Related papers: Tao's Equational Proof Challenge Accepted (Technic…
We showcase a collection of practical strategies to deal with a problem arising from an analysis of integral estimators derived via quasi-Monte Carlo methods. The problem reduces to a triple binomial sum, thereby enabling us to open up the…
Algorithmic recourse is a process that leverages counterfactual explanations, going beyond understanding why a system produced a given classification, to providing a user with actions they can take to change their predicted outcome.…
In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit…
Training large reasoning models (LRMs) with reinforcement learning in STEM domains is hindered by the scarcity of high-quality, diverse, and verifiable problem sets. Existing synthesis methods, such as Chain-of-Thought prompting, often…
Credal networks are a popular class of imprecise probabilistic graphical models obtained as a Bayesian network generalization based on, so-called credal, sets of probability mass functions. A Java library called CREMA has been recently…
Molecular retrosynthesis is a significant and complex problem in the field of chemistry, however, traditional manual synthesis methods not only need well-trained experts but also are time-consuming. With the development of big data and…
In this paper, we describe TRIPs-Py, a new Python package of linear discrete inverse problems solvers and test problems. The goal of the package is two-fold: 1) to provide tools for solving small and large-scale inverse problems, and 2) to…
In 2007, Terence Tao wrote on his blog an essay about soft analysis, hard analysis and the finitization of soft analysis statements into hard analysis statements. One of his main examples was a quasi-finitization of the infinite pigeonhole…
Mathematical reasoning is central to artificial intelligence, with applications in education, code generation, and research-level mathematical discovery. Mathematical competitions highlight two problem types: theorem proving, requiring…
We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of Matlab and requiring no user input parameters. Even on a disk or interval the algorithm may outperform…
We present heyoka, a new, modern and general-purpose implementation of Taylor's integration method for the numerical solution of ordinary differential equations. Detailed numerical tests focused on difficult high-precision gravitational…
Mathematical reasoning through Chain-of-Thought (CoT) has emerged as a powerful capability of Large Language Models (LLMs), which can be further enhanced through Test-Time Scaling (TTS) methods like Beam Search and DVTS. However, these…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
We present $\textbf{P}$robabilistically $\textbf{T}$ightened $\textbf{Li}$near $\textbf{R}$elaxation-based $\textbf{P}$erturbation $\textbf{A}$nalysis ($\texttt{PT-LiRPA}$), a novel framework that combines over-approximation techniques from…
The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: (i) extending the representation to the process of setting the problem, (ii)…
The Single-Source Shortest Path (SSSP) problem is well-known for the challenges in developing fast, practical, and work-efficient parallel algorithms. This work introduces a novel shortest path search method. It allows paths with different…
The use of deductive techniques, such as theorem provers, has several advantages in safety verification of hybrid sys- tems; however, state-of-the-art theorem provers require ex- tensive manual intervention. Furthermore, there is often a…
For small number of equations, systems of linear (and sometimes nonlinear) equations can be solved by simple classical techniques. However, for large number of systems of linear (or nonlinear) equations, solutions using classical method…
The hierarchy of pure states (HOPS) is a wavefunction-based method which can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However,…
Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and…