Papers

Mutual information (MI)-inspired feature learning techniques are capable of generating low-dimensional embeddings that retain nonlinear dependence structures, but direct estimations of MI suffer from noisy probability distribution estimates in the low-data regime. The H-Score objective, computed from second-order statistics, provides a practical proxy metric for training feature extraction networks. We prove that H-Score is invariant to invertible transformations in the unrestricted functional setting, but becomes sensitive to input basis rotations under constrained approximation classes. Consequently, we study unitary preconditioning for H-Score networks and show that selecting an appropriate basis rotation reduces finite-width truncation error by concentrating predictive dependence into fewer dominant modes. We identify the fast Fourier transform (FFT) as an effective data-independent, low-cost preconditioner for approximately stationary processes, where spectral structure induces concentration of the cross-covariance singular value spectrum. We introduce training-free metrics based on spectral entropy and cumulative dependence energy to quantify basis suitability and predict downstream inference gains prior to network training. Experiments across eight multivariate datasets demonstrate that FFT preconditioning is particularly useful in resource-constrained regimes, achieving up to 50% normalized mean squared error (NMSE) reduction, while the proposed metrics correlate with observed performance gains and correctly identify cases where spectral preconditioning is detrimental.

We study online resource allocation when both rewards and consumption sizes may be continuously distributed. Requests arrive sequentially and must be accepted or rejected irrevocably under fixed resource capacities. Each request belongs to one of finitely many observable types; conditional on an observable request type, both the reward and the scalar size are random, and the realized size scales a fixed type-specific resource-consumption vector. The model allows the deterministic fluid relaxation to be degenerate. We show that additive regret is governed by the size-weighted mass of requests whose value-to-size ratios lie near the active acceptance cutoffs. We formalize this quantity through an active weighted-mass exponent p. When p > 1, this cutoff mass is thin, and the problem is genuinely hard: every online policy must incur regret of order at least $T^{1/2 - 1/(2p)}$, and this holds for every p > 1. A sample-path marginal policy matches this lower bound up to polylogarithmic factors; and when p = 1, so that the mass grows linearly near the cutoff, it attains $O((\log T)^2)$ regret. For example, if the size and the value-to-size ratio are independent and uniformly distributed, then p = 1; if instead the size and the reward are independent and uniformly distributed, then p = 2. Thus the policy achieves $o(\sqrt{T})$ regret throughout this regularity class without any fluid non-degeneracy assumption, allowing both primal degeneracy and dual non-uniqueness.

Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers. The obstacle is increasingly understood to be one of optimisation, owing to the severely ill-conditioned loss landscape. We present $\textbf{DSGNAR}$: Doubly-Sketched Gauss-Newton with Adaptive Ratio, a scalable second-order optimisation framework that confronts this ill-conditioning and, in doing so, obtains unprecedented accuracy and speed. $\textbf{DSGNAR}$ couples a doubly-sketched Gauss-Newton model with a novel strategy that carefully controls both regularisation and step length. Across a suite of problems spanning nonlinear, chaotic, multi-scale, high-dimensional, and Navier-Stokes, the framework greatly improves on the state of the art: able to attain relative $\ell_2$ errors as low as $3\times10^{-16}$ in double precision, improve contemporary results by five orders of magnitude on the canonical Burgers' equation, and as much as eight orders on a high-dimensional Poisson problem, while remaining markedly faster. We further show that, in single precision, solutions at the limit of round-off error can be obtained very quickly: Burgers' equation to $\ell_2^{\text{rel}} = 4.75 \times 10^{-7}$ in under ten seconds. The framework is also robust to the choice of architecture, arithmetic precision, and initial hyperparameters. The code is available at https://www.github.com/wephy/physics-informed-neural-networks

