. Simulations show accurate recovery of hierarchical structure and effective selection of task-relevant components. On multimodal electronic health records, HCL yields more informative representations and consistently improves predictive performance.

Obtaining high-quality labels is costly, whereas unlabeled covariates are often abundant, motivating semi-supervised inference methods with reliable uncertainty quantification. Prediction-powered inference (PPI) leverages a machine-learning predictor trained on a small labeled sample to improve efficiency, but it can lose efficiency under model misspecification and suffer from coverage distortions due to label reuse. We introduce Machine-Learning-Assisted Generalized Entropy Calibration (MEC), a cross-fitted, calibration-weighted variant of PPI. MEC improves efficiency by reweighting labeled samples to better align with the target population, using a principled calibration framework based on Bregman projections. This yields robustness to affine transformations of the predictor and relaxes requirements for validity by replacing conditions on raw prediction error with weaker projection-error conditions. As a result, MEC attains the semiparametric efficiency bound under weaker assumptions than existing PPI variants. Across simulations and a real-data application, MEC achieves near-nominal coverage and tighter confidence intervals than CF-PPI and vanilla PPI.

We study a controlled partial-KV decoding setting in which exact unnormalized softmax contributions are computed for sink/tail anchors and a retrieved token set, while the remaining prefill tokens are represented by a residual estimate. We focus on the accounting rule after the query-dependent exact support has been selected, and use exhaustive Top-K only as an oracle selector, not as a deployable retrieval system. The proposed rule leaves the backbone language model and the exact-branch KV tensors unchanged. It builds fixed-size summary states $(S,u)$ from learned positive feature maps $\phi$, subtracts retrieved-token feature contributions to keep the exact and residual sets non-overlapping, and merges the estimated residual numerator and denominator with the exact branch under one normalization. At a 1% exact-support budget, our residual-completion method improves over the selection-only Top-K baseline on RULER and BABILong across frozen 1B and 3B Llama-3.2-Instruct backbones at all reported context lengths. In the 0.5-4% exact-support budget sweeps, this trend largely persists. On LongBench, summarization results are mostly favorable, while multi-document QA is mixed. Attention-output diagnostics support retrieved-token subtraction as the partition-consistent accounting rule, while indicating that the main remaining error is imperfect learned-$\phi$ approximation of the unretrieved residual mass.

Low-Rank Adaptation (LoRA) is now the dominant method for parameter-efficient fine-tuning of large language models, but achieving a high-quality adapter often requires systematic hyperparameter tuning because LoRA performance is highly sensitive to configuration choices. In practice, this leads to many concurrent LoRA jobs, often spanning heterogeneous tasks in multi-tenant environments. Existing systems largely handle these jobs independently, which both wastes computation on weak candidates and leaves GPUs underutilized. We present ALTO (Adaptive LoRA Tuning and Orchestration), a co-designed training system that accelerates LoRA hyperparameter tuning while enabling efficient cluster sharing across heterogeneous tasks. The central insight behind ALTO is that when multiple tuning jobs run concurrently over a shared frozen backbone, they expose optimization opportunities that single-job designs cannot exploit. Building on this, ALTO monitors loss trajectories to terminate unpromising configurations early, uses fused grouped GEMM together with a new rank-local adapter parallelism to co-locate surviving adapters and reclaim freed GPU capacity, and combines intra-task and inter-task scheduling to improve multi-task placement by leveraging the predictable duration of LoRA jobs. Extensive evaluation shows that ALTO achieves up to $13.8\times$ speedup over state-of-the-art without sacrificing adapter quality.

Recent work has shown that removing orthogonalization during training and applying it only at inference improves rotation estimation in deep learning, with empirical evidence favoring 9D representations with SVD projection. However, the theoretical understanding of why SVD orthogonalization specifically harms training, and why it should be preferred over Gram-Schmidt at inference, remains incomplete. We provide a detailed gradient analysis of SVD orthogonalization specialized to $3 \times 3$ matrices and $SO(3)$ projection. Our central result derives the exact spectrum of the SVD backward pass Jacobian: it has rank $3$ (matching the dimension of $SO(3)$) with nonzero singular values $2/(s_i + s_j)$ and condition number $\kappa = (s_1 + s_2)/(s_2 + s_3)$, creating quantifiable gradient distortion that is most severe when the predicted matrix is far from $SO(3)$ (e.g., early in training when $s_3 \approx 0$). We further show that even stabilized SVD gradients introduce gradient direction error, whereas removing SVD from the training loop avoids this tradeoff entirely. We also prove that the 6D Gram-Schmidt Jacobian has an asymmetric spectrum: its parameters receive unequal gradient signal, explaining why 9D parameterization is preferable. Together, these results provide the theoretical foundation for training with direct 9D regression and applying SVD projection only at inference.

