Related papers: Computing Non-Repetitive Sequences with a Computab…

We give a simple combinatorial algorithm to deterministically approximately count the number of satisfying assignments of general constraint satisfaction problems (CSPs). Suppose that the CSP has domain size $q=O(1)$, each constraint…

We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically…

This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…

Replication of experimental results has been a challenge faced by many scientific disciplines, including the field of machine learning. Recent work on the theory of machine learning has formalized replicability as the demand that an…

Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…

A sequence is nonrepetitive if it does not contain two adjacent identical blocks. The remarkable construction of Thue asserts that 3 symbols are enough to build an arbitrarily long nonrepetitive sequence. It is still not settled whether the…

We provide an alternative constructive proof of the Asymmetric Lov\'asz Local Lemma. Our proof uses the classic algorithmic framework of Moser and the analysis introduced by Giotis, Kirousis, Psaromiligkos, and Thilikos in "On the…

Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.

We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function.…

While there has been significant progress on algorithmic aspects of the Lov\'{a}sz Local Lemma (LLL) in recent years, a noteworthy exception is when the LLL is used in the context of random permutations. The breakthrough algorithm of Moser…

A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and…

Probabilistic programming is an approach to reasoning under uncertainty by encoding inference problems as programs. In order to solve these inference problems, probabilistic programming languages (PPLs) employ different inference…

Repetitive action counting, which aims to count periodic movements in a video, is valuable for video analysis applications such as fitness monitoring. However, existing methods largely rely on regression networks with limited…

The \textit{local learning coefficient} (LLC) is a principled way of quantifying model complexity, originally derived in the context of Bayesian statistics using singular learning theory (SLT). Several methods are known for numerically…

A locally recoverable code (LRC code) is a code over a finite alphabet such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. In this paper we derive new finite-length and…

Autoregressive Large Language Models (LLMs) trained for next-word prediction have demonstrated remarkable proficiency at producing coherent text. But are they equally adept at forming coherent probability judgments? We use probabilistic…

We propose locally rewritable codes (LWC) for resistive memories inspired by locally repairable codes (LRC) for distributed storage systems. Small values of repair locality of LRC enable fast repair of a single failed node since the lost…

The recently proven Quantum Lovasz Local Lemma generalises the well-known Lovasz Local Lemma. It states that, if a collection of subspace constraints are "weakly dependent", there necessarily exists a state satisfying all constraints. It…

Large language models (LLMs) are increasingly used for high-stakes decision-making, yet existing approaches struggle to reconcile scalability, interpretability, and reproducibility. Black-box models obscure their reasoning, while recent…

Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…