Distributed machine learning enables collaborative model training without centralizing data, but it also exposes learning processes to privacy leakage and malicious manipulation. Existing defenses typically address these threats in isolation and are often tailored to specific learning paradigms or model architectures, limiting their applicability in realistic deployments. In particular, federated learning and decentralized learning exhibit distinct adversarial surfaces that are rarely addressed within a unified framework. In this paper, we present a model-agnostic framework for adversary-resistant distributed learning that jointly addresses privacy preservation and malicious behavior across both federated and decentralized settings. Our approach combines paradigm-specific defense mechanisms with GPBACC, a privacy-enhancing coded computing technique applicable to arbitrary machine learning models. For federated learning, we integrate robust aggregation strategies to mitigate the impact of malicious participants, while for decentralized learning we employ approximate decode-and-compare and group testing techniques to enable lightweight verification and adversary isolation without relying on a trusted aggregator. Crucially, we evaluate the proposed framework through an explicit, attack-driven analysis. We implement representative privacy attacks and malicious behaviors, and empirically demonstrate that the combination of GPBACC with robust aggregation and verification mechanisms significantly reduces privacy leakage and improves resilience against active adversaries. These results suggest that privacy-enhancing coded computing, when combined with appropriate adversary-resistance strategies, provides a practical and deployable foundation for secure distributed machine learning.

Large language models (LLMs) exhibit remarkable reasoning capabilities, but their task-specific fine-tuning is notoriously plagued by overconfidence, severely hindering trustworthy deployment. We propose Data-Adaptive Lower-Rank Adaptation (DALorRA), a simple and effective variational Bayesian sparse framework that shifts the paradigm of uncertainty quantification from the dense parameter space to the lightweight rank level of low-rank adaptation (LoRA). With the insight that LoRA essentially aggregates multiple rank-one components that may provide superfluous model capacity, DALorRA imposes stochastic masking on rank dimensions, enabling Bayesian regularization of model capacity during training and ensemble-like calibration during inference. Extensive experiments demonstrate DALorRA's excellent calibration of LLMs without compromising reasoning accuracy.

Multiple-choice medical benchmarks are increasingly saturated, and recent rubric-based evaluations such as HealthBench have shown that open-ended clinical performance is far from solved - its "Hard" subset top score remains 32%. We present a small, deliberately difficult evaluation dataset of five clinician-authored clinical scenarios spanning four specialties (anaesthesia, internal/family medicine, emergency medicine, and obstetrics), each accompanied by an atomic, weighted, MECE rubric (25-62 criteria per task; 184 criteria total) authored from a clinician-drafted golden answer. We evaluate three frontier models: GPT 5.4, Claude Opus 4.7, and Gemini 3.1 Pro. Mean rubric pass rates were 0.47 (Claude), 0.38 (GPT), and 0.37 (Gemini). The central finding is an inversion of clinical priority: the highest-weighted (weight-5, critical) criteria passed at only 32.4-41.7%, while low-stakes weight-1 criteria passed at 80-90%. 55 of 108 critical (weight-5) criteria (51%) were satisfied by no model. Three LLM autoraters reproduced expert met/not-met labels on 92.8-94.6% of 552 graded criteria. We position this as a methods-and-preliminary-findings contribution: the five tasks demonstrate a scalable, defensible pipeline ready to develop into a large-scale benchmark.

The rapid advancements in using neural networks as implicit data representations have attracted significant interest in developing machine learning methods that analyze and process the weight spaces of other neural networks. However, efficiently handling these highdimensional weight spaces remains challenging. Existing methods often overlook the sequential nature of layer-by-layer processing in neural network inference. In this work, we propose a novel approach using dynamic graphs to represent neural network parameters, capturing the temporal dynamics of inference. Our Dynamic Neural Graph Encoder (DNG-Encoder) processes these graphs, preserving the sequential nature of neural processing. Additionally, we also leverage DNG-Encoder to develop INR2JLS (Implicit Neural Representation to Joint Latent Space) for facilitate downstream applications, such as classifying Implicit Neural Representations (INRs). Our approach demonstrates significant improvements across multiple tasks, surpassing the state-of-the-art INR classification accuracy by approximately 10% on the CIFAR-100-INR.

This paper studies additive regret in the multi-secretary problem, defined as the gap between the expected offline prophet reward and the reward of the best online policy. Prior work established \(O(\log T)\) regret for bounded-density distributions with connected support and \(O((\log T)^2)\) upper bounds for bounded-density distributions with support gaps. It was unknown whether the extra logarithmic factor is necessary even in the one-resource model. We prove that it is necessary. For a mixture of two separated uniform distributions at the critical capacity, the optimal regret grows at least on the order of \((\log T)^2\). Thus the existing \(O((\log T)^2)\) upper bounds for bounded-density gapped instances, including those implied by network revenue management models with continuous rewards, are tight in this simplest specialization. The same framework also yields a matching lower bound for gapped distributions whose gap-facing densities vanish near the support edges; this companion result is given in the appendix. The proofs use Bellman certificates: feasible solutions to a relaxation of the exact Bellman recursion. This framework converts lower bounds into explicit certificate constructions and identifies why support gaps permit larger regret.