Continuous-time stochastic control with time-inhomogeneous jump-diffusion dynamics is central in finance and economics, but computing optimal policies is difficult under explicit time dependence, discontinuous shocks, and high dimensionality. We propose an actor-critic framework that serves as a mesh-free solver for entropy-regularized control problems and stochastic games with jumps. The approach is built on a time-inhomogeneous little q-function and an appropriate occupation measure, yielding a policy-gradient representation that accommodates time-dependent drift, volatility, and jump terms. To represent expressive stochastic policies in continuous-action spaces, we parameterize the actor using conditional normalizing flows, enabling flexible non-Gaussian policies while retaining exact likelihood evaluation for entropy regularization and policy optimization. We validate the method on time-inhomogeneous linear-quadratic control, Merton portfolio optimization, and a multi-agent portfolio game, using explicit solutions or high-accuracy benchmarks. Numerical results demonstrate stable learning under jump discontinuities, accurate approximation of optimal stochastic policies, and favorable scaling with respect to dimension and number of agents.

The sequential recommendation (SR) task aims to predict the next item based on users' historical interaction sequences. Typically trained on historical data, SR models often struggle to adapt to real-time preference shifts during inference due to challenges posed by distributional divergence and parameterized constraints. Existing approaches to address this issue include test-time training, test-time augmentation, and retrieval-augmented fine-tuning. However, these methods either introduce significant computational overhead, rely on random augmentation strategies, or require a carefully designed two-stage training paradigm. In this paper, we argue that the key to effective test-time adaptation lies in achieving both effective augmentation and efficient adaptation. To this end, we propose Retrieve-then-Adapt (ReAd), a novel framework that dynamically adapts a deployed SR model to the test distribution through retrieved user preference signals. Specifically, given a trained SR model, ReAd first retrieves collaboratively similar items for a test user from a constructed collaborative memory database. A lightweight retrieval learning module then integrates these items into an informative augmentation embedding that captures both collaborative signals and prediction-refinement cues. Finally, the initial SR prediction is refined via a fusion mechanism that incorporates this embedding. Extensive experiments across five benchmark datasets demonstrate that ReAd consistently outperforms existing SR methods.

Linear matrix inequalities (LMIs) have played a central role in certifying stability, robustness, and forward invariance of dynamical systems. Despite rapid development in learning-based methods for control design and certificate synthesis, existing approaches often fail to preserve the hard matrix inequality constraints required for formal guarantees. We propose LMI-Net, an efficient and modular differentiable projection layer that enforces LMI constraints by construction. Our approach lifts the set defined by LMI constraints into the intersection of an affine equality constraint and the positive semidefinite cone, performs the forward pass via Douglas-Rachford splitting, and supports efficient backward propagation through implicit differentiation. We establish theoretical guarantees that the projection layer converges to a feasible point, certifying that LMI-Net transforms a generic neural network into a reliable model satisfying LMI constraints. Evaluated on experiments including invariant ellipsoid synthesis and joint controller-and-certificate design for a family of disturbed linear systems, LMI-Net substantially improves feasibility over soft-constrained models under distribution shift while retaining fast inference speed, bridging semidefinite-program-based certification and modern learning techniques.

Retrieval-augmented generation (RAG) mitigates hallucination but does not eliminate it: a deployed system must still decide, at inference time, whether its answer is actually supported by the retrieved evidence. We introduce LatentAudit, a white-box auditor that pools mid-to-late residual-stream activations from an open-weight generator and measures their Mahalanobis distance to the evidence representation. The resulting quadratic rule requires no auxiliary judge model, runs at generation time, and is simple enough to calibrate on a small held-out set. We show that residual-stream geometry carries a usable faithfulness signal, that this signal survives architecture changes and realistic retrieval failures, and that the same rule remains amenable to public verification. On PubMedQA with Llama-3-8B, LatentAudit reaches 0.942 AUROC with 0.77,ms overhead. Across three QA benchmarks and five model families (Llama-2/3, Qwen-2.5/3, Mistral), the monitor remains stable; under a four-way stress test with contradictions, retrieval misses, and partial-support noise, it reaches 0.9566–0.9815 AUROC on PubMedQA and 0.9142–0.9315 on HotpotQA. At 16-bit fixed-point precision, the audit rule preserves 99.8% of the FP16 AUROC, enabling Groth16-based public verification without revealing model weights or activations. Together, these results position residual-stream geometry as a practical basis for real-time RAG faithfulness monitoring and optional verifiable deployment.

The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the individual-heterogeneous sub-Gaussian mixture model, a flexible framework that assigns each observation its own heterogeneity parameter, thereby explicitly capturing the heterogeneity inherent in practical applications. Built upon this model, we propose an efficient spectral method that provably achieves exact recovery of the true cluster labels under mild separation conditions, even in high-dimensional settings where the number of features far exceeds the number of samples. Numerical experiments on both synthetic and real data demonstrate that our method consistently outperforms existing clustering algorithms, including those designed for classical Gaussian mixture models.

