相关论文: Randomness and lowness notions via open covers

Large Language Models (LLMs) have the potential to revolutionize scientific research, yet their robustness and reliability in domain-specific applications remain insufficiently explored. In this study, we evaluate the performance and…

Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…

In supervised machine learning, models are typically trained using data with hard labels, i.e., definite assignments of class membership. This traditional approach, however, does not take the inherent uncertainty in these labels into…

Compact convolutional neural networks (CNNs) have witnessed exceptional improvements in performance in recent years. However, they still fail to provide the same predictive power as CNNs with a large number of parameters. The diverse and…

The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…

A major problem in the study of large language models is to understand their inherent low-dimensional structure. We introduce an approach to study the low-dimensional structure of language models at a model-agnostic level: as sequential…

Recurrent networks have achieved great success on various sequential tasks with the assistance of complex recurrent units, but suffer from severe computational inefficiency due to weak parallelization. One direction to alleviate this issue…

We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation $r$ of the training data, and then fitting a simple (e.g., linear) classifier $g$ to the labels.…

Supervised classification methods often assume that evaluation data is drawn from the same distribution as training data and that all classes are present for training. However, real-world classifiers must handle inputs that are far from the…

The low for random reals are characterized topologically, as well as in terms of domination of Turing functionals on a set of positive measure.

Martin-L\"of (ML)-reducibility compares $K$-trivial sets by examining the Martin-L\"of random sequences that compute them. We show that every $K$-trivial set is computable from a c.e.\ set of the same ML-degree. We investigate the interplay…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for…

We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically…

Open-set classification is a problem of handling `unknown' classes that are not contained in the training dataset, whereas traditional classifiers assume that only known classes appear in the test environment. Existing open-set classifiers…

Fine-tuning Large Language Models (LLMs) and storing them for each downstream task or domain is impractical because of the massive model size (e.g., 350GB in GPT-3). Current literature, such as LoRA, showcases the potential of low-rank…

This is a survey of constructive and computable measure theory with an emphasis on the close connections with algorithmic randomness. We give a brief history of constructive measure theory from Brouwer to the present, emphasizing how…

A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…

In Part I, we defined a LASSO condition number and developed an algorithm -- for computing support sets (feature selection) of the LASSO minimisation problem -- that runs in polynomial time in the number of variables and the logarithm of…

Large reasoning models (LRMs) produce a textual chain of thought (CoT) in the process of solving a problem, which serves as a potentially powerful tool to understand the problem by surfacing a human-readable, natural-language explanation.…