Alzheimers disease (AD) is a brain disorder that develops slowly and mainly affects memory, thinking, language, and daily activities. It is one of the most common causes of dementia and creates many difficulties for patients as well as their families. In the early stage, the symptoms are often mild and may look like normal ageing. For this reason, many people are diagnosed late, when the disease has already progressed. At present, there is no complete cure for AD. Still, early detection can help doctors manage the condition better and take suitable steps at the right time. In this study, a machine learning model is proposed to detect the early stages of Alzheimers disease using clinical details, neuropsychological test scores, and neuroimaging-related measures. The data used in this work is collected from the Alzheimers Disease Neuroimaging Initiative (ADNI). As the dataset has missing values, iterative imputation is applied to fill them. The dataset also has class imbalance, which is handled using Borderline SVM-SMOTE. After that, feature selection is carried out using wrapper-based and embedded methods so that only important features are used for training. The selected features are divided into training and testing sets, and feature scaling is applied. A stacking ensemble model is developed using Logistic Regression, Extra Trees, Bagging KNN, and LightGBM as base classifiers. Along with this, an artificial neural network is also trained on the same dataset. The performance of these models is compared using precision, recall, F1-score, and AUC-ROC. This study aims to find the best classifier and also identify important biomarkers that may help in the early diagnosis of Alzheimers disease.

Chemical language models (CLMs) are trained with linearized representations such as SMILES, yet it remains unclear which chemically meaningful substructures they encode. To foster a better understanding of CLMs, we conduct a systematic study and probe for 78 molecular substructures across eight pre-trained and six randomly initialized models. We furthermore study how fine-tuning on chemical downstream tasks affects the learned representations of molecular substructures. Our results show that pre-training generally improves molecular structure awareness of CLMs, particularly in the upper layers. Moreover, randomly initialized models already encode ring structures well in the first layer. Our analysis on two chemical downstream tasks further reveals that, interestingly, fine-tuning affects task-relevant molecular substructures more than others, indicating that the changes in the representations follow chemical theory.

We study timestep allocation for score-based diffusion sampling, where a learned reverse-time dynamics is discretized on a finite grid. Uniform and hand-crafted schedules are standard choices, but they rely on fixed prescriptions and can therefore be suboptimal. To address this limitation, we propose Adaptive Reparameterized Time (ART), a continuous-time control formulation that learns a time change by treating the speed of the sampling clock as the control, so that a uniform grid on the learned clock induces adaptive timesteps in the original diffusion time. Based on a leading-order Euler error surrogate, ART provides a principled objective for allocating timesteps along the sampling trajectory. To solve this deterministic control problem, we introduce ART-RL, an auxiliary randomized formulation with Gaussian policies that turns schedule learning into a continuous-time reinforcement learning problem. We prove that the randomized ART-RL formulation is equivalent to ART at the optimizer level, in the sense that its optimal Gaussian policy recovers the optimal ART time-warping rate through its mean. We further establish policy evaluation and policy improvement characterizations and derive trajectory-based moment identities that yield implementable actor–critic updates for learning the schedule. Across experiments ranging from controlled low-dimensional settings to image generation, ART-RL can be plugged into existing diffusion samplers by changing only the timestep grid, consistently improving sample quality over strong baseline schedules at matched budgets while leaving the rest of the sampling pipeline unchanged. The learned schedules also exhibit broad generalization, transferring without retraining across sampling budgets, datasets, solvers, pipelines, and representation spaces.

