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Paper Abstract and Keywords
Presentation 2026-07-03 13:30
[Invited Talk] Statistical Provability of Theorem Proving AI
Sho Sonoda (RIKEN) NC2026-12 IBISML2026-12
Abstract (in Japanese) (See Japanese page) 
(in English) Modern theorem proving AI combines reasoning models with proof assistants, search, retrieval, and verifier feedback, yet classical worst-case hardness does not explain why such systems work on biased mathematical workloads. This talk formulates interactive theorem proving as a finite-horizon MDP with deterministic verifier transitions and defines statistical provability as the probability of reaching a verified proof within a fixed budget on a problem distribution. Case I analyzes offline action-value regression followed by greedy proving, showing how local value error accumulates through average proof length, coverage, and margins. Case II studies teacher-student imitation, contrasting flat traces with hierarchical proof DAGs and quantifying how reusable subproofs can reduce sufficient sample size. This talk is based on [1,2].
[1] S. Sonoda, S. Akiyama, and Y. Uezato, “Why agentic theorem prover works: A statistical provability theory of mathematical reasoning models,” Proceedings of the 43rd International Conference on Machine Learning, 2026.
[2] S. Sonoda, S. Akiyama, and Y. Uezato, “Exponential sample complexity separation between flat and hierarchical agentic theorem provers,” ArXiv preprint 2602.10512, 2026.
Keyword (in Japanese) (See Japanese page) 
(in English) AI theorem proving / interactive theorem proving / statistical provability / / / / /  
Reference Info. IEICE Tech. Rep., vol. 126, no. 91, IBISML2026-12, pp. 54-54, July 2026.
Paper # IBISML2026-12 
Date of Issue 2026-06-25 (NC, IBISML) 
ISSN Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF NC2026-12 IBISML2026-12

Conference Information
Committee NC IBISML IPSJ-BIO IPSJ-MPS  
Conference Date 2026-07-01 - 2026-07-03 
Place (in Japanese) (See Japanese page) 
Place (in English) OIST 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To IBISML 
Conference Code 2026-07-NC-IBISML-BIO-MPS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Statistical Provability of Theorem Proving AI 
Sub Title (in English)  
Keyword(1) AI theorem proving  
Keyword(2) interactive theorem proving  
Keyword(3) statistical provability  
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1st Author's Name Sho Sonoda  
1st Author's Affiliation RIKEN Center for Advanced Intelligence Project (RIKEN)
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Speaker Author-1 
Date Time 2026-07-03 13:30:00 
Presentation Time 60 minutes 
Registration for IBISML 
Paper # NC2026-12, IBISML2026-12 
Volume (vol) vol.126 
Number (no) no.90(NC), no.91(IBISML) 
Page p.54 
#Pages 1 
Date of Issue 2026-06-25 (NC, IBISML) 

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