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Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. A narrowing-based equational unification algorithm relying on the concept of the…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
We investigate systems of equations, involving parameters from the point of view of both control theory and computer algebra. The equations might involve linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference as…
Large language models (LLMs) have demonstrated strong reasoning capabilities. Nevertheless, they still suffer from factual errors when tackling knowledge-intensive tasks. Retrieval-augmented reasoning represents a promising approach.…
Large language models (LLMs) can solve arithmetic word problems with high accuracy, but little is known about how well they generalize to more complex problems. This is difficult to study, as (i) much of the available evaluation data has…
The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relatively recently. In this paper, we address the average-case…
Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…
A notion of generalized quantifier in computational complexity theory is explored and used to give a unified treatment of leaf language definability, oracle separations, type 2 operators, and circuits with monoidal gates. Relations to…
Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…
In our implementation of geometric resolution, the most costly operation is subsumption testing (or matching): One has to decide for a three-valued, geometric formula, if this formula is false in a given interpretation. The formula contains…
Large Language Models (LLMs) struggle with reliably generating highly structured outputs, such as program code, mathematical formulas, or well-formed markup. Constrained decoding approaches mitigate this problem by greedily restricting what…
This paper offers a new perspective to ease the challenge of domain generalization, which involves maintaining robust results even in unseen environments. Our design focuses on the decision-making process in the final classifier layer.…
Language models (LMs) estimate a probability distribution over strings in a natural language; these distributions are crucial for computing perplexity and surprisal in linguistics research. While we are usually concerned with measuring…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…
Language models typically tokenize raw text into sequences of subword identifiers from a predefined vocabulary, a process inherently sensitive to typographical errors, length variations, and largely oblivious to the internal structure of…
Constraint Programming (CP) and Machine Learning (ML) face challenges in text generation due to CP's struggle with implementing "meaning'' and ML's difficulty with structural constraints. This paper proposes a solution by combining both…
Knowledge graphs are structured representations of facts in a graph, where nodes represent entities and edges represent relationships between them. Recent research has resulted in the development of several large KGs. However, all of them…
We show that large language models (LLMs) are remarkably good at working with interpretable models that decompose complex outcomes into univariate graph-represented components. By adopting a hierarchical approach to reasoning, LLMs can…
Machine generation of Arithmetic Word Problems (AWPs) is challenging as they express quantities and mathematical relationships and need to be consistent. ML-solvers require a large annotated training set of consistent problems with language…