arXiv subjects

Masaya Taniguchi

Publications and source records attributed to Masaya Taniguchi.

8 recordsLinked to original sources

arXiv2026

Lean-Quantum: Toward AI-Assisted Formalization of Quantum Information

Quantum information theory is built on entropic quantities; among them, the sandwiched R\'enyi relative entropy is a fundamental divergence with various applications, and its data processing inequality (DPI) under quantum channels is a cornerstone result. In this work, we present a Lean 4 library for quantum information, designed as a reusable formal infrastructure for theoretical analysis. As a central demonstration of the library, we formalize the DPI for the sandwiched R\'enyi relative entropy for positive semidefinite operators on finite-dimensional quantum systems. The library provides a basis-independent operator-theoretic framework for finite-dimensional quantum mechanics compatible with the standard mathematical library Mathlib, including reusable interfaces for finite-dimensional systems, states, channels, tensor products, partial traces, Choi operators, Kraus representations, and Stinespring representations. It also builds infrastructure for noncommutative trace inequalities, including operator monotonicity and convexity via the real continuous functional calculus, block-operator positivity, Hilbert-Schmidt operator spaces, Jensen's operator inequality, generalized perspectives, operator power means, and Lieb-Ando trace inequalities. On top of this framework, we formalize entropy-specific ingredients for the DPI: variational formulas for the sandwiched quasi-entropy via Young and reverse-Young inequalities, tensor-product compatibility of real powers, and Haar measures on unitary groups. Together, these components yield a Lean formalization of the DPI, give strong subadditivity as a corollary, and provide the last missing component needed to complete the Lean formalization of the generalized quantum Stein's lemma. More broadly, the development provides machine-checkable foundations for future formalized and AI-assisted research in quantum information theory.

quant-ph↗

arXiv2026

LLMs Faithfully and Iteratively Compute Answers During CoT: A Systematic Analysis With Multi-step Arithmetics

This study investigates the internal information flow of large language models (LLMs) while performing chain-of-thought (CoT) style reasoning. Specifically, with a particular interest in the faithfulness of the CoT explanation to LLMs' final answer, we explore (i) when the LLMs' answer is (pre)determined, especially before the CoT begins or after, and (ii) how strongly the information from CoT specifically has a causal effect on the final answer. Our experiments with controlled arithmetic tasks reveal a systematic internal reasoning mechanism of LLMs. They have not derived an answer at the moment when input was fed into the model. Instead, they compute (sub-)answers while generating the reasoning chain on the fly. Therefore, the generated reasoning chains can be regarded as faithful reflections of the model's internal computation.

cs.CL↗

arXiv2025

Non-commutative linear logic fragments with sub-context-free complexity

We present new descriptive complexity characterisations of classes REG (regular languages), LCFL (linear context-free languages) and CFL (context-free languages) as restrictions on inference rules, size of formulae and permitted connectives in the Lambek calculus; fragments of the intuitionistic non-commutative linear logic with direction-sensitive implication connectives. Our identification of the Lambek calculus fragments with proof complexity REG and LCFL is the first result of its kind. We further show the CFL complexity of one of the strictly `weakest' possible variants of the logic, admitting only a single inference rule. The proof thereof, moreover, is based on a direct translation between type-logical and formal grammar and structural induction on provable sequents; a simpler and more intuitive method than those employed in prior works. We thereby establish a clear conceptual utility of the Cut-elimination theorem for comparing formal grammar and sequent calculus, and identify the exact analogue of the Greibach Normal Form in Lambek grammar. We believe the result presented herein constitutes a first step toward a more extensive and richer characterisation of the interaction between computation and logic, as well as a finer-grained complexity separation of various sequent calculi.

cs.LO↗

arXiv2025

Discovering New Theorems via LLMs with In-Context Proof Learning in Lean

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called Conjecturing-Proving Loop (CPL), which iteratively generates mathematical conjectures and attempts to prove them in Lean 4. A key feature of CPL is that each iteration conditions the LLM on previously generated theorems and their formal proofs, enabling parameter-free improvement of proof strategies via in-context learning. We provide both theoretical and experimental evidence that CPL increases the discovery rate of hard-to-prove theorems compared to frameworks that generate statements and proofs simultaneously. Moreover, our experiments show that reusing the LLM's own formally verified outputs as context consistently improves subsequent proof success, demonstrating the effectiveness of self-generated in-context learning for neural theorem proving. The source code is available at https://github.com/auto-res/ConjecturingProvingLoop.

