Papers

We study adversarial bandit maximization of monotone submodular functions under a matroid constraint. For a rank-$k$ matroid on $n$ elements, we give a randomized oracle-polynomial algorithm that makes one feasible value query per round and has expected $(1-1/e)$-regret $\widetilde O(n^{1/3}k^{2/3}T^{2/3})$. This is the first sublinear-regret algorithm for adversarial bandit submodular maximization under general matroid constraints. Technically, we view the problem as learning an exchange policy for the Poisson base walk. This connects the problem to contextual bandits and gives an information-theoretic sublinear-regret guarantee, but directly learning the exponentially many policies requires exponential time and space. We therefore introduce balanced fractional exchanges, which compress the policy mixture into a single fractional base while retaining the exchange information needed by the Poisson analysis. This leads to an polynomial time algorithm with the same regret guarantee.

Electroencephalography (EEG) is a widely used window into human brain function, but most EEG models remain tied to a one-dataset-one-model supervised paradigm. Recent EEG foundation models offer a route toward reusable representations, but most remain reconstruction-centered, assuming that EEG content predictable from local context is necessarily transferable neural information. Here we present INCEPT, an invariance-oriented EEG foundation model trained on over 11,000 hours of unlabelled clinical EEG. Rather than prioritizing signal recovery alone, INCEPT learns representation-level stability across correlated EEG observations, separating stable neural structure and essential subject-sensitive information from the nuisance variability that dominates scalp recordings while preserving subject-, state- and condition-discriminative information. We evaluate INCEPT on a broad-spectrum benchmark of ten datasets spanning three levels of post-acquisition EEG analysis: signal-level assessment, brain-state decoding, and brain-health evaluation. INCEPT ranks first among recent EEG foundation models on 26 of 30 linear-probing metrics and 24 of 30 fine-tuning metrics, and also surpasses strong task-specific specialist encoders across diverse downstream settings. Objective ablations and representation analyses further show that invariance-oriented pre-training improves transfer and organizes subject-sensitive neural representations beyond reconstruction alone. These results establish invariance learning as a promising principle for building reusable EEG foundation models.

Adaptive optimizers retain gradient history in moment variables, allowing a local change in loss weighting to alter later updates. We examine whether this delayed transport is large enough to change prospective short-horizon decisions. On committed future-minibatch sequences, we differentiate eight-step AdamW trajectories through the complete model–optimizer state and select exposure-matched Math–Code loss schedules before independent evaluation. Across 12 unused 0.3M Transformer histories, full transport lowers token-disjoint loss relative to an optimizer-aware immediate derivative in 10/12 histories (mean benefit $4.71\times10^{-4}$; exact one-sided sign test, $p=0.0193$). The two controllers act equally often but select different schedules in 60/96 windows. Crossed checkpoint–future-path tests attribute this reordering to the interaction between optimizer state and near-future data, while an independent Ising–CNN experiment shows that deleting moment-state transport destroys accurate response prediction. Full-transport scores also concentrate exact-rollout winners in larger candidate libraries, focusing finite-amplitude evaluation on a shortlist. On these committed short paths, optimizer memory and near-future data order are therefore actionable components of the training state, providing a mechanism-based criterion for when finite-horizon rather than one-step intervention is required.

Large Language Model (LLM) agents increasingly solve long-horizon tasks through multi-turn interactions with users and external tools. In these settings, relevant task information often unfolds over time rather than being fully specified at the initial prompt. Service agents make this challenge especially concrete: users may clarify or revise their goals, while tool responses provide information needed for subsequent decisions. Thus, a final reward alone cannot indicate which actions contributed to resolving the task. Recent methods rely on comparative evidence from other trajectories or resampled continuations, or on separately constructed step-level learning signals, to refine credit. However, a completed rollout already records how information and errors flow between agent actions. We introduce Influence-Aware Policy Optimization (IAPO), which represents each rollout as a typed influence-dependency graph over trainable agent actions, with user and tool observations serving as evidence. IAPO converts support-use and failed-use structure into routing weights that redistribute the same trajectory-level advantage. Experiments with Qwen3-4B and Qwen3-8B demonstrate superior performance over multi-turn reinforcement learning (RL) baselines across three service-agent benchmarks: ${\tau^2}$-Bench, UserBench, and AgentChangeBench. BFCL-v4 Multi-Turn further shows that these gains do not compromise multi-turn function-calling performance. This work advances the understanding of credit assignment in multi-turn user interactions and provides a principled approach to training service agents from sparse outcome feedback.

Credit risk models increasingly need to combine predictive accuracy with transparent explanations and auditable fairness constraints. Logistic regression remains attractive because its coefficients are easy to interpret, but it can miss nonlinear structure. Flexible models can improve prediction, but their explanations are often post-hoc and may not describe the decision rule itself. We introduce $\texttt{findr}$, short for flexible, interpretable deep regression, a semi-structured framework for binary credit risk modelling that decomposes the logit into an interpretable structured component and an orthogonal neural residual. The orthogonalisation separates coefficient-based effects from residual nonlinear variation, while an in-processing Wasserstein penalty mitigates group disparities by comparing score distributions during training. The framework also includes diagnostics that measure the structured component's contribution to logit variation, decision agreement, and local directional consistency. We evaluate $\texttt{findr}$ in a simulation study and on eight public credit datasets using score-level accuracy-fairness frontiers. The results show that $\texttt{findr}$ behaves close to logistic regression when the signal is approximately linear, while recovering much of the predictive gain of neural models when nonlinear structure is relevant. The diagnostics identify when coefficient-based explanations remain close to the full fitted model and when residual variation must also be examined. These findings support semi-structured modelling as a practical way to make performance, fairness, and interpretability trade-offs explicit in credit risk decisions.

Deep neural networks generalize well despite their highly nonconvex, overparameterized loss landscapes, a phenomenon often associated with the geometry of the minima found by stochastic optimization. We study how incremental grow-and-optimize strategies bias training toward flatter regions by viewing growth as progressive constraint relaxation. Starting from a low-dimensional submodel, we iteratively expand the trainable parameters by unlocking nested random subspaces while freezing the orthogonal complement at the network initialization, re-optimizing after each expansion until the full architecture is reached. Under standard local regularity conditions around non-degenerate minima, we prove that local sublevel sets are well approximated by ellipsoids and that basin accessibility under frozen constraints can be characterized by an explicit effective curvature in the frozen directions. This leads to an explanation of the bias: progressive growth increases the relative weight of wide basins and suppresses sharp ones through a volume effect induced by the frozen constraints. We empirically validate these predictions in controlled toy landscapes and in a realistic ResNet/CIFAR-100 setting and confirm that although progressive subspace growth reliably produces flatter solutions, curvature reductions do not universally translate into improved test performance, highlighting subtleties in the flatness-generalization connection. The code is available at https://github.com/p0lcAi/Across-the-Loss-Landscape.

Rapid earthquake magnitude estimation is central to earthquake early warning, yet many operational systems depend on dense regional seismic networks and region-specific calibration. This creates a spatial coverage barrier for high-risk areas with sparse sensing infrastructure. Single-station learning offers a lower-cost alternative, but existing models often face an accuracy–latency trade-off and may degrade under regional distribution shift. We present SeisMamba, a lightweight Mamba-based architecture for low-latency magnitude estimation from minimally processed three-component seismic waveforms recorded at a single station. SeisMamba combines hierarchical convolutional encoding, sparse selective state-space modelling, multi-scale feature fusion, and an auxiliary temporal prediction head to support efficient long-sequence waveform analysis. On the STEAD benchmark, SeisMamba achieves the best MSE, RMSE, and $R^2$ among tested baselines while requiring only 0.55 ms for a batch of 32 waveforms on an NVIDIA T4 GPU, making it about three times faster than transformer-based baselines. We further conduct a Chile–Taiwan regional hold-out experiment as a diagnostic test of cross-region deployment, where SeisMamba retains useful performance on geographically unseen seismic regions. These results suggest that selective state-space waveform modelling provides a promising accuracy–latency backbone for spatially distributed, low-cost earthquake early warning.

Machine learning models are widely used in financial fraud and credit-risk detection, yet their adversarial robustness remains difficult to evaluate because financial tabular data involve domain-specific constraints, severe class imbalance, and asymmetric attacker capability. We argue that, in this setting, robustness is not only an attribute of the model, but also an attribute of the evaluation protocol. Different ways of enforcing constraints and capability can lead to substantially different robustness conclusions. This paper presents FraudBench, a protocol-sensitive benchmark for adversarial robustness evaluation in financial fraud and credit-risk detection. Rather than treating domain constraints as post-hoc validity checks, FraudBench evaluates the same dataset–model–attack–defence setting under three matched protocols: unconstrained attacks, post-hoc feasibility filtering, and deployment-aware constraint-integrated attacks. FraudBench covers four public financial datasets, and evaluates neural, tree-based, and ensemble models using three attack settings. Our results show that robustness conclusions are highly protocol-sensitive. On Lending Club Loan Data under the white-box setting, post-hoc filtering leaves only 3.7 feasible-flipped examples on average, whereas in-attack projection with attacker mutability masking produces 2,832.3 feasible-flipped examples under the same perturbation budget. The results on IEEE-CIS further show that feasibility and attacker capability are separate axes, while black-box evaluation shows that protocol choice can alter model-family rankings. These findings suggest that fraud robustness evaluation should report predictive degradation and attack feasibility jointly, and should incorporate domain constraints into attack generation rather than treating them as post-processing checks.

Persistent entropy is the Shannon entropy of a persistence-based probability measure defined on a persistence diagram. However, its cross-entropy version is not naturally defined because two persistence diagrams generally have different event spaces. To bridge these event spaces, we combine a similarity function with persistence weighting to define an induced probability. The induced probability reflects information from one diagram on the event space of the other diagram and assigns unexplained probability mass to the unexplained event. Using the induced probability, we extend cross entropy to persistence diagrams, called persistent cross entropy (PCE). We establish the main properties of both the induced probability and PCE and prove stability theorems for both. Through three numerical studies, we show that PCE distinguishes diagrams with the same persistent entropy, separates causal directions in dynamical systems without constructing a joint persistent diagram, and can be used as a directional topology loss for knowledge distillation.

Simulation is central to modern engineering and science, but the cost of numerical solvers for partial differential equations (PDEs) remains a bottleneck whenever fast or many-query evaluations are required. Neural emulators trained on solver-generated data promise significant speedups, yet they are usually framed as opaque alternatives to the very methods that produce their training signal. This thesis argues the two paradigms are more alike than different: neural architectures mirror classical discretizations, their errors are amenable to the same spectral analysis, and insight flows profitably in both directions. We approach the relationship by disentangling the multiple roles a solver plays in the emulator learning pipeline. Mode-wise Fourier analysis then provides a common language in which solver errors, architectural inductive biases, and training objectives can all be read off simultaneously. Taken together, this allows synthesizing three contributions. (1) APEBench, a comprehensive benchmarking suite for autoregressive neural emulators of PDEs that uses fast differentiable pseudo-spectral solvers in JAX. (2) Progressively Refined Differentiable Physics, an investigation of the effect of unconverged solvers on surrogate training. (3) Neural Emulator Superiority, an analysis of the influence of numerical errors and architectural inductive biases.

Probabilistic full-field reconstruction provides uncertainty-aware response evidence for structural reliability assessment, yet inference from sparse and noisy measurements remains underdetermined. Most existing methods overlook shifts between offline training and operational distributions. Under such shifts, posterior intervals may become miscalibrated, causing the reported uncertainty to lose its probabilistic meaning. This study proposes Modal Residual Flow Matching with Context-Conditioned Affine Spread Transport (MoRF-AST) for calibrated structural virtual sensing under changing operating conditions. MoRF constructs an analytic Gaussian reference posterior in normalized modal coordinates and trains a conditional flow only on posterior-whitened residuals. At deployment, AST estimates response scale from historical measurements at installed sensors and uses gated, mean-preserving Bures-Wasserstein transport to adjust posterior spread. On a bridge-deck benchmark, MoRF achieves a posterior-mean normalized root-mean-square error (NRMSE) of 7.20%, compared with 16.1% and 17.9% for two direct conditional flows. Across eight shifted traffic domains, AST reduces MoRF's cross-domain average coverage error from 0.0535 to 0.0236, a 55.9% reduction, while preserving posterior-mean accuracy. The same transport does not improve the tested alternatives in aggregate, showing that calibration gains require its direction to match the base posterior's dispersion bias. MoRF-AST provides a data-efficient framework for probabilistic full-field reconstruction whose uncertainty remains interpretable under scale-dominated operational distribution shifts. More broadly, this work highlights the need to calibrate uncertainty under changing operational distributions, thereby supporting trustworthy probabilistic modeling and reliability-informed decision-making in civil and infrastructure engineering.

