相关论文: Tao's Equational Proof Challenge Accepted (Technic…

Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the…

We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project successfully determined all 22 028 942 edges of the implication…

We introduce two new metrics of "simplicity" for knight's tours: the number of turns and the number of crossings. We give a novel algorithm that produces tours with $9.25n+O(1)$ turns and $12n+O(1)$ crossings on an $n\times n$ board, and we…

Equational Theories Project is a collaborative effort, which explores the validity of certain first-order logic implications of certain kind. The project has been completed but triggered further research. This report investigates how much…

A benchmark test was conducted for a new symplectic integration method originally developed by Molei Tao. The method raises interest due to its explicit evolution equation, with applicability to both separable and non-separable Hamiltonian…

How many free variables do we really need to build a credible model of a physical system? Currently there is no systematic approach; we appeal to some physical principles, tune free variables by comparing with canonical cases, and hope our…

During the past decade of continuous development, the theorem prover Vampire has become an automated solver for the combined theories of commonly-used data structures. Vampire now supports arithmetic, induction, and higher-order logic.…

We propose and evaluate experimentally an approach to quantum process tomography that completely removes the scaling problem plaguing the standard approach. The key to this simplification is the incorporation of prior knowledge of the class…

Yupana is an Inca device used for arithmetic operations. This article describes a new arithmetical system: Tawa Pukllay (TP), where arithmetic operations do not require mental calculations: no carries, no borrows, no memorization of…

The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the main points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that…

Multiple hypothesis testing is widely used to evaluate scientific studies involving statistical tests. However, for many of these tests, p-values are not available and are thus often approximated using Monte Carlo tests such as permutation…

Recent advances in large language models (LLMs) have popularized test-time scaling, where models generate additional reasoning tokens before producing final answers. These approaches have demonstrated significant performance improvements on…

We present the results from Meno, a simple autoformalizer that proves theorems in Lean by systematically exploring the space of both formal and informal proofs, and tactic ablation, a new method for exploring mathematical creativity under…

As a present to Mizar on its 50th anniversary, we develop an AI/TP system that automatically proves about 60\% of the Mizar theorems in the hammer setting. We also automatically prove 75\% of the Mizar theorems when the automated provers…

The Weighted Path Order of Yamada is a powerful technique for proving termination. It is also supported by CeTA, a certifier for checking untrusted termination proofs. To be more precise, CeTA contains a verified function that computes for…

Hyper-parameter optimization is crucial for pushing the accuracy of a deep learning model to its limits. A hyper-parameter optimization job, referred to as a study, involves numerous trials of training a model using different training…

Group Relative Policy Optimization (GRPO) has become the dominant method for reinforcement learning with verifiable rewards in large language models, but it suffers from two critical limitations: gradient vanishing and diversity collapse.…

Despite significant progress, Vision-Language Models (VLMs) still struggle with complex visual reasoning, where multi-step dependencies cause early errors to cascade through the reasoning chain. Existing post-training paradigms are limited:…

This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can…

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…