Selected work

Representative Papers

Vibe Compiler: A Research-Logic Synthesis Tool That Runs without Prompt Engineering -Toward Enhancing Metacognition for Sustaining Agency in the Age of Generative AI-

Aug 05, 2026

This study addresses the risk that generative AI, when used to support research, may lead users to uncritically accept its outputs, thereby undermining human cognitive agency. To counter this, the authors propose a Synthesis-Analysis Reciprocity Model and implement it in the Vibe Compiler system, which translates researchers’ vague intuitions (“Vibes”) into rigorous logical structures via a 16-dimensional academic ontology. When logical gaps are detected, the system prompts users with reflective questions to autonomously complete the reasoning rather than relