Achieving generalization in neural approaches across different scales and distributions remains a significant challenge for routing problems. A key obstacle is that neural networks often fail to learn robust principles for identifying universal patterns and deriving optimal solutions from diverse instances. In this paper, we first uncover Purity Law, a fundamental structural principle for optimal solutions of routing problems, defining that edge prevalence grows exponentially with the sparsity of surrounding vertices. Statistically and theoretically validated across diverse instances, Purity Law reveals a consistent bias toward local sparsity in global optima. Building on this insight, we propose Purity Policy Optimization (PUPO), a novel training paradigm that explicitly aligns characteristics of neural solutions with Purity Law during the solution construction process to enhance generalization. Extensive experiments demonstrate that PUPO can be seamlessly integrated with popular neural solvers, significantly enhancing their generalization performance without incurring additional computational overhead during inference. The code is available at https://github.com/Kejun0627/PUPO.

This work introduces a novel approach, Pairwise Epistemic Estimators (PairEpEsts), for epistemic uncertainty estimation in ensemble models for regression tasks using pairwise-distance estimators (PaiDEs). By utilizing the pairwise distances between model components, PaiDEs establish bounds on entropy. We leverage this capability to enhance the performance of Bayesian Active Learning by Disagreement (BALD). Notably, unlike sample-based Monte Carlo estimators, PairEpEsts can estimate epistemic uncertainty up to 100 times faster and demonstrate superior performance in higher dimensions. To validate our approach, we conducted a varied series of regression experiments on commonly used benchmarks: 1D sinusoidal data, Pendulum, Hopper, Ant, and Humanoid, demonstrating PairEpEsts' advantage over baselines in high-dimensional regression active learning.

Data attribution for text-to-image models aims to identify the training images that most involv significantly e considerable influenced computational a generated resources output.

Test-Time Discovery (TTD) addresses the critical challenge of identifying and adapting to novel classes during inference while maintaining performance on known classes, which is a capability essential for dynamic real-world environments such as healthcare and autonomous driving. Recent TTD methods adopt training-free, memory-based strategies but rely on frozen models and static representations, resulting in poor generalization. In this paper, we propose a DiscrepancyAmplifying Adapter (DAA), a trainable module that enables real-time adaptation by amplifying feature-level discrepancies between known and unknown classes. During training, DAA is optimized using simulated unknowns and a novel warmup strategy to enhance its discriminative capacity. To ensure continual adaptation at test time, we introduce a Short-Term Memory Renewal (STMR) mechanism, which maintains a queue-based memory for unknown classes and selectively refreshes prototypes using recent, reliable samples. DAA is further updated through self-supervised learning, promoting knowledge retention for known classes while improving discrimination of emerging categories. Extensive experiments show that our method maintains high adaptability and stability, and significantly improves novel class discovery performance.

The Johnson-Lindenstrauss (JL) lemma is a cornerstone of dimensionality reduction in Euclidean space, but its applicability to non-Euclidean data has remained limited. This paper extends the JL lemma beyond Euclidean geometry to handle general dissimilarity matrices that are prevalent in real-world applications. We present two complementary approaches: First, we show the JL transform can be applied to vectors in pseudo-Euclidean space with signature (p,q), providing theoretical guarantees that depend on the ratio of the (p,q)norm and Euclidean norm of two vectors, measuring the deviation from Euclidean geometry. Second, we prove that any symmetric hollow dissimilarity matrix can be represented as a matrix of generalized power distances, with an additional parameter representing the uncertainty level within the data. In this representation, applying the JL transform yields multiplicative approximation with a controlled additive error term proportional to the deviation from Euclidean geometry. Our theoretical results provide fine-grained performance analysis based on the degree to which the input data deviates from Euclidean geometry, making practical and meaningful reduction in dimensionality accessible to a wider class of data.

We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is costly, e.g.

