Existing analyses of the edge of stability (EoS) treat it as a global property of optimization. We show that it is also selective: the stability constraint redistributes learning across subsets of the training distribution, amplifying progress on some groups while suppressing progress on others. Using a branching intervention that enters or exits the EoS regime from the same training state, we causally demonstrate this trade-off and identify two necessary conditions for a group to benefit. First, its aggregate gradient must align with the top Hessian eigenvector. We isolate this mechanism with a controlled perturbation that preserves distance but randomizes direction, destroying alignment and eliminating the advantage. Second, the group must sustain non-vanishing gradient magnitude over time. Under cross-entropy loss, gradient saturation decouples confidently classified groups, shifting the advantage to output-outliers, whose gradients persist. Together, these results show that EoS functions not only as a stability boundary, but as a mechanism governing the allocation of learning across the data distribution.

Non-alcoholic fatty liver disease (NAFLD) affects roughly 25% of global adults, posing substantial hepatic and cardiovascular risks. Yet, population-level screening tools remain inadequate. We present Method, a machine-learning framework for NAFLD risk prediction coupling gradient-boosted decision trees with conformal prediction to yield calibrated, distribution-free coverage guarantees on individual risk estimates. It integrates a mutual-information-based stability selection procedure to identify a compact, clinically interpretable feature subset via bootstrap resampling, constructing prediction sets whose marginal coverage provably exceeds a user-specified confidence level. We evaluated Method on a multicenter cohort from Guangzhou, China (primary n=2,187; external validation n=412) using 78 candidate features across demographics, metabolic biomarkers, and lifestyle factors. Method achieves an AUROC of 0.912 internally and 0.891 externally, outperforming deep neural networks, TabNet, support vector machines, and logistic regression. Conformal prediction sets achieve 91.3% empirical coverage at the 90% nominal level. A three-tier risk stratification derived from these scores separates the population into distinct groups, with the high-risk subgroup showing a 12-month progression rate 4.7 times that of the low-risk tier. The selected features -- notably waist circumference, ALT, GGT, triglycerides, fasting glucose, and BMI -- align with established metabolic risk factors, providing biological plausibility.

Existing methods rely predominantly on token-level signals, leaving the geometric structure of intermediate hidden states underused. In this paper, we take the geometric complexity of hidden-state matrices as a measure of the global uncertainty of LLMs, while treating token-level uncertainty estimation as a local metric. We show that hidden-state geometric entropy (global uncertainty) and token-level entropy (local uncertainty) are statistically near-orthogonal, capturing distinct failure regimes for reliability prediction. In particular, global geometry recovers the confident-but-wrong failure mode that local signals systematically miss. Building on this, we propose Global-Local Uncertainty (GLU), an unsupervised, single-pass score that fuses the two signals via a multiplicative gate. Across three model families and six benchmarks, GLU matches or outperforms all unsupervised baselines while requiring only a single forward pass and remaining length-normalized and architecture-agnostic. Code is available on https://github.com/qcri/GLU.git.

Few-shot example retrieval is the dominant paradigm for grounding large language models (LLMs) in domain-specific text-to-SQL systems. However, the quality of the annotated example bank directly governs system accuracy, and expert annotation is prohibitively expensive. We formalize the active selection of these examples as a constrained experimental design problem over the intrinsic, low-dimensional manifold of semantic query embeddings. Unlike standard active learning frameworks, our setting introduces three critical challenges: varying, query-dependent annotation reliability (heteroscedasticity), strict requirements for spatial diversity across semantic topics (partition matroid constraints), and the inherent reality that the true covariance structure of the embedding space is unknown (misspecification). To address these, we propose a stratified greedy algorithm that maximizes a heteroscedastic mutual information objective. We prove that this objective remains submodular and approximately monotonic on the intrinsic manifold, yielding a theoretical constant-factor approximation guarantee. We establish a spectral bound demonstrating that this approximation guarantee degrades gracefully, rather than catastrophically, when the assumed surrogate kernel diverges from the true underlying data-generating process. Empirical results demonstrate that the proposed strategy significantly reduces labeling effort while maintaining high text-to-SQL retrieval accuracy.

Reconstruction-based methods are widely used for time series anomaly detection, where models are trained to reconstruct subsequences, and anomalies are identified through reconstruction errors. However, reported results are often hard to compare due to heterogeneous evaluation practices and underspecified inference procedures. In this paper, we revisit reconstruction-based anomaly detection in the univariate offline setting and study the role of the inference stride, which controls whether subsequences are processed as disjoint windows or with overlap. We propose a unified training, tuning, and multi-seed evaluation protocol on the curated TSB-AD benchmark, and study how overlapping inference affects anomaly detection performance for a range of reconstruction models, including PCA-based baselines, DLinear, an AutoEncoder, TimesNet, and Transformer variants. The results show that across all models, overlapping windows yield consistent improvements, with average relative gain up to +28%, and can alter method rankings. We further analyze variability across datasets, random seeds, and hyperparameter configurations. Finally, we complement the benchmark study with an evaluation on the full UCR archive using localization criteria aligned with sliding-window reconstruction. Overall, our results highlight that reconstruction-based anomaly detection performance depends not only on model architecture and training, but also on inference choices, motivating a clear and reproducible protocol. Our results show that reconstructionbased baselines achieve strong performance on both TSB-AD and UCR benchmarks, supporting them as competitive and practical approaches for univariate time series anomaly detection.