Restoring archival film remains a fundamentally challenging problem due to the absence of paired training data and the lack of standardized evaluation benchmarks. Pristine versions of deteriorated footage are physically unrecoverable, requiring supervised methods to rely on synthetic data that often fail to capture the complex, temporally coherent nature of real film degradation. At the same time, existing real-world datasets are limited in scale, quality, and accessibility, hindering reliable evaluation and fair comparison across methods. We address both limitations with AbsoluteDegradation, a physics-inspired, modular pipeline for synthesizing realistic film degradations, and a new large-scale archival benchmark. The proposed pipeline models the analog-to-digital process as a structured composition of artifact families, incorporating signal-dependent grain, parametric scratches, and temporally coherent camera motion, enabling controlled generation of diverse degradation regimes. In parallel, we introduce a curated dataset of 81,576 high-resolution frames sourced from real archival footage, designed for consistent evaluation under real-world conditions. Together, these contributions provide a unified framework for training and benchmarking restoration models. Experiments across six restoration architectures, evaluated with no-reference image quality metrics, clip-level temporal quality assessment, and a blinded human preference study (93 raters, 1,395 trials), show that models trained with AbsoluteDegradation generalize better to real-world footage: human raters preferred them in 64.7% of comparisons and for every evaluated architecture. The proposed benchmark also reveals systematic failure modes of current methods and of no-reference metrics. We hope this work establishes a foundation for reproducible and domain-authentic evaluation in archival film restoration.

Penile measurement is clinically relevant across male reproductive and urogenital health, including conditions such as micropenis, congenital and endocrine disorders, and sexual or urinary dysfunction. However, quantitative assessment of penile size has relied mainly on external length or circumference measurements, which are difficult to standardize, sensitive to measurement conditions, and unable to capture the internal portion of the penis. MRI enables volumetric assessment of the whole penis in vivo, but automated segmentation has not previously been established at population scale. Automated whole-organ volumetry would enable high-throughput phenotyping for multi-omics and clinical studies of male reproductive disease. Here, we present a deep learning framework for whole-penis segmentation in multi-channel DIXON MRI. Using a newly curated expert-annotated training dataset ($n = 145$ subjects; $13,050$ annotated slices) and a double-annotated independent test benchmark ($n = 24$ subjects; $2,160$ double-annotated slices), we optimized a 3D nnU-Net architecture. The model achieved a 5-fold cross-validation Dice score of $0.90$ and performed at observer-level accuracy on the independent test set (Dice: $0.92$; Hausdorff distance: $3.58$). We deployed the model in $34,412$ UK Biobank participants, enabling automated quantification of total penile tissue, including both external and internal components. Longitudinal evaluation in 2,282 men demonstrated high inter-session reproducibility ($r = 0.87$). This framework establishes a reproducible and population-scalable method for MRI-based assessment of penile anatomy and provides an open technical resource for future studies in urological imaging and male reproductive health. The trained model weights will be publicly released.

Conventional traction control architectures intervene only after the adhesion limit of a tire has already been breached. This paper investigates whether Rolling Split Conformal Prediction , monitoring the volatility of non-conformity residuals from a per-driver Random Forest model of expected slip behavior , can serve as a statistically grounded pre-incident warning signal, ahead of gross traction loss. Unlike an earlier internal draft of this work, the evaluation reported here corrects a confound in the slip proxy (vehicle speed is included as an explicit model feature, not left implicit in the target's denominator), uses every racing lap for each driver rather than only the fastest lap, and is scored against real, timestamped incident labels extracted from FIA Race Control Messages and track-limits lap deletions rather than narrated post-hoc. The result is negative: across 19 drivers and 55,563 test-phase telemetry samples, the rolling-volatility detector achieves a mean precision of essentially 0.0 and mean recall of 0.0 against 14 ground-truth incidents, while flagging on average 15.3% of all samples as anomalous , too high a false-alarm rate for any early-warning use. A static 95th-percentile threshold baseline performs no better in any way that would justify the added complexity of the conformal-volatility formulation. Residual autocorrelation diagnostics show the split-conformal exchangeability assumption is violated for every driver (Ljung-Box p < 0.001, n = 19/19), which is one plausible driver of the high false-alarm rate. We report this as a methodologically rigorous negative finding, diagnose its likely causes, and outline what a genuinely predictive version of this approach would require.