We prove the first quantum-classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-\beta E}$ on the torus $\mathbb{T}^d$ with smooth ($s$-Gevrey) potential and barrier amplitude $\alpha=e^{\beta\Delta}$, where $\Delta = \max E-\min E$, every classical algorithm querying the value, gradient, or any higher-order derivatives of the log-density requires $\Omega(\alpha)$ queries to sample at constant accuracy in total variation distance, while a quantum algorithm based on quantum singular value thresholding and temperature annealing samples with $\tilde{O}\left(\sqrt{\alpha}\right)$ queries to an oracle for the gradient. The advantage is quadratic in the barrier amplitude, which becomes exponential in the dimension, $e^{\Omega(d)}$, at low temperature. The classical bound is information-theoretic, holding for every classical algorithm with query access to the Gibbs potential and its derivatives at any order.

Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-dimensional output spaces. This paper addresses the dual nature of uncertainty – aleatoric and epistemic – focusing on their joint integration in high-dimensional regression tasks. For example, in applications like medical image segmentation or restoration, aleatoric uncertainty captures inherent data noise, while epistemic uncertainty quantifies the model's confidence in unfamiliar conditions. Modeling both jointly enables more reliable predictions by reflecting both unavoidable variability and knowledge gaps, whereas modeling only one limits transparency and robustness. We propose a novel approach that approximates the resulting joint uncertainty using a low-rank plus diagonal covariance structure, capturing essential output correlations while avoiding the computational burdens of full covariance matrices. Unlike prior work, our method explicitly combines aleatoric and epistemic uncertainties into a unified second-order distribution that supports robust downstream analyses like sampling and log-likelihood evaluation. We further introduce stabilization strategies for efficient training and inference, achieving superior UQ in the tasks of image inpainting, colorization, optical flow, and depth estimation.

Satellite-based distributed learning promises to train machine-learning models directly in orbit using massive, globally dispersed sensor data, thereby avoiding large-scale data downloads to ground servers. However, training convergence is significantly slowed by severe non-IID data, specifically label imbalance, as each satellite observes different geographic regions with distinct labels. This imbalance extends training duration and increases energy consumption for solar-powered satellites. Existing approaches either fully redistribute data to enforce IID conditions - accelerating convergence but incurring substantial communication delays - or avoid redistribution entirely by modifying local learning algorithms to mitigate the impact of label imbalance, which, however, still prolong training and increase energy use. Both extremes result in excessive total end-to-end learning time (data-transfer delay plus training time) and thus elevated onboard energy consumption. We present SatDL, a data-redistribution framework designed to minimize total end-to-end learning time. At its core, SatDL develops a Distributor-Critic framework that jointly models and optimizes data-transfer delay and training time. Evaluations through trace-driven simulations of a 1,584-satellite Starlink constellation and hardware emulations using NVIDIA Jetson and A100 GPUs across five datasets show SatDL reduces total end-to-end learning time by up to 18.6% and onboard energy consumption by 12.23-88.00%, while maintaining inference accuracy within a few percentage points of state-of-the-art baselines.

Uncertainty quantification (UQ) methods are widely used for hallucination detection in large language models (LLMs) in closed-book settings where ground-truth evidence is unavailable at inference time. Prior work has proposed combining UQ signals via learned ensembles, but empirical investigations into the robustness of these ensembles are limited. We study a supervised ensembling framework that trains a classifier over heterogeneous UQ-based scorer outputs on a small, domain-specific dataset of labeled LLM responses, then applies it to out-of-sample hallucination classification without retrieval, tools, or reference documents. Across four LLMs, nine datasets, and three generation regimes (short-form QA, long-form generation, and code generation), we provide a systematic robustness analysis along three axes: sample efficiency, in-domain dataset transfer, and generation regime dependence. We find that supervised ensembles outperform the best individual scorer in 30 of 32 settings, with gains realized from as few as 100 labeled instances. Ensembles retain most of their advantage in cases of in-domain transfer under distribution shift, outperforming the best non-ensemble scorer in 23 of 28 transfer settings. Sampling-based black-box ensembles are nearly as effective as full ensembles, while single-generation white-box ensembles offer limited benefit.

