Reliable probability estimates are critical in many machine learning applications, yet modern classifiers are often poorly calibrated. Post-hoc calibration provides a simple and widely used solution, but the large number of proposed methods, combined with small-scale and inconsistent evaluations, makes it difficult to determine which approaches are truly effective in practice. We introduce a large-scale, standardized benchmark for post-hoc calibration, covering nearly 2000 experiments across tabular and computer vision tasks, including binary, multiclass, and large-scale classification settings. Our benchmark aggregates predictions from a diverse set of classical models, modern deep learning architectures, and foundation models, and provides unified, reproducible implementations of dozens of calibration methods within a common evaluation framework. We argue that Post-Hoc Improvement (PHI) in proper scoring rules offers a principled alternative to traditional calibration error estimators for comparing post-hoc methods, capturing both calibration quality and potential degradation to the model's predictive performance. Using this framework, we conduct the most comprehensive empirical study of post-hoc calibration to date. Our results reveal consistent patterns across domains: smooth calibration functions outperform binning-based approaches, dedicated multiclass methods are essential in high-dimensional settings, and generic machine learning models are not competitive without calibration-specific design. To facilitate future research, we release all data, code, and evaluation tools, providing a plug-and-play benchmark for developing and comparing calibration methods.

This paper proposes a general machine learning framework called the localization method, which is fundamentally built on two core concepts: localization kernels and local means -- key components that underpin the self-attention mechanism. To establish a rigorous theoretical foundation, the framework is formally defined through two essential pillars: the formulation of the local(-ized) model and the localization trick. We systematically investigate the connections between the localization method and a wide range of existing machine learning models/methods, including (but not limited to) kernel methods, lazy learning, the MeanShift algorithm, relaxation labeling, Hopfield networks, local linear embedding (LLE), fuzzy inference, and denoising autoencoders (DAEs). By dissecting these relationships, we clarify the broader theoretical significance of the localization method and demonstrate its practical applicability across diverse machine learning tasks. Furthermore, we explore advanced extensions of the framework, such as adaptive kernels, hierarchical local models, and non-local models. Notably, we show that the Transformer -- a cornerstone of modern sequence modeling -- can be constructed using hierarchical local models, revealing the ability of the localization method to unify and generalize state-of-the-art architectures. This work not only provides a unified theoretical lens to reinterpret existing models but also offers new methodological tools for designing flexible, data-adaptive learning systems.

This paper addresses structured out-of-distribution (OOD) testing in high-stakes machine learning applications. Traditional conformal methods rely on joint exchangeability, making it difficult to incorporate auxiliary information such as spatiotemporal or grouping structures. To overcome this limitation, we propose the structure-adaptive conformal q-value (SCQ), a significance index that integrates individual test evidence with structural patterns. We also develop pseudo-score-guided transductive automated model selection (P-TAMS), which adapts conformalized model selection to structured OOD testing across a toolbox of candidate models. Together, SCQ and P-TAMS form a unified framework under pairwise exchangeability, providing finite-sample error-rate control, improved power, and enhanced interpretability. Experiments on simulated and real data demonstrate that the proposed approach controls the false discovery rate and performs well across diverse settings.

AsInstrategic classification, aninstitution(e.g., a bank) anticipates adaptation from userswe develop better algorithms under varying assumpwho change their features to increase utilitytions about adaptation (Levanon and Rosenfeld, 2022; in a classification task (e.g., loan repayment). Kleinberg and Raghavan, 2018), there are growing Since a key challenge is the distribution shiftconcerns about negative social impact on the agents who adapt to these systems, whether outcomes areinduced by users, we turn to causal models, which have been shown to bound the worst-static (Milli et al., 2019) or dynamic (G ois et al., case out-of-distribution (OOD) risk, and es-2025). When agents adapt, depending on the untablish several new results that link causal-derlying causal model (Horowitz and Rosenfeld, 2018; ity and strategic classification. First, we Miller et al., 2020), some changes improve agent outcomes while others constitute gaming the classifier,show that causal classification leads to optimal classification error after any sufficientlyworsening classification error. In this paper, we study large adaptation, when the noise is boundedwhether classifiers can maintain accuracy without sacin a certain way. Second, when these as-rificing alignment with predicted agent's goals.

We study the problem of identifying dynamically distinct basins of attraction in high dimensional time-homogeneous Markov processes using only trajectory sampling. This problem is fundamental in the analysis of metastable dynamical systems, where the process rapidly mixes within basins while transitions between basins occur rarely on the timescale of interest, or even when the state space is reducible. Existing approaches typically rely on spatial discretization or spectral analysis of estimated transition operators, which can become unreliable in high dimensional settings or when the underlying basin geometry is highly nonlinear. We propose a discriminative approach to basin identification based on marginal trajectory distribution comparison. We prove a simple risk separation result: if two initial states belong to the same basin, the Bayes-optimal classifier distinguishing their marginal trajectory distributions achieves risk close to 1/2, whereas if they lie in distinct basins, the optimal risk is close to zero. This observation reduces basin detection to a two-sample discrimination problem between marginal trajectory distributions. Motivated by this principle, we develop a neural algorithm that receives a set of candidate basin representatives and iteratively merges them by estimating classification risk with a neural network that approximates the Bayes classifier. We evaluate the method on various metastable systems. These include synthetic systems constructed by embedding low-dimensional dynamics into high dimensional noisy ambient spaces. In these settings, standard spectral and clustering-based methods often fail, while our approach accurately recovers the underlying basin structure. These results display a shortcoming of existing methods and highlight trajectory discrimination as an effective tool for identifying dynamical basins in high dimensional stochastic systems.