Large language models (LLMs) are increasingly used as cheap, scalable judges that compare candidate outputs pairwise. Because such judges prefer verbose or well-formatted answers, the natural fix is to add bias covariates to a Bradley–Terry model and estimate the bias away. We show this cannot work as advertised: the quality/bias split is not identified by pairwise comparisons, and the failure is exact – across $48$ real judge-pools the profile likelihood over the coefficient is flat to $\mathbf{0.0000}$ nats, and scaling the comparisons $26\times$ buys none. A “debiased” score is selected by the prior, not recovered from data. Our contribution is accordingly not a better estimator but a characterization of when prior-based correction is justified, plus designs that supply the missing information when it is not. The assumption the prior encodes – quality is a priori uncorrelated with the covariate – pays only while $\mathrm{corr}(\theta,x)$ stays below a crossing point (configuration-dependent, $0.22$–$0.60$), which is what makes the same model help on LLMBar and hurt on SummEval and Nectar. We give two escapes: a trusted-anchor gate that decides per (judge, covariate, task) (no false enables in $6{,}000$ decisions at $K\ge10$ anchors, a rate our sample bounds at $\le6\%$), and a paired rendering design. Across fifteen real LLM judges bias is heterogeneous and capability-dependent: correction improves \topk{} recall by $0.20$–$0.32$ on five biased-but-competent cheap judges and is a no-op on frontier ones (Spearman $\rho{=}{-}0.84$ between competence and gain over the $14$ competent judges, $p{<}10^{-3}$), concentrating the benefit where at-scale evaluation happens.

Classifying heterogeneous omics data remains a fundamental challenge in computational biology, particularly in high-dimensional, small-sample settings where nonlinear interactions dominate and class imbalance further complicates reliable prediction of minority phenotypes. While traditional kernel methods rely on feature abundance, they fail to leverage the known interaction landscapes of biological systems. In this work, we propose a structured Gaussian process classification framework that integrates graph-encoded biological pathways directly into the kernel construction. By propagating information along known interaction networks and combining this with abundance-derived features, the resulting classifier captures both quantitative measurements and topological context. We benchmark our proposed methodology on three publicly available gut and fecal microbiome datasets. To address severe class imbalance, we evaluate complementary strategies, including data-level resampling, threshold calibration, and confusion-matrix-based adjustments, and report minority-class performance alongside accuracy. The hybrid approach yields a performance gain over unstructured baselines and matches the performance of established benchmarks for similar datasets. Furthermore, the probabilistic nature of the framework naturally provides calibrated predictive uncertainty, enabling robust differentiation between confident predictions and ambiguous samples.

Large kernel depthwise convolutions achieve strong performance but suffer from significant degradation as kernel size grows due to irregular memory access from gather-based computation; while Large Kernel Acceleration (LKA) helps on small feature maps, it becomes counterproductive on large feature maps, even slower than non-accelerated implementations. We propose Windowed Batch Matrix Multiplication (WBMM), which partitions input into contiguous windows and indexes a compact relative position bias table to construct weight matrices, enabling regular memory access via batched matrix multiplication. This yields a unique property: WBMM's throughput improves with larger windows, opposite to depthwise convolutions that degrade with larger kernels. Operator-level benchmarks show WBMM with 14x14 windows outperforms 5x5 depthwise convolution baselines in speed while providing a 7.8x larger per-layer receptive field. Combined with inter-block cross-window communication and hierarchical window reparameterization, WBMM achieves comparable or higher accuracy on ImageNet-1K, COCO, and ADE20K with 1.31-1.88x training speedup, and demonstrates consistent advantages across GPU, CPU, and edge devices without requiring specialized acceleration kernels. Our code is available at https://github.com/wansong-s/WBMM.

We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-Bénard convection by predicting time increments instead of full solutions, achieving higher accuracy than a standard FNO baseline. The resulting model is compact (314k parameters, 1.26 MB) and fast (7 ms inference), while maintaining similar accuracy as demonstrated in previous benchmarks. We show that although FNOs generalize to finer meshes, accuracy remains limited by the resolution of the training data.

