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In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are…

Long-tailed distributions frequently emerge in real-world data, where a large number of minority categories contain a limited number of samples. Such imbalance issue considerably impairs the performance of standard supervised learning…

This study explores the application and performance of Transformational Machine Learning (TML) in drug discovery. TML, a meta learning algorithm, excels in exploiting common attributes across various domains, thus developing composite…

Large Language Models (LLMs), like GPT-3.5-turbo, have demonstrated the ability to understand graph structures and have achieved excellent performance in various graph reasoning tasks, such as node classification. Despite their strong…

This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…

Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel…

Large language models (LLMs) provide powerful means to leverage prior knowledge for predictive modeling when data is limited. In this work, we demonstrate how LLMs can use their compressed world knowledge to generate intrinsically…

Asymptotic separation index is a parameter that measures how easily a Borel graph can be approximated by its subgraphs with finite components. In contrast to the more classical notion of hyperfiniteness, asymptotic separation index is…

In this paper, a new approach for classification of target task using limited labeled target data as well as enormous unlabeled source data is proposed which is called self-taught learning. The target and source data can be drawn from…

The Strong Lottery Ticket Hypothesis (SLTH) stipulates the existence of a subnetwork within a sufficiently overparameterized (dense) neural network that -- when initialized randomly and without any training -- achieves the accuracy of a…

We derive sufficient conditions for a probability measure on a finite product space (a spin system) to satisfy a (modified) logarithmic Sobolev inequality. We establish these conditions for various examples, such as the (vertex-weighted)…

\textit{Mallows model} is a widely-used probabilistic framework for learning from ranking data, with applications ranging from recommendation systems and voting to aligning language models with human preferences~\cite{chen2024mallows,…

We study the problem of approximating a discrete probability distribution, such as the next-token distribution of a large language model, by a dyadic distribution induced by a binary tree under encoding rate constraints. The objective is to…

Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…

We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…

The Kolmogorov-Arnold representation is a proven adequate replacement of a continuous multivariate function by an hierarchical structure of multiple functions of one variable. The proven existence of such representation inspired many…

In this work, we give a unifying view of locality in four settings: distributed algorithms, sequential greedy algorithms, dynamic algorithms, and online algorithms. We introduce a new model of computing, called the online-LOCAL model: the…

This paper considers the average complexity of maximum likelihood (ML) decoding of convolutional codes. ML decoding can be modeled as finding the most probable path taken through a Markov graph. Integrated with the Viterbi algorithm (VA),…

In-context learning has established itself as an important learning paradigm for Large Language Models (LLMs). In this paper, we demonstrate that LLMs can learn encoding keys in-context and perform analysis directly on encoded…

In the framework of the probabilistic method in combinatorics, we revisit the entropy compression method clarifying the setting in which it can be applied and providing a theorem yielding a general constructive criterion. We finally…