Safety classifiers deployed in production operate under a stationarity assumption that fails silently: when input distributions drift, accuracy degrades with no error signal until ground-truth labels arrive. We present an online monitor that detects distributional shift in classifier scores via a sliding-window KS statistic with empirically calibrated alarm thresholds. In a pre-registered factorial evaluation (4 classifiers $\times$ 5 shift conditions $\times$ 20 seeds $\times$ 2 window sizes; 800 cells), the monitor achieves 86.6% valid detection (mean latency 39.5 steps) across synthetic-onset, real-jailbreak, and adversarial regimes; a classifier $\times$ shift interaction ($η^2 = 0.185$) shows that monitoring must be tuned per classifier. Attempting to recover post-detection coverage via weighted conformal prediction exposes a failure mode: density-ratio estimation collapses for generative classifiers because logistic regression separates source from target perfectly in 3584-4096-dimensional embedding space, clipping all importance weights to zero; projecting to $\leq 32$ dimensions restores coverage. We then extend the framework to gradient-based evasion and give the first threat-model characterisation of score-disagreement monitoring as a canary. We falsify three assumptions: that architectural diversity drives the signal (false, $η^2 = 0.011$), that it is generic out-of-distribution detection (false, GCG-specific, $p < 10^{-12}$), and that an adaptive attacker can suppress it (false while the canary is confident). We derive the exact security boundary, a confidence-gated equilibrium at which a monitor-aware attacker stalls at gap $= 1/(2λ)$, and provide a calibration-free scan martingale achieving false-alarm rate $\leq 1\%$ across all classifiers with no per-model tuning.

This paper presents a methodology-centered transfer learning framework for fragility adaptation under domain shift, class imbalance, and scarce target labels while preserving engineering interpretability and supporting decision-making under uncertainty. Four transfer learning strategies (instance-based, parameter-based, hierarchical Bayesian, and multi-source) are demonstrated through three complementary case studies: (i) instance-based transfer learning via importance weighting, demonstrated on coastal bridge fragility using Hurricane Katrina observations; (ii) parameter-based transfer learning together with hierarchical Bayesian transfer learning, enabling partial pooling across strata and posterior uncertainty quantification, demonstrated on residential building fragility using Hurricane Ian observations; and (iii) multi-source transfer learning that fuses multiple analytical fragility models with learned source weights and regularized target-domain adaptation, demonstrated on seismic bridge fragility using observations from the 2001 Nisqually earthquake. Across these case studies, direct transfer of source models (i.e. using existing state-of-the-art models) fails under domain shift and severe class imbalance, while targeted adaptation substantially improves failure detection and predictive stability in low-data regimes. These findings highlight the need for systematic guidance on diagnostics, strategy selection, and uncertainty reporting when developing and adapting fragility models.

Inference-time scaling trades efficiency for increased reasoning accuracy by generating longer or more parallel sequences. However, in Transformer LLMs, generation cost is bottlenecked by the size of the key-value (KV) cache, rather than the number of generated tokens. Hence, we explore inference-time hyper-scaling: by compressing the KV cache, we can generate more tokens within the same compute budget and further improve the accuracy of scaled inference. The success of this approach, however, hinges on the ability of compression methods to preserve accuracy even at high compression ratios. To make hyper-scaling practical, we introduce Dynamic Memory Sparsification (DMS), a novel method for sparsifying KV caches that only requires 1K training steps to achieve 8 compression, while maintaining better accuracy than training-free sparse attention.

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.

This paper proposes a collapsible method for estimating causal effects that maintains the estimator's consistency before and after marginalization over some variables in completed partially directed acyclic graphs (CPDAGs). We first introduce the estimate collapsibility for CPDAGs and characterize the minimal collapsible sets as strong d-convex hulls. An efficient algorithm is devised to obtain such sets in DAGs and is generalized to CPDAGs. Then, we combine the graph reduction procedure with the IDA framework.

Estimating local mean curvature at each point of a high-dimensional dataset is a key ingredient of geometry-aware machine learning algorithms, such as the Mean Curvature Boundary Points (MCBP) method. The naive implementation of this computation, based on a local shape operator approximated from k-nearest neighbor patches, involves an explicit construction of a matrix $H$ whose trace form yields an $O(m^4)$ cost per point, rendering the approach intractable for datasets with more than a few dozen features. This paper introduces two complementary contributions that together reduce this cost by several orders of magnitude. The first contribution is an exact algebraic identity. This identity, derived from the orthogonality of the eigenvectors of the covariance matrix and the cyclicity of the trace operator, eliminates $H$ entirely and reduces the per-point cost to $O(m^2)$ after the eigendecomposition. The second contribution addresses the remaining $O(m^3)$ bottleneck of the full eigendecomposition. Since the local covariance matrix has rank at most $k-1 \ll m$, we replace it with a truncated SVD of the $k \times m$ centered data matrix, an $O(k^2 m)$ operation, and derive an analytical approximation for the contribution of the null-space eigenvectors based on the expected value of their outer product under the Haar measure. The resulting estimator has total cost $O(k^2 m + k m p^2)$, where $p = k-1$. Experiments on real-world datasets confirm speedups of 50 to 300 times relative to the original implementation, with negligible loss when the fast estimator is used to replace the original version. By providing a scalable and data-driven estimate of local curvature, the proposed method establishes curvature as a practical geometric feature for a broad range of machine learning tasks, from classical to modern deep learning pipelines.