Hierarchical state-space models (HSSMs) offer a promising approach to long-horizon prediction by segmenting sequences into temporal chunks. However, their performance hinges on how chunk boundaries are determined. While prior HSSMs typically rely on fixed-length chunking or similarity-based boundary detection, these methods often misalign with the intrinsic temporal structure of the data. We argue that chunking should instead be driven by prediction errors, which more directly indicate when longer-range context becomes necessary. Nevertheless, integrating surprise-based chunking into HSSMs introduces critical challenges, including hierarchical collapse during end-to-end training and the absence of surprise signals during open-loop prediction. To address these issues, we propose Surprise-based Nested Temporal Abstraction (SUNTA), a method that employs a decoupled training strategy to preserve surprise signals and uses internal inconsistency as a top-down surprise metric to determine chunk boundaries within imagined rollouts. Experiments on video prediction tasks in 2D and 3D environments demonstrate that SUNTA outperforms baselines, uniquely maintaining accurate predictions over 250 timesteps, whereas all baselines degrade within the first 10 timesteps.

We present HaloGuard 1.0, an open-weights implementation of the constitutional-classifier paradigm for input safety. It achieves state-of-the-art performance on English and multilingual prompt-safety benchmarks at roughly one-tenth the model size of current leading open guard models. The safety constitution is the organising structure of the corpus: a natural-language constitution of 46 policies and 2,940 subcategories drives synthetic data generation, with exhaustive one-to-one paired counterfactuals that hold topic and vocabulary fixed while flipping intent, a two-tier harmless design that separately targets boundary and baseline false positives (FPs), and balanced multilingual materialisation across 46 languages that treats language as a surface form appearing on both sides of the boundary rather than as an adversarial signal. Across seven prompt-safety benchmarks, HaloGuard 1.0-0.8B attains the best average F1 (90.9) of any open guard we evaluate, outperforming baselines up to 27B parameters (over 30 times larger) while holding false-positive rate (FPR) to 4.3 and false-negative rate (FNR) to 9.5. The HaloGuard 1.0-4B variant reaches average F1 of 92.1 and FPR of 3.5, spending its extra capacity on precision rather than recall. A structured adjudication of the remaining failures indicates that most apparent missed-harm cases are benchmark mislabels rather than genuine model misses. An always-on adversarial red-teaming protocol continuously hardens the guard against both content-level and agentic attacks. We release the models as open weights.

Long-context reasoning requires models to locate, revise, and synthesize evidence distributed across lengthy inputs. Existing long-context RL methods usually reward final answers or static evidence extraction, offering little feedback on how intermediate actions change the model's evidence state. We propose Maven, a reinforcement learning framework with an editable evidence memory. Maven defines an answer-conditioned evidence-state value and rewards action-level state transitions: add actions are credited by marginal gain and hindsight contribution, link actions by evidence synergy, and drop actions by improved answer support after removing misleading evidence. These rewards are assigned to the corresponding action spans in GRPO. Across Llama and Qwen models on LongBench v2, LongReason, and RULER, Maven outperforms outcome-only RL and evidence-identification baselines, producing more sufficient evidence sets and lower distractor retention. Our results show that long-context RL benefits from optimizing stateful evidence navigation rather than one-shot evidence extraction.

Large language models (LLMs) are increasingly deployed in domains requiring guardrails to detect unsafe, off-topic, or adversarial prompts. Existing guardrails predominantly rely on fine-tuning to build classifiers, which often suffer from low generalization and high inference latency. We present kNNGuard, a training-free guardrail that utilizes the activation space of an off-the-shelf LLM. Given a small bank of 50 safe and unsafe prompts, kNNGuard extracts hidden activations and performs multi-layer kNN fusing activation-space and embedding-space scores for classification. Across six domains spanning topical and security prompts, kNNGuard achieves competitive or superior F1 compared to fine-tuned state-of-the-art guardrails while running 2.7x faster than the best comparable guardrail, and 10x faster than a fine-tuned safety classifier without gradient updates or fine-tuning. Domain adaptation requires only updating the labeled bank, which can be constructed in under 10 seconds and several orders of magnitude faster than established guardrails. We also analyze the impact of system prompts, layer selection, and integration into production LLM pipelines as a configurable, low-latency guardrail.