Many continuous-control policies are optimized as unbounded Gaussians and then mapped into bounded actions. We show that where entropy is measured changes the policy geometry learned by proximal policy optimization (PPO). In an 80-muscle MyoLeg task, a clipped Gaussian executes 89.07% of actions within 5% of a bound. A same-state decomposition shows that this is not due to variance alone: setting variance to zero still leaves 83.83% of actions near a bound, while 82.12% of state-conditioned means lie outside the executable interval. Replacing clipping with a tanh map does not remove the high-variance regime. For latent Gaussian entropy H(u), the entropy loss has zero gradient with respect to the mean and a constant variance-increasing gradient. For executed-action entropy H(a), the transform Jacobian adds an inward gradient on the mean. Across three matched MyoLeg seeds, near-boundary occupancy is 71.42%, 29.76%, and 18.83% under latent entropy, no entropy, and executed-action entropy. A 38-dimensional Dog-Stand replication with an independent CleanRL-based PPO implementation reproduces the ordering in mean geometry, which also survives shared-state evaluation and boundary margins from 1% to 10%. Direct mean penalties can match or exceed the centering produced by H(a), showing that interior means are not unique to executed entropy. However, matched mean geometry can coexist with substantially different variance and return. Entropy measurement space is therefore a coupled mean-variance design choice, and task return alone does not characterize bounded-policy geometry.

Automated parking commonly assumes marked slots and short approach maneuvers. Delivery and service vehicles, however, may need to reach an operator-specified pose in an irregular bounded environment from a distant start. Existing learning-based parking planners often rely on local observations, which can restrict long-range route reasoning. To address this problem, we present NeuralParker, a reinforcement learning-based hybrid planner for arbitrary-pose parking. NeuralParker encodes full-environment obstacle and boundary geometry in a target-relative vertex representation, allowing the policy to retain route-defining context throughout the approach. It further couples a learned curvature–length arc policy with an in-loop terminal ensemble that selects from diverse cubic Hermite connections using a curvature-regularized cost. We also establish factorial and long-range route-choice benchmarks to evaluate planning success and trajectory quality. Experiments on these benchmarks show that NeuralParker achieves higher planning success and better overall trajectory quality than the evaluated baselines, while ablation studies support the benefits of the target-relative global representation and terminal ensemble. Finally, a real-vehicle evaluation confirms that the planner transfers effectively to real delivery-vehicle perception at a working parking site, planning successfully at low computational cost.

Mechanistic Localization bridges mechanistic interpretability and post-training optimization by isolating critical parameters via interpretative approaches and then guiding parameter-efficient Supervised Fine-Tuning (SFT) in a “locating-then-tuning” paradigm. However, due to the retrospective nature of mechanistic interpretability, directly interpreting pre-SFT models introduces misleading conclusions. Specifically for novel tasks, initially identified neurons differ drastically from those governing the final model, introducing biases that actively disrupt SFT. To address this, we propose a forward-looking localization framework that accurately estimates the post-SFT interpretability state using only pre-SFT parameters and the target dataset. Theoretically, we model SFT as a continuous parameter evolution, leveraging Taylor expansion to rigorously bridge the post-tuning mechanistic objective with the pre-SFT model's dynamic gradients. Practically, we design dual-granularity (neuron- and component-level) localization pipelines. Extensive experiments demonstrate that our approach not only provides superior SFT guidance but also exhibits robust performance and temporal scalability across increasing model sizes. This work transcends the fundamental limitation of traditional interpretability-its inability to identify task-critical mechanisms before they are trained-pioneering a predictive frontier that unites mechanistic interpretability with targeted optimization.

ES-HyperNEAT evolves substrate topology through adaptive quadtree subdivision; to our knowledge, no implementation with full population-level GPU parallelization exists. We present JAX-ESHN, a JAX-based implementation targeting GPU parallelization with batched CPPN queries, and benchmark it against the CPU-based PUREPLES Baseline across five tasks: XOR, Parity-3, circle classification, sine regression, and CartPole. The core limitation is structural: each CPPN discovers a unique set of substrate positions, preventing population-level vectorization via vmap. On XOR, the CPU Baseline's runtime scales exponentially with depth while JAX-ESHN's construction cost on GPU (compilation plus first-generation evaluation) plateaus at deep substrates, so JAX-ESHN solves reliably where the Baseline rarely succeeds, with lower runtime variance. A CPU-vs-CPU multi-benchmark control reproduces the same scaling divergence across Boolean, continuous, and control task types, confirming it is a property of the substrate-discovery implementation, not of GPU hardware. An alternative data structure (Hierarchical Spatial Hash Grid) fails not because it precomputes positions but because it applies the variance test independently per position, discarding the quadtree's parent-gated filtering and with it the adaptive sparsity essential to ES-HyperNEAT. These findings define the structural constraints any substrate-discovery method must satisfy to scale coordinate-based neuroevolution; the companion EMR-HyperNEAT reformulation, which replaces adaptive subdivision with eager evaluation of a static multi-resolution grid, satisfies them and resolves the bottleneck this paper characterizes.

