Related papers: A Toolbox for Refined Information-Theoretic Analys…
Automatic translation of natural language mathematics into faithful Lean 4 code is hindered by the fundamental dissonance between informal set-theoretic intuition and strict formal type theory. This gap often causes LLMs to hallucinate…
We are presenting a set of multilingual text analysis tools that can help analysts in any field to explore large document collections quickly in order to determine whether the documents contain information of interest, and to find the…
We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement…
We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or time-dependent partial differential equations. For the efficiency of such exponential…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
The program synthesis problem within the Inductive Logic Programming (ILP) community has typically been seen as untyped. We consider the benefits of user provided types on background knowledge. Building on the Meta-Interpretive Learning…
Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…
This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms. The main technical tool is a probabilistic decorrelation lemma based on a change of measure and a relaxation of…
Target-oriented discovery under limited evaluation budgets requires making reliable progress in high-dimensional, heterogeneous design spaces where each new measurement is costly, whether experimental or high-fidelity simulation. We present…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
Brief Description: The book provides a unique highly self-contained text introducing the reader to the classical and modern theory of polyanalytic functions and their generalizations. This is a subbranch of complex analysis of several…
In this work, we fully explore three refined convergence structures of the lowest-order rectangular Raviart-Thomas element in solving the Laplace eigenvalue problem. Firstly, the scheme possesses a property of supercloseness between the…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
Studying the impact of new-physics models on low-energy observables necessitates matching to effective field theories at the relevant mass thresholds. We introduce the first public version of Matchete, a computer tool for matching…
Session types express and enforce safe communication in concurrent message-passing systems by statically capturing the interaction protocols between processes in the type. Recent works extend session types with arithmetic refinements, which…
In the context of statistical learning, the Information Bottleneck method seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description…
This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…
Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…
This paper introduces Jensen, an easily extensible and scalable toolkit for production-level machine learning and convex optimization. Jensen implements a framework of convex (or loss) functions, convex optimization algorithms (including…
System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the…