Graph Neural Networks (GNNs) have been widely used to capture spatial functional connectivity patterns to improve electroencephalography (EEG)-based depression recognition performance. However, the functional connectivity of brain networks in patients with depression exhibits an inherent hierarchical structure, making it difficult to capture accurate connection patterns. To address these issues, this paper proposes a novel model named Sample-Adaptive Hyperbolic Graph Neural Network (SA-HGNN), which aims to accurately extract the authentic hierarchical structure of depression-affected brain networks. Specifically, the proposed model comprises three core modules. First, a Sample-Adaptive Graph Construction module dynamically constructs personalized brain network topologies to capture more complex spatial relationships within the brain network. Second, hyperbolic graph convolution is employed to overcome the representation bottlenecks of Euclidean space, leveraging hyperbolic geometry to precisely capture latent hierarchical relationships within the brain network. Finally, an Attention Pooling module adaptively filters out highly redundant noise channels in EEG signals, effectively mitigating the interference of inherent noise on the authentic hierarchical topology. Extensive experiments on public EEG datasets demonstrate the superior performance of our method across resting-state and task-related paradigms, validating its robustness to noise and efficacy in capturing abnormal functional connectivity patterns in brain networks of patients with depression.

Performance evaluation in AI systems commonly assumes that random dataset splits produce independent and identically distributed (i.i.d.) subsets. We show that this assumption often breaks down in spatiotemporally correlated domains such as aerial surveillance, precision agriculture, and medical imaging, leading to two systematic failures: data leakage, where correlated samples span training and validation splits and inflate performance estimates, and hidden stratification, where errors on minority subpopulations are obscured by aggregate metrics. To address these issues, we propose a unified evaluation and training framework for spatially correlated data. We introduce Structure-Aware Stratified Partitioning (SASP), which constructs validation splits that reduce spatiotemporal leakage while preserving meaningful class balance, and Curriculum Distributionally Robust Optimization (CDRO), a curriculum-based relaxation of distributionally robust training that stabilizes optimization under these stricter splits. Across multiple benchmarks, this combination yields consistently improved generalization, more reliable confidence calibration, and exposes failure modes that remain hidden under conventional random-split evaluation.

Motivated by the challenge of stabilizing a general unknown linear dynamical system (LDS) from observations, we study the natural prerequisite of online prediction. Our goal is to achieve sublinear regret with a memory footprint that adapts to the intrinsic complexity of the dynamics rather than the full hidden-state dimension. We focus on the practically central regime of systems with low instability complexity – eigenvalues outside the real stable interval that do not decay rapidly, together with non-semisimple modes – potentially embedded in an otherwise stable real spectrum of much higher dimension; we write $k$ for this count. This regime is the primary setting in which stabilization is plausible: we show that many systems with high instability complexity cannot be stabilized without exponentially large controls. Thus, prediction is meaningful for stabilization precisely when the instability complexity is small. Within this regime, we introduce a unified online algorithm that handles every LDS (including non-diagonalizable systems with complex or exploding modes) with a learnable parameter count of $\widetilde{O}(k)$. Finally, we prove a lower bound showing that $k$ is a valid complexity measure: any filter-based predictor needs at least $k$ filters. Experiments corroborate our theory: on a high-dimensional system, our predictor sharply outperforms prior methods at an equal parameter budget.

Anomaly detection is a critical and evolving field in Machine Learning, with applications targeting different domains such as cybersecurity, finance, healthcare, manufacturing and IoT (Internet of Things) systems. Traditionally, anomaly detection algorithms have been designed using both supervised and unsupervised learning paradigms. The fundamental challenge in real-world anomaly detection scenarios is related to the inherent class imbalance (anomalies are typically rare) and, for supervised methods, to the scarcity of labelled anomalous data. Indeed, labelling is both expensive and time-consuming. Conversely unsupervised methods do not require labelling, but may suffer from high false positive rates when deployed in safety-critical applications. In this work we introduce a novel unsupervised algorithm for anomaly detection in time series based on the Haar discrete wavelet and a suitably designed $t$-test. We establish the theoretical foundation of the proposed $t$-test and, through extensive experimentation across 343 datasets, demonstrate that our algorithm outperforms state-of-the-art unsupervised and self-supervised benchmarks.