cs.LG↗

arXiv2025

LeanConjecturer: Automatic Generation of Mathematical Conjectures for Theorem Proving

We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem statement generation, addressing the data scarcity challenge in formal theorem proving. Through iterative generation and evaluation, LeanConjecturer produced 12,289 conjectures from 40 Mathlib seed files, with 3,776 identified as syntactically valid and non-trivial, that is, cannot be proven by \texttt{aesop} tactic. We demonstrate the utility of these generated conjectures for reinforcement learning through Group Relative Policy Optimization (GRPO), showing that targeted training on domain-specific conjectures can enhance theorem proving capabilities. Our approach generates 103.25 novel conjectures per seed file on average, providing a scalable solution for creating training data for theorem proving systems. Our system successfully verified several non-trivial theorems in topology, including properties of semi-open, alpha-open, and pre-open sets, demonstrating its potential for mathematical discovery beyond simple variations of existing results.

cs.AI↗

arXiv2025

FinchGPT: a Transformer based language model for birdsong analysis

The long-range dependencies among the tokens, which originate from hierarchical structures, are a defining hallmark of human language. However, whether similar dependencies exist within the sequential vocalization of non-human animals remains a topic of investigation. Transformer architectures, known for their ability to model long-range dependencies among tokens, provide a powerful tool for investigating this phenomenon. In this study, we employed the Transformer architecture to analyze the songs of Bengalese finch (Lonchura striata domestica), which are characterized by their highly variable and complex syllable sequences. To this end, we developed FinchGPT, a Transformer-based model trained on a textualized corpus of birdsongs, which outperformed other architecture models in this domain. Attention weight analysis revealed that FinchGPT effectively captures long-range dependencies within syllables sequences. Furthermore, reverse engineering approaches demonstrated the impact of computational and biological manipulations on its performance: restricting FinchGPT's attention span and disrupting birdsong syntax through the ablation of specific brain nuclei markedly influenced the model's outputs. Our study highlights the transformative potential of large language models (LLMs) in deciphering the complexities of animal vocalizations, offering a novel framework for exploring the structural properties of non-human communication systems while shedding light on the computational distinctions between biological brains and artificial neural networks.

cs.CL↗

arXiv2024

First Heuristic Then Rational: Dynamic Use of Heuristics in Language Model Reasoning

Multi-step reasoning instruction, such as chain-of-thought prompting, is widely adopted to explore better language models (LMs) performance. We report on the systematic strategy that LMs employ in such a multi-step reasoning process. Our controlled experiments reveal that LMs rely more heavily on heuristics, such as lexical overlap, in the earlier stages of reasoning, where more reasoning steps remain to reach a goal. Conversely, their reliance on heuristics decreases as LMs progress closer to the final answer through multiple reasoning steps. This suggests that LMs can backtrack only a limited number of future steps and dynamically combine heuristic strategies with rationale ones in tasks involving multi-step reasoning.

cs.CL↗

arXiv2024

J-UniMorph: Japanese Morphological Annotation through the Universal Feature Schema

We introduce a Japanese Morphology dataset, J-UniMorph, developed based on the UniMorph feature schema. This dataset addresses the unique and rich verb forms characteristic of the language's agglutinative nature. J-UniMorph distinguishes itself from the existing Japanese subset of UniMorph, which is automatically extracted from Wiktionary. On average, the Wiktionary Edition features around 12 inflected forms for each word and is primarily dominated by denominal verbs (i.e., [noun] +suru (do-PRS)). Morphologically, this form is equivalent to the verb suru (do). In contrast, J-UniMorph explores a much broader and more frequently used range of verb forms, offering 118 inflected forms for each word on average. It includes honorifics, a range of politeness levels, and other linguistic nuances, emphasizing the distinctive characteristics of the Japanese language. This paper presents detailed statistics and characteristics of J-UniMorph, comparing it with the Wiktionary Edition. We release J-UniMorph and its interactive visualizer publicly available, aiming to support cross-linguistic research and various applications.

cs.CL↗