Achieving resilient and high-quality manufacturing requires reliable data-driven anomaly detection methods that are capable of addressing differences in behaviors among different individual machines which are nominally the same and are executing the same processes. To address the problem of detecting anomalies in a machine using sensory data gathered from different individual machines executing the same procedure, this paper proposes a cross-machine time-series anomaly detection framework that integrates a domain-invariant feature extractor with an unsupervised anomaly detection module. Leveraging the pre-trained foundation model MOMENT, the extractor employs Random Forest Classifiers to disentangle embeddings into machine-related and condition-related features, with the latter serving as representations which are invariant to differences between individual machines. These refined features enable the downstream anomaly detectors to generalize effectively to unseen target machines. Experiments on an industrial dataset collected from three different machines performing nominally the same operation demonstrate that the proposed approach outperforms both the raw-signal-based and MOMENT-embedding feature baselines, confirming its effectiveness in enhancing cross-machine generalization.

Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d. test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such as error rate are well-defined, and test error reliably approximates population error given sufficiently large datasets. In contrast, evaluation is more challenging for generative models due to their open-ended nature: it is unclear which metrics are appropriate and whether such metrics can be reliably evaluated from finite samples. In this work, we introduce a theoretical framework for evaluating generative models and establish evaluability results for commonly used metrics. We study two categories of metrics: test-based metrics, including integral probability metrics (IPMs), and Rényi divergences. We show that IPMs with respect to any bounded test class can be evaluated from finite samples up to multiplicative and additive approximation errors. Moreover, when the test class has finite fat-shattering dimension, IPMs can be evaluated with arbitrary precision. In contrast, Rényi and KL divergences are not evaluable from finite samples, as their values can be critically determined by rare events. We also analyze the potential and limitations of perplexity as an evaluation method.

A deep neural network (DNN) has been developed to accurately predict nuclear charge density distributions for nuclei with proton numbers $Z \geq 8$. By incorporating essential nuclear structure features, the model achieves a significant improvement in predictive accuracy over conventional methods. The charge density distributions are analyzed using a Fourier-Bessel (FB) series expansion, and the DNN is trained on a comprehensive dataset derived from relativistic continuum Hartree-Bogoliubov (RCHB) theory calculations. The model demonstrates exceptional performance, with root-mean-square deviations of 0.0123 fm and 0.0198 fm for charge radii on the training and validation sets, respectively, remarkably surpassing the precision of the original RCHB calculations. Beyond advancing nuclear physics research, this high-precision model provides critical data for applications in atomic physics, nuclear astrophysics, and related fields.

Large language models (LLMs) often produce confident yet incorrect answers, which can lead to risky failures in real-world applications. We study whether post-training can make a model's self-assessment explicit: when the model is uncertain, can it be trained to signal so within its own response? A central design question is where in the response this signal should be exposed – during reasoning, while the answer is still being formed, or at the end, once the answer has been produced. We study both. For end-of-reasoning self-assessment, we train the model to verbalize a confidence score for its response, with the aim of high confidence on correct answers and low confidence on incorrect ones. For during-reasoning self-assessment, we train the model to emit the marker <uncertain> whenever its current reasoning state appears unreliable. Across factual reasoning tasks, both forms sharply reduce overconfident errors while improving answer quality, and both can be used as triggers for retrieval augmented generation (RAG) to improve the final response. We further analyze their internal mechanisms: end-of-reasoning verbalized confidence sharpens a confidence-related structure already present in the pretrained model, whereas during-reasoning <uncertain> emission teaches the model to mark high-risk reasoning steps, with parameter changes concentrated in the model's late layers.

Sampling physical systems with rough energy landscapes is hindered by rare events and metastable trapping. While Boltzmann generators already offer a solution, their reliance on the reverse Kullback–Leibler divergence frequently induces catastrophic mode collapse, missing specific modes in multi-modal distributions. Here, we introduce the Jeffreys Flow, a robust generative framework that mitigates this failure by distilling empirical sampling data from Parallel Tempering trajectories using the symmetric Jeffreys divergence. This formulation effectively balances local target-seeking precision with global modes coverage. We show that minimizing Jeffreys divergence suppresses mode collapse and structurally corrects inherent inaccuracies via distillation of the empirical reference data. We demonstrate the framework's scalability and accuracy on highly non-convex multidimensional benchmarks, including the systematic correction of stochastic gradient biases in Replica Exchange Stochastic Gradient Langevin Dynamics and the massive acceleration of exact importance sampling in Path Integral Monte Carlo for quantum thermal states.