Autonomous surface vehicles vary widely in hydrodynamic and actuation characteristics, yet most controllers are designed for single-platform deployment. We present an adaptive reinforcement learning approach for trajectory tracking that enables zero-shot cross-platform deployment using a single policy. Since the deployment platform's dynamics are unknown to the policy, we address cross-platform generalization with the standard partial-observability approach of conditioning on interaction history, employing a teacher-student architecture in which a learned module infers a latent representation of the platform dynamics. The policy is trained in simulation under randomized vessel dynamics and is deployed zero-shot to two real-world platforms without any fine-tuning, despite relying on a simple analytical dynamics model rather than a high-fidelity hydrodynamic simulator. In real-world experiments on two different platforms, the adaptive policy outperforms non-adaptive learning-based baselines by up to 58% in position mean absolute error while approaching the tracking accuracy of a platform-specific tuned controller.

Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochastic heuristics. In this work, we propose a paradigm shift by replacing the discrete training problem of shallow neural networks with a well-posed continuum variational surrogate. We identify a family of $\lambda$-convex functionals over parameter densities in weighted Sobolev spaces and prove that these variational problems are globally well-posed, stable, and exhibit unexpected almost $C^3$ regularity. Unlike existing Wasserstein-based or Mean-Field approaches, which often face limited regularity and discretization challenges, our formulation provides direct access to elliptic regularity and convex analysis. This allows us to prove that the optimal parameter density can be obtained by solving a single linear system, bypassing iterative optimization entirely. We establish explicit generalization error controls at a rate of $1/\alpha$ relative to the regularization parameter, and prove that finite-width networks of size $N$ achieve the continuum optimum at an $O(1/N)$ rate. This perspective bridges the gap between the Neural Tangent Kernel (NTK) and feature-learning regimes, providing a principled framework for understanding over-parameterization through the lens of variational calculus.

The silhouette is one of the most widely used measures to assess the quality of a $k$-clustering of a dataset of $n$ elements. Its evaluation requires no information beyond the clustering assignment. In addition, the silhouette is extremely easy to interpret, providing a score to measure the quality of a clustering as a whole or for each element. The exact computation of the: (i) silhouette of each element of a dataset; and (ii) the global silhouette of the clustering; require $\Theta(n^2)$ distance calculations, under general metrics. The quadratic complexity $\Theta(n^2)$ is extremely prohibitive, especially on massive modern datasets. Surprisingly, existing approximate methods using $O(n^2)$ distance calculations are heuristics not offering provable and controllable guarantees on the quality of their results. We introduce the first rigorous and efficient algorithms to estimate: (i) the (local) silhouette of each element of a dataset; and (ii) the (global) silhouette; of any metric $k$-clustering. Our methods, based on sampling, perform $O(nk\varepsilon^{-2}\ln (nk/\delta))$ distance computations, and provide estimates with additive error $O(\varepsilon)$ with probability at least $1-\delta$. That is, parameters $\varepsilon$ and $\delta$ in $(0,1)$ control the trade-off between accuracy and efficiency. We also introduce a scalable and distributed design of our methods for the MapReduce and Massively Parallel Computing (MPC) frameworks. Our distributed algorithms use a constant number of rounds and sublinear local memory. Finally, we perform extensive experiments against state-of-the-art approaches. The results show that our new techniques yield the best trade-off between accuracy and efficiency for both local and global silhouette estimation. In addition, our methods scale efficiently to massive datasets for which an exact computation of the silhouette is not practical.

Multivariate time-series models for prognostics are often evaluated by point prediction accuracy, yet their internal states rarely expose a coherent degradation process. We study liquid neural networks as latent dynamics models for aircraft engine health monitoring on the C-MAPSS benchmark. The proposed model encodes a history window into a latent state, evolves that state with a liquid transition model, and decodes future sensor observations. To separate health evolution from operating-condition variation, the latent state is factorized into degradation and condition components. Remaining useful life, monotonic risk, and latent-consistency losses supervise the degradation component, while condition prediction and decorrelation losses discourage operating-condition leakage. Across FD001–FD004, the full disentangled model improves overall sensor forecasting RMSE from 0.2438 for a GRU baseline to 0.2266, with the largest gains on the multi-condition subsets FD002 and FD004. The learned degradation state also forms a clearer temporal degradation axis, reaching an average state-speed Spearman correlation of 0.5960. Direct remaining-useful-life regression remains stronger for the GRU baseline, indicating that the proposed representation is currently more effective as an interpretable world model for degradation dynamics than as a calibrated lifetime regressor. These results suggest that liquid latent dynamics can bridge predictive maintenance forecasting and inspectable health-state modeling.