Arnav Mehta | Searcharxiv

arXiv2026

LeanTutor: Towards a Verified AI Mathematical Proof Tutor

This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for provable-correctness, but these are hard for students to learn. We present a proof-of-concept system (LeanTutor) by combining the complementary strengths of LLMs and theorem provers. LeanTutor is composed of three modules: (i) an autoformalizer/proof-checker, (ii) a next-step generator, and (iii) a natural language feedback generator. To evaluate the system, we introduce PeanoBench, a dataset of 371 Peano Arithmetic proofs in human-written natural language and formal language, derived from the Natural Numbers Game.

cs.LG↗

arXiv2025

LeanTutor: Towards a Verified AI Mathematical Proof Tutor

This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for provable-correctness, but these are hard for students to learn. We present a proof-of-concept system (LeanTutor) by combining the complementary strengths of LLMs and theorem provers. LeanTutor is composed of three modules: (i) an autoformalizer/proof-checker, (ii) a next-step generator, and (iii) a natural language feedback generator. To evaluate the system, we introduce PeanoBench, a dataset of 371 Peano Arithmetic proofs in human-written natural language and formal language, derived from the Natural Numbers Game.

cs.AI↗

arXiv2025

Learning collective variables that preserve transition rates

Collective variables (CVs) play a crucial role in capturing rare events in high-dimensional systems, motivating the continual search for principled approaches to their design. In this work, we revisit the framework of quantitative coarse graining and identify the orthogonality condition from Legoll and Lelievre (2010) as a key criterion for constructing CVs that accurately preserve the statistical properties of the original process. We establish that satisfaction of the orthogonality condition enables error estimates for both relative entropy and pathwise distance to scale proportionally with the degree of scale separation. Building on this foundation, we introduce a general numerical method for designing neural network-based CVs that integrates tools from manifold learning with group-invariant featurization. To demonstrate the efficacy of our approach, we construct CVs for butane and achieve a CV that reproduces the anti-gauche transition rate with less than ten percent relative error. Additionally, we provide empirical evidence challenging the necessity of uniform positive definiteness in diffusion tensors for transition rate reproduction and highlight the critical role of light atoms in CV design for molecular dynamics.

math.NA↗

arXiv2025

MARS6: A Small and Robust Hierarchical-Codec Text-to-Speech Model

Codec-based text-to-speech (TTS) models have shown impressive quality with zero-shot voice cloning abilities. However, they often struggle with more expressive references or complex text inputs. We present MARS6, a robust encoder-decoder transformer for rapid, expressive TTS. MARS6 is built on recent improvements in spoken language modelling. Utilizing a hierarchical setup for its decoder, new speech tokens are processed at a rate of only 12 Hz, enabling efficient modelling of long-form text while retaining reconstruction quality. We combine several recent training and inference techniques to reduce repetitive generation and improve output stability and quality. This enables the 70M-parameter MARS6 to achieve similar performance to models many times larger. We show this in objective and subjective evaluations, comparing TTS output quality and reference speaker cloning ability. Project page: https://camb-ai.github.io/mars6-turbo/

eess.AS↗