Machine learning methods provide a methodological innovation that can help screen for cardiovascular disease through noninvasive and readily available measurement modalities. Recent investments in using electrocardiogram (ECG) data to screen for structural heart disease (SHD) are one example, where ECGs provide a low-cost, available modality for screening. This has led to the EchoNext dataset, a paired ECG-echocardiogram data repository for testing new methods of SHD detection. However, relatively few studies have investigated how more probabilistic classification through Bayesian inference may improve uncertainty quantification in this setting. Moreover, few studies have considered how triage systems can be developed to alleviate healthcare bottlenecks, such as the review of data from underserved, rural clinics by expert sonographers for SHD assessment. In this study, we leverage existing ECG-echocardiogram data to compare frequentist and Bayesian neural network classifiers. We show that the Bayesian approach is comparable or better than frequentist methods in SHD classification, and that they have a more robust uncertainty quantification attached to them. We provide an example of how this uncertainty-aware classification scheme can be used for screening SHD, providing a proof-of-concept for how machine learning can help with triage in getting individuals expert sonographer input when SHD is highly likely or measurements are highly uncertain.

Accurate boundary detection in high-dimensional data remains a central challenge in unsupervised learning, particularly in the presence of non-linear structures and heterogeneous densities. In this work, we introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning that departs from traditional density-based approaches by explicitly modeling the intrinsic curvature of the data manifold. The method relies on a discrete approximation of the shape operator, estimated from local k-nearest neighbor patches, to compute pointwise mean curvature without requiring explicit manifold parametrization. The key insight of MCBP is to use mean curvature as a principled descriptor of boundary structure: high-curvature regions naturally correspond to transitions between clusters, geometric irregularities, and low-density interfaces. This yields a unified geometric interpretation of boundary, outlier, and transition points. We further introduce an adaptive percentile-based thresholding scheme that enables multiscale boundary extraction without relying on ad hoc density parameters. Beyond detection, we propose a curvature-driven data decomposition that separates samples into smooth (low-curvature) and boundary (high-curvature) subsets, effectively acting as a non-linear geometric filtering mechanism. This representation enhances cluster separability and improves the robustness of downstream unsupervised algorithms. Extensive experiments on synthetic and real-world datasets demonstrate that MCBP consistently improves clustering performance, particularly in complex and high-dimensional scenarios. These results position MCBP as a concrete contribution to Geometric Machine Learning, highlighting the potential of curvature-aware analysis as a unifying paradigm bridging differential geometry and data-driven modeling.

This paper develops a conformal method to compute prediction intervals for nonparametric regression that can automatically adapt to skewed data. Leveraging black-box machine learning algorithms to estimate the conditional distribution of the outcome using histograms, it translates their output into the shortest prediction intervals with approximate conditional coverage. The resulting prediction intervals provably have marginal coverage in finite samples, while asymptotically achieving conditional coverage and optimal length if the black-box model is consistent. Numerical experiments with simulated and real data demonstrate improved performance compared to state-of-the-art alternatives, including conformalized quantile regression and other distributional conformal prediction approaches.

Vision-language models (VLMs) are increasingly used as automated judges for multimodal systems, yet their scores provide no indication of reliability. We study this problem through conformal prediction, a distribution-free framework that converts a judge's point score into a calibrated prediction interval using only score-token log-probabilities, with no retraining. We present the first systematic analysis of conformal prediction for VLM-as-a-Judge across 3 judges and 14 visual task categories. Our results show that evaluation uncertainty is strongly task-dependent: intervals cover ~40% of the score range for aesthetics and natural images but expand to ~70% for chart and mathematical reasoning, yielding a quantitative reliability map for multimodal evaluation. We further identify a failure mode not captured by standard evaluation metrics, ranking-scoring decoupling, where judges achieve high ranking correlation while producing wide, uninformative intervals, correctly ordering responses but failing to assign reliable absolute scores. Finally, we show that interval width is driven primarily by task difficulty and annotation quality, i.e., the same judge and method yield 4.5x narrower intervals on a clean, multi-annotator captioning benchmark. Code: https://github.com/divake/VLM-Judge-Uncertainty