Related papers: Tight Typings and Split Bounds

The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…

Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…

The lambda-calculus with de Bruijn indices assembles each alpha-class of lambda-terms in a unique term, using indices instead of variable names. Intersection types provide finitary type polymorphism and can characterise normalisable…

Aligning Large Language Models (LLMs) with human preferences through finetuning is resource-intensive, motivating lightweight alternatives at test time. We address test-time alignment through the lens of sequential decision making, a…

Due to their architecture and vast pre-training data, large language models (LLMs) demonstrate strong text classification performance. However, LLM output - here, the category assigned to a text - depends heavily on the wording of the…

Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower…

We propose cognitive prompting as a novel approach to guide problem-solving in large language models (LLMs) through structured, human-like cognitive operations, such as goal clarification, decomposition, filtering, abstraction, and pattern…

We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…

Indexed Linear Logic has been introduced by Ehrhard and Bucciarelli, it can be seen as a logical presentation of non-idempotent intersection types extended through the relational semantics to the full linear logic. We introduce an…

Large Language Models (LLMs) using Chain-of-Thought (CoT) prompting excel at complex reasoning but generate verbose thought processes with considerable redundancy, leading to increased inference costs and reduced efficiency. We introduce a…

We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…

Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form x' <= y + c, and describe that the value of x in the current state is at most the value of y in the…

An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…

Sampling-based motion planners have proven to be efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that…

This paper addresses a key limitation in existing counterfactual inference methods for Markov Decision Processes (MDPs). Current approaches assume a specific causal model to make counterfactuals identifiable. However, there are usually many…

We devise a method to exactly compute the length of the longest simple path in factored state spaces, like state spaces encountered in classical planning. Although the complexity of this problem is NEXP-Hard, we show that our method can be…

Centroid based clustering methods such as k-means, k-medoids and k-centers are heavily applied as a go-to tool in exploratory data analysis. In many cases, those methods are used to obtain representative centroids of the data manifold for…

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…

We consider a class of convex optimization problems over the simplex of probability measures. Our framework comprises optimal experimental design (OED) problems, in which the measure over the design space indicates which experiments are…