Related papers: On Lexicographic Proof Rules for Probabilistic Ter…

The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…

The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

Calculating the probability of an individual solution being selected under lexicase selection is an important problem in attempts to develop a deeper theoretical understanding of lexicase selection, a state-of-the art parent selection…

We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities).…

It is commonly known that any Bayesian network can be implemented as a probabilistic program, but the reverse direction is not so clear. In this work, we address the open question to what extent a probabilistic program with user-labelled…

Pragmatic reasoning helps interlocutors infer intended meaning from ambiguous or underspecified messages by considering shared context and counterfactual alternatives. Similar challenges arise in natural language-to-code generation, where…

Set theory is foundational to mathematics and, when sets are finite, to reasoning about the world. An intelligent system should perform set operations consistently, regardless of superficial variations in the operands. Initially designed…

Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…

In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…

We introduce for the first time a neural-certificate framework for continuous-time stochastic dynamical systems. Autonomous learning systems in the physical world demand continuous-time reasoning, yet existing learnable certificates for…

Several generic summarization algorithms were developed in the past and successfully applied in fields such as text and speech summarization. In this paper, we review and apply these algorithms to music. To evaluate this summarization's…

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…

Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…

Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…

We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all…

This paper describes an investigation of the robustness of large language models (LLMs) for retrieval augmented generation (RAG)-based summarization tasks. While LLMs provide summarization capabilities, their performance in complex,…

In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…

Large Language Models (LLMs) perform best with well-crafted prompts, yet prompt engineering remains manual, inconsistent, and inaccessible to non-experts. We introduce Promptomatix, an automatic prompt optimization framework that transforms…

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

Many reasoning, planning, and problem-solving tasks share an intrinsic algorithmic nature: correctly simulating each step is a sufficient condition to solve them correctly. We collect pairs of naturalistic and synthetic reasoning tasks to…