We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks. Under the assumption that the loss function is analytic and non-polynomial, we prove that data symmetries generically do not induce any additional integrals of motion. For mean squared error (MSE) loss, on the other hand, there are situations in which data augmentation yields extra conserved quantities. We build a framework, utilizing tensorizable networks to describe this phenomenon. Tensorizable networks are a family of architectures whose dependence on parameters and inputs can be separated using an intermediate representation. They include linear and Figure 1: A display of how data symmetry can give polynomial networks, as well as Lightning At-rise to conservation laws. The top row shows the tention.

Tamed stochastic-gradient Langevin dynamics (SGLD) stabilizes large drifts by adding a denominator to the update. If this denominator uses the same stochastic-gradient sample as the update step, it can also change the conditional mean drift. We study deterministic denominators: the state-dependent envelope is fixed before the current oracle sample is drawn. The main question is how to design this envelope in practice. The design starts from an oracle score, builds a low-cost proxy score on pilot states, chooses activation thresholds by empirical quantiles, and then applies a small calibration layer. The analysis tracks three steps: proxy and threshold errors become envelope errors; envelope errors perturb one SGLD step; and the local residuals give stationary errors through a conditional perturbation bridge. Experiments show that the proxy-quantile denominators are close to oracle-score behavior, avoid the random-denominator mean-shift channel, and improve simple deterministic taming choices.

Mixture-of-Experts large language models (LLMs) scale efficiently through sparse activation, yet their deployment is fundamentally constrained by the large static parameter footprint of experts. Existing compression approaches either remove entire experts, disrupting routing topology and harming performance, or rely on unstructured weight pruning with limited practical efficiency. To address the limitations, we propose TENP, a structured Trapezoidal ExpertNeuron Pruning framework. Using a few samples, we identify and retain important experts, while applying expert neuron pruning (ENP) to less important experts, reserving model parameters in a trapezoidal pattern from shallow to deep layers. When evaluating expert importance, we jointly consider both the magnitude of the expert output and its ability to change the direction of the input vector. For ENP, we measure each neuron's projected contribution to the expert output to identify and retain important neurons. We conduct extensive experiments on the Qwen and DeepSeek models. Under a routing expert sparsity of 40% and an average of 63.76% activated expert parameters, the DeepSeek model suffers only a 1-point drop in accuracy compared to the full-parameter model. Moreover, it outperforms the full-parameter model by 10% on code generation tasks.

We develop a decision-calibrated conformal framework for pacing decisions in streaming advertising. Pacing depends on uncertain future inventory, demand pressure, incremental response, and member-experience load. Instead of calibrating a generic forecast residual, the framework measures forecast error by its largest impact on the policies that could actually be deployed. The main theorem shows that the proposed score is the smallest valid uncertainty measure that uniformly protects all deployable pacing policies. Geometrically, it is the support function of the signed policy sensitivity set. Split conformal calibration gives finite-sample coverage for this score. A high-dimensional separation theorem shows that traditional residual calibration can be arbitrarily more conservative by paying for nuisance inventory dimensions, and a robust pacing result combines inventory, response, and experience uncertainty. On public-data-calibrated pacing replays built from Criteo Uplift and KuaiRand datasets, traditional conformal pacing remains unresolved with high residual radii of 7236.7 on Criteo and 4629.4 on KuaiRand. With the proposed decision calibration approach, the uncertainty radii are reduced to 18.4 and 278.6 respectively, with separate margins for value, delivery, budget, and member load. On Criteo, the proposed method certifies a less aggressive pacing policy than the point-forecast baseline, and reduces held-out any-violation rate from 16.7% to 3.3%, with zero budget and member-load violations. On KuaiRand, the choice remains unresolved. In a nutshell, the paper establishes that forecasts, response estimates, and member-experience models should be judged by whether they shrink the uncertainty that the pacing decision uses, as this leads to confident decisions that are not overly conservative.

We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual-curvature term. In the linear case, where the curvature term vanishes, this recovers the classical effective dimension of the Jacobian kernel covariance, but evaluated at the trained model rather than at initialization as is typical in neural tangent kernel analyses. We further bound this effective dimension via covering complexity of the gradient features, leading to guarantees that depend on learned geometry rather than parameter count. In particular, for manifold-supported data and piecewise Lipschitz Jacobians, the bounds scale with intrinsic dimension, while for one-hidden-layer ReLU networks, the mechanism can be made explicit through counts of activation-stable regions. Experiments on synthetic manifolds, clustered distributions, and benchmark datasets illustrate trained-Jacobian compression, the tightness of the residual-curvature linearization, and agreement between the stability bound and observed generalization gaps. A key feature of our bounds is the simplicity of their derivation, which follows from first principles using the Brascamp-Lieb inequality under strongly log-concave noise.