Massively parallel simulation changes the data regime in which off-policy reinforcement learning (RL) is trained, challenging stabilizers designed for data-limited replay. Through controlled experiments across eight benchmark families, we show that these stabilizers are data-regime-dependent: parameter normalization helps with narrow replay coverage but restricts value fitting when data are abundant, while clipped double-Q can be relaxed in high-throughput manipulation. Age-biased replay weighting improves learning efficiency across regimes, especially with limited network capacity. Based on these findings, we propose WarpSAC, a regime-aware family of off-policy RL algorithms. WarpSAC uses Sample Weight Decay for efficient exploitation and provides two variants: WarpSAC-L (Norm ON, clipped double-Q) for data-limited CPU-scale training, and WarpSAC-A (Norm OFF, single-Q) for data-abundant GPU-parallel training. WarpSAC improves normalized score–step AUC over FlashSAC by 4.5% across nine CPU-scale environments and 23.1% across fourteen GPU-parallel environments. It increases UnitreeG1TransportBox-v1 success rate from 19.8% to 96.4%, improves mean normalized wall-time AUC on MuJoCo Playground by 19.1%, and achieves 36.4% faster sim-to-real deployment on Unitree G1 than FlashSAC. These results show that scalable off-policy RL should adapt its stabilizers to the available data regime.

Ternary transformers offer extreme memory and compute efficiency, but existing low-bit LoRA-based methods cannot directly fine-tune ternary weights. Current approaches either require dequantization, restoring low-bit base weights to higher precision to merge with adaptation weight, or update only quantization parameters, preventing a merged model that remains ternary. We propose ternary multiplicative adaptation, which represents discrete updates of ternary weights such as sign flips or zeroing through a low-rank Kronecker factorization into two small ternary matrices applied element-wise to ternary weights. This design is parameter-efficient and expressive, preserves the ternary domain, and supports direct merging without dequantization. Experiments on six models across language and vision, including ternarized LLaMA-3 1B and 3B and a ternary ViT-B/16, demonstrate that our method recovers much of the performance lost to quantization and outperforms strong low-bit and ternary baselines. Code is available at https://github.com/alexmanoo/ternary_adaptation.

Wearable device data enables continuous health monitoring, but suffers from structured missingness: features sharing a physical sensor drop out together. Deep imputation methods such as BRITS and SAITS have seen limited evaluation on multimodal physiological data under realistic missingness, and existing benchmarks use random-point holdout protocols that incorrectly assume missingness is independent across features and time. Using data from a person with epilepsy recorded on a Garmin smartwatch, we develop an evaluation protocol that mines contiguous missing-run templates from training data, stratifies them by per-feature gap-length quantiles, and injects them as block masks with preserved co-missingness structure. A matched training protocol exposing models to the same missingness distribution reduces BRITS's severe-gap MAE by 43%, demonstrating the potential benefit of the proposed evaluation and training protocol within this single-participant dataset. We further extend BRITS with time-of-day encoding and a circadian harmonic channel. No single model dominates: linear interpolation is optimal for slow-moving features over short gaps; extended BRITS achieves lower MAE on dynamic cardiac features in moderate and severe gaps; and SAITS better preserves the ground-truth distribution by Jensen-Shannon distance despite higher MAE. Ultimately, model rankings strongly depend on evaluation designs. By exposing how traditional evaluation methods obscure true model capabilities, our transferable protocol establishes critical steps towards developing better imputation strategies for future multi-sensor wearable datasets.

Unsupervised domain adaptation (UDA) has been widely concerned in the fields of machine learning, pattern recognition, and computer vision. Traditional UDA learning usually assumes that the label spaces of the source and target domains are exactly the same and only needs to solve the problem of sample distribution drift existing between two domains. However, in real world applications, the label spaces between two domains may be different. In this case, there are both sample distribution drift and class spatial difference between domains, namely Universal Domain Adaptation (UniDA) learning scenario. At present, existing works rarely offer theoretical analysis for universal domain adaptation. In this paper, we provide an upper bound of the generalization error for universal domain adaptation. According to the proposed generalization error bound, we propose a novel UniDA algorithm called Joint Distribution Alignment for Universal Domain Adaptation (JAUA), which aligns the joint distributions by minimizing the distribution discrepancy calculated by Chi-Square divergence. Furthermore, we propose a progressive pseudo-labeling method to assign the pseudo labels to unlabeled target samples. The experiment results on six public image datasets demonstrate the superiority of JAUA in handling the UniDA problem.