Calibration is a fundamental concept that aims at ensuring the reliability of probabilistic predictions by aligning them with real-world outcomes. There is a surge of studies on new calibration measures that are easier to optimize compared to the classical ℓ1-Calibration while still having strong implications for downstream applications. One such recent example is the work by Fishelson et al. (2025) who show that it is possible to achieve O(T1/3)pseudo ℓ2-Calibration error via minimizing pseudo swap regret of the squared loss, which in fact implies the same bound for all bounded proper losses with a smooth univariate form. In this work, we significantly generalize their result in the following ways: (a) in addition to smooth univariate forms, our algorithm also simultaneously achieves O(T1/3) swap regret for any proper loss with a twice continuously differentiable univariate form (such as Tsallis entropy); (b) our bounds hold not only for pseudo swap regret that measures losses using the forecaster's distributions on predictions, but also hold for the actual swap regret that measures losses using the forecaster's actual realized predictions. We achieve so by introducing a new stronger notion of calibration called (pseudo) KL-Calibration, which we show is equivalent to the (pseudo) swap regret with respect to log loss. We prove that there exists an algorithm that achieves O(T1/3) KL-Calibration error and provide an explicit algorithm that achieves O(T1/3) pseudo KL-Calibration error. Moreover, we show that the same algorithm achieves O(T1/3(logT) 13 log(T/δ)) swap regret with probability at least 1 δ for any proper loss with a smooth univariate form, which implies O(T1/3) ℓ2-Calibration error. A technical contribution of our work is a new randomized rounding procedure and a non-uniform discretization scheme to minimize the swap regret for log loss.

Recent studies empirically reveal that large reasoning models (LRMs) can automatically allocate more reasoning strengths (i.e., the number of reasoning tokens) for harder problems, exhibiting difficulty-awareness for better task performance. While this automatic reasoning strength allocation phenomenon has been widely observed, its underlying mechanism remains largely unexplored. To this end, we provide explanations for this phenomenon from the perspective of model activations. We find evidence that LRMs pre-plan the reasoning strengths in their activations even before generation, with this reasoning strength causally controlled by the magnitude of a pre-allocated directional vector. Specifically, we show that the number of reasoning tokens is predictable solely based on the question activations using linear probes, indicating that LRMs estimate the required reasoning strength in advance.

While substantial advances have been achieved in TTS for languages such as English and Mandarin, Korean remains comparatively underrepresented due to the lack of rigorous preprocessing methods, systematically constructed datasets, a shortage of standardized Korean TTS benchmarks, and explicitly optimized models for Korean. To address these limitations, we propose a Korean-tailored data-refinement and coreset selection pipeline. It refines speech data and performs textual normalization especially for numerals and English terms, followed by a novel coreset selection strategy that leverages Jamo-based linguistic and phonological features unique to Korean. As a result, we release CoreaSpeech, an efficient and robust Korean speech corpus comprising 700 hours across 21,449 speakers. This refined core subset, evenly balanced across utterances ranging from 0 to 30 seconds, is derived from 2,058 hours of widely used Korean datasets. Building on this, we conducted extensive experiments via cross-lingual fine-tuning with our CoreaSpeech dataset. Furthermore, we introduce a new universal Korean TTS benchmark dataset including clean, noisy, and numeric subsets. Additionally, we demonstrate that our Korean-specific text normalization serves as a plug-and-play module, reliably improving performance regardless of the underlying TTS architecture.

Drug recommendation systems aim to identify optimal drug combinations for patient care, balancing therapeutic efficacy and safety. Advances in large-scale longitudinal EHRs have enabled learning-based approaches that leverage patient histories such as diagnoses, procedures, and previously prescribed drugs, to model complex patient-drug relationships. Yet, many existing solutions overlook standard clinical practices that favor certain drugs for specific conditions and fail to fully integrate the influence of molecular substructures on drug efficacy and safety. In response, we propose SubRec, a unified framework that integrates representation learning across both patient and drug spaces. Specifically, SubRec introduces a conditional information bottleneck to extract core drug substructures most relevant to patient conditions, thereby enhancing interpretability and clinical alignment. Meanwhile, an adaptive vector quantization mechanism is designed to generate patient-drug interaction patterns into a condition-aware codebook which reuses clinically meaningful patterns, reduces training overhead, and provides a controllable latent space for recommendation. Crucially, the synergy between condition-specific substructure learning and discrete patient prototypes allows SubRec to make accurate and personalized drug recommendations. Experimental results on the real-world MIMICIII and IV demonstrate our model's advantages. The source code is available at https://DrugRecommendation/.