相关论文: Randomness and lowness notions via open covers

Complex classifiers may exhibit "embarassing" failures in cases where humans can easily provide a justified classification. Avoiding such failures is obviously of key importance. In this work, we focus on one such setting, where a label is…

Robustness of neural networks has recently attracted a great amount of interest. The many investigations in this area lack a precise common foundation of robustness concepts. Therefore, in this paper, we propose a rigorous and flexible…

Reinforcement Learning with Verifiable Rewards (RLVR) has become a central approach for improving the reasoning ability of large language models. Recent work studies RLVR through token entropy, arguing that high-entropy tokens drive…

Many latent-variable applications, including community detection, collaborative filtering, genomic analysis, and NLP, model data as generated by low-rank matrices. Yet despite considerable research, except for very special cases, the number…

In assignment problems, the rank distribution of assigned objects is often used to evaluate match quality. Rank-minimizing (RM) mechanisms directly optimize for average rank. While appealing, a drawback is RM mechanisms are not…

In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of…

Label smoothing (LS) is a popular regularisation method for training neural networks as it is effective in improving test accuracy and is simple to implement. ``Hard'' one-hot labels are ``smoothed'' by uniformly distributing probability…

Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…

A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with…

High-dimensional inference methods often rely on coefficient sparsity, an assumption that can be restrictive when signals are dense but individually weak. In such settings, valid inference may still be possible if the covariates exhibit…

Demonstration-based learning has shown great potential in stimulating pretrained language models' ability under limited data scenario. Simply augmenting the input with some demonstrations can significantly improve performance on few-shot…

A naive likelihood ratio (LR) estimation using the observed frequencies of events can overestimate LRs for infrequent data. One approach to avoid this problem is to use a frequency threshold and set the estimates to zero for frequencies…

Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework…

We study Martin-L\"{o}f random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider variants of conditional randomness defined by ML-randomness on Bayes models and those of…

A data analyst might worry about generalization if dropping a very small fraction of data points from a study could change its substantive conclusions. Checking this non-robustness directly poses a combinatorial optimization problem and is…

Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…

Learning with rejection (LWR) allows development of machine learning systems with the ability to discard low confidence decisions generated by a prediction model. That is, just like human experts, LWR allows machine models to abstain from…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional…

We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…