Related papers: Tao's Equational Proof Challenge Accepted (Technic…
In this work, the authors give a new method for phase determination, the Tian pseudo atom method (TPAM) or pseudo atom method (PAM) for short. In this new method, the figure of merit function, Rtian, replaces Rcf in the charge flipping…
As automated web accessibility testing tools become enriched with new and improved tests, it can be impractical to leverage those advances. Each tool offers unique benefits, but effectively using multiple tools would require integrating…
In this work we describe a new learning-based proof guidance -- ENIGMAWatch -- for saturation-style first-order theorem provers. ENIGMAWatch combines two guiding approaches for the given-clause selection implemented for the E ATP system:…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
In this paper we first extend the diminishing stepsize method for nonconvex constrained problems presented in [4] to deal with equality constraints and a nonsmooth objective function of composite type. We then consider the particular case…
We consider the $s$-$t$-path TSP: given a finite metric space with two elements $s$ and $t$, we look for a path from $s$ to $t$ that contains all the elements and has minimum total distance. We improve the approximation ratio for this…
Several physics and engineering applications involve the solution of a minimisation problem to compute an approximation of the input signal. Modern computing hardware and software apply high-performance computing to solve and considerably…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
Answering real-world open-domain multi-hop questions over massive corpora is a critical challenge in Retrieval-Augmented Generation (RAG) systems. Recent research employs reinforcement learning (RL) to end-to-end optimize the…
Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…
We address the problem of translating informal mathematical proofs expressed in natural language into formal proofs in Lean4 under a constrained computational budget. Our approach is grounded in two key insights. First, informal proofs tend…
We announce a tool for mapping derivations of the E theorem prover to Mizar proofs. Our mapping complements earlier work that generates problems for automated theorem provers from Mizar inference checking problems. We describe the tool,…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
This paper studies the numerical approximation of solution of the Dirichlet problem for the fully nonlinear Monge-Ampere equation. In this approach, we take the advantage of reformulation the Monge-Ampere problem as an optimization problem,…
The totally asymmetric simple exclusion process (TASEP) is a paradigmatic lattice model for one-dimensional particle transport subject to excluded-volume interactions. Solving the inhomogeneous TASEP in which particles' hopping rates vary…
LLMs can solve complex tasks by generating long, multi-step reasoning chains. Test-time scaling (TTS) can further improve performance by sampling multiple variants of intermediate reasoning steps, verifying their correctness, and selecting…
Large reasoning models that use long chain-of-thought excel at problem-solving yet waste compute on redundant checks. Curbing this overthinking is hard: training-time length penalties can cripple ability, while inference-time early-exit…
The support for higher-order reasoning in the Vampire theorem prover has recently been completely reworked. This rework consists of new theoretical ideas, a new implementation, and a dedicated strategy schedule. The theoretical ideas are…
A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…