Using monthly Niño-3.4 anomalies through July 2026, we investigate how much predictive information is contained in delayed observations of the index. Ridge regression identifies informative delays, while multilayer perceptron and sparse identification of nonlinear dynamics (SINDy) models test whether nonlinear complexity provides additional direct forecast skill; gated recurrent unit (GRU) and long short-term memory (LSTM) networks provide a complementary test in which the temporal representation is learned internally. Delayed observations substantially improve forecasts over persistence and climatology at leads of up to six months, but increasing model complexity provides no systematic improvement. Historical recursive experiments favor a simple explicit SINDy recurrence and select shallow recurrent architectures, with no appreciable gain from learning the temporal representation internally. These results support a compact predictive representation of Niño-3.4 evolution in which the representation of past information is more consequential than model complexity. As a prospective application, the selected models are used to forecast the developing 2026 event beyond the last available observation and to compare its predicted evolution with completed historical El Niño events.

Learning operators from sequentially collected data arises in adaptive experimental design, Bayesian optimization, and dynamical-system modelling, where observations may be dependent, and future inputs or sensing operators may depend on preceding data. We derive time-uniform self-normalized concentration bounds for stochastic processes in Hilbert spaces with vector-valued noise. We use these bounds to obtain regression-error guarantees for linear operators, including targets outside the Hilbert estimation space, and for nonlinear parametric operators trained with strongly convex losses and regularizers. Our results allow possibly infinite-dimensional inputs and outputs without independence or mixing assumptions, providing a major step towards convergence guarantees for adaptive operator learning and learning from stochastic dynamical data.

Tensor-valued prediction is fundamental to geometric deep learning, yet uncertainty quantification (UQ) for such outputs remains an open challenge. While E(3)-equivariant neural networks excel at point estimates, they lack rigorous confidence measures. We focus on symmetric rank-2 tensor prediction, where the target has six Kelvin–Mandel coordinates and full uncertainty is represented by a $6\times6$ covariance matrix. We introduce a framework for E(3)-equivariant UQ, modeling the full predictive distribution where both mean and covariance preserve rotational symmetry. Our approach decomposes the covariance into irreducible representations $\mathrm{Sym}^2(\rho_c) \cong 2\times(l=0) \oplus 2\times(l=2) \oplus 1\times(l=4)$. By mapping from the flat Lie algebra $\mathfrak{sym}(6)$ to the curved SPD manifold via matrix exponentiation, we strictly ensure positive-definite covariances while maintaining exact equivariance. Furthermore, we formulate a Log-Euclidean Equivariant Scoring Objective (LE-ESO)—a robust surrogate loss based on the Multivariate Laplace distribution—providing robustness to heavy-tailed errors and stable optimization. Validation on ModelNet40 inertia tensors and Materials Project dielectric tensors demonstrates that our method achieves competitive performance and provides physically consistent, symmetry-preserving uncertainty estimates with useful risk and OOD sensitivity.

In this work, we conduct an empirical study on self-supervised learning (SSL) for tabular data. Our experiments examine limited label regimes (that is, 1%, 5%, 10%, and 20% of the labels) and highlight limitations and opportunities in current tabular SSL. Contrary to what is expected, our mask-and-recover approach shows its largest improvements for datasets that have little to no recorded numeric missingness, whereas it more often leads to degradation on datasets that are characterized by native numeric missingness (post hoc split). Random Forest achieves an average AUC of 0.9015 across the 14 tasks for the 10% labels setting, whereas SSL shows a performance of ~0.8954 (RF: 1 draw; SSL: 3-draw mean). Moreover, the gain of SSL compared to training from scratch exhibits a high variance across tasks and is not significant (1 run; Wilcoxon p = 0.626, Holm-adjusted p = 1.000, for both the 5% and 10% settings). On the other hand, we observe that SSL-pretrained models achieve a higher average AUC when MNAR and MCAR missingness were injected at test-time. In comparison to models trained from scratch, our SSL-pretrained models show an improvement of +0.0245 (MCAR) and +0.0418 AUC (MNAR) under test-time missingness (single seed), with 11 (MCAR; plus one tie) and 8 (MNAR) positive results across the 14 tasks. However, after Holm-Bonferroni correction neither improvement is significant (Holm-adjusted p = 0.118 for MCAR and 0.518 for MNAR). Finally, when comparing mask-and-recover with three other approaches, namely, simplified VIME, SCARF and SubTab implementations using an identical encoder, we observe no significant difference in performance (Holm-adjusted p = 0.459 for VIME, 1.000 for SCARF, 1.000 for SubTab).