Confidence calibration for classification models is vital in safety-critical decision-making scenarios and has received extensive attention. General confidence calibration methods assume training and test data are independent and identically distributed, limiting their effectiveness under covariate shifts. Previous calibration methods under covariate shift struggle with class-wise or canonical calibrations and often rely on unstable importance weighting when density ratios are large or unbounded. Given the above limitations, this paper rethinks confidence calibration under covariate shifts. First, we derive a necessary and sufficient condition for confidence calibration under covariate shifts, named Expectation consistency condition, which reveals covariate shifts do not necessarily lead to uncalibrated confidence and provides a weaker condition for confidence calibration than global covariate distribution alignment. Then, utilizing Expectation consistency condition, this paper proposes an unsupervised domain adaptation loss to calibrate confidence of the target domain, named Expectation consistency loss (ECL), which is compatible with canonical calibration, class-wise calibration, and top-label calibration. Third, we prove that computing ECL loss has the same sample complexity as Expected Calibration Error (ECE) and provide a theoretically grounded mini-batch trainable scheme for ECL loss. Finally, we validate the effectiveness of our method on both simulated and real-world covariate shift datasets.

Interpretable text representations should expose coordinates that are not only predictive, but also meaningful enough for independent auditors to apply. Existing discriminative representations often use anonymous embedding directions, while concept-bottleneck and LLM-assisted methods attach natural-language names to features without ensuring that those definitions are reproducible or distinct from the target label. We propose an operational criterion for interpretable discriminative text representations: each coordinate should satisfy conceptual clarity, measured by chance-adjusted agreement between independent annotators applying the feature definition, and label disentanglement, meaning the feature should not merely paraphrase the prediction target. We instantiate this criterion in LLM-assisted Feature Discovery (LFD), an iterative method that proposes lexical and semantic features from contrastive outcome-opposed text pairs, screens candidates using cross-LLM Cohen's $κ$, and selects features by residual held-out predictive gain. A stylized analysis connects the $κ$ screen to a per-feature annotation-noise bound, formalizing agreement as a reliability check. Across ten text-classification tasks spanning seven corpora, LFD matches the predictive performance of a strong text bottleneck baseline while producing substantially clearer and less label-entangled features. Human audits with 232 raters show that LFD features achieve higher human--human and human--LLM agreement than baseline concepts, and raters consistently judge them as less label-leaking. These results suggest that agreement-tested, label-disentangled coordinates provide a practical auditability standard for interpretable text classification.

Accurate and well-calibrated Machine Learning (ML) models are mandatory in high-stakes settings, yet effective multiclass calibration remains challenging: global approaches assume calibration errors are homogeneous across the latent space, while local methods often rely on latent-space dimensionality reduction, which leads to information loss. To address these issues, we propose a compositional approach to multiclass calibration, where region-specific calibration maps are constructed from shared codeword-dependent factors. We instantiate this idea via Vector Quantization (VQ), which induces a structured partition of the representation space, and an indexed parameterization of Dirichlet concentrations that enables parameter sharing across regions. Our approach learns heterogeneous calibration maps that generalize well even to sparse regions of the latent space. Experiments on benchmark datasets show significant improvements in local calibration while maintaining competitive global calibration and predictive performance.

We developed a tool for detecting domain shifts, namely subtle differences in the probability distributions of datasets. We identify these shifts using an algorithm designed to detect localised density anomalies in high-dimensional feature spaces. If an anomaly is present, we then identify the feature subspace in which the anomaly is most pronounced. This allows us to trace the domain shift to a small set of features, making the shift interpretable. Moreover, we provide a protocol for compensating domain shifts by extracting, from two unlabelled datasets, subsets of samples with no detectable residual distributional difference. We validate the framework on controlled 20-dimensional benchmarks with known ground truth, recovering both broad and localized shifts together with their supporting feature subspaces. We then apply it to healthy electrocardiogram (ECG) recordings represented by 782 features. In age- and sex-matched cohort comparisons differing in measurement-device composition, the method detects device-induced shifts, extracts representative subsets enriched in the imbalanced device components, and identifies ECG features associated with the acquisition contrast. These results suggest that density-shift detection and subspace attribution provide a practical framework for uncovering hidden cohort biases before downstream modelling.

We propose a variational quantum classifier operating on high dimensional deep representations via amplitude encoding, stabilized by a learnable classical pre encoding layer.By combining normalized amplitude embeddings with bounded quantum observables, the resulting model induces a structured and smooth hypothesis class with controlled sensitivity to input variations. Model reliability is assessed using SAFE-AI metrics derived from the Cramer von Mises divergence, enabling consistent evaluation across accuracy, robustness, and explainability dimensions. Empirical results show that the proposed quantum model provides competitive predictive performance compared with strong classical baselines while exhibiting a more balanced SAFE reliability profile, with improved robustness to noise and stability under structured feature removal. These findings suggest that variational quantum circuits offer a principled mechanism for stability oriented SAFE learning in safety critical settings.