The prediction of student engagement from the online tutoring videos is difficult because engagement is a multidimensional construct comprising distinct behavioral, emotional, and cognitive states. A reliable prediction requires bringing together different types of behavioral signals as well as expressive cues. Through our analysis of the CASED dataset, it is clear that engagement prediction gets even harder due to the high inter-person variability as well as the subjectivity of the engagement annotation. To tackle these challenges, we develop a multimodal framework that integrates the implicit spatiotemporal features extracted from pretrained video, audio, and image encoders along with structured behavioral modalities like head pose, gaze, facial action units, emotion, and wavelet-based audio features. We integrate these modalities via a Perceiver IO latent bottleneck. Moreover, student and instructor personalities are modeled as variational posteriors over learnable embeddings to enable partial pooling across participants. We employ evidential regression and spectral-normalized Gaussian process classification heads for uncertainty-aware prediction to further improve robustness and calibration. Benchmark on the CASED challenge test set shows that all participating methods converge near random-chance performance, revealing the difficulty of the dataset. In this highly ambiguous regime, our framework achieves competitive performance while uniquely offering well-calibrated uncertainty metrics, demonstrating that reliable risk-quantification is an essential prerequisite for deploying engagement models in real-world educational tools.

In this work, we propose a structural variant of the Factorial Hidden Markov Model (FHMM) for the analysis of disease trajectories in patients with Type 2 diabetes mellitus (T2DM). The model represents a patient's latent health state as a combination of multiple independent, simultaneously evolving components, associated with comorbidities and lab results. This structured latent representation facilitates the identification of clinically meaningful patient states and clustering of common disease trajectories. We evaluate the proposed approach using The IQVIA Medical Research Data incorporating data from THIN, a Cegedim database of anonymized electronic health records (EHR), identifying patients with a first-ever prescription for a non-insulin antidiabetic drug (NIAD) between January 2006 and December 2019. The model identifies multiple clinically coherent latent components corresponding to known patterns of diabetes-related complications and reveals heterogeneous progression pathways, including distinct microvascular-dominant and multi-organ trajectories associated with elevated comorbidity burden and mortality. These results demonstrate that the proposed framework captures meaningful longitudinal structure in EHR data and provides interpretable insights into the evolution of T2DM and its comorbidities.

An intelligent system does not merely reason: it governs its own reasoning - how much to compute, when to stop, which module to activate. Can that role be played by a dynamic internal field - a low-dimensional homeostatic state with explicit physics and certified stability - that modulates cognition without performing it? Ours is a field on the module graph governed by a family of PDEs on the graph Laplacian, advancing with an adaptive-depth reasoner. We certify the stability of the integrator of the whole family - an integrator certificate, not a closed-loop one. New, and proved here: a discrete Schur-Cohn criterion for Verlet with velocity coupling, necessary and sufficient per latent root, with no commutation hypothesis. The answer is threefold: substance no, structure only in part, certifiability yes. The type of the field's physics is irrelevant for accuracy: wave, diffusion, gated mixtures and a 2D Navier-Stokes substrate tie. A twenty-seed preregistered deconfounding campaign bounds the structural claim: at equalized caps the second-order effect is strong in one family (+0.087 [+0.042, +0.132], t=4.0) but is not detected in the other (+0.014 [-0.013, +0.040], n.s.), so part of the original contrast was capacity, not order; and a matched-interface GRU is indistinguishable in the first and nominally exceeds the field in the second (-0.035 [-0.067, -0.002]). What distinguishes the field is not capability but that its one-step operator admits an exact runtime stability check - a difference of kind, not of existence: learned recurrences carry certificates too, sufficient and conservative ones. A kill-gate with a positive control finds no evidence for the field as evidence accumulator (Delta AUC +0.0007 [-0.0065, +0.0079] vs a 0.03 threshold). A dynamic internal field is a viable, certifiable compute governor, but not an enhancer of cognition: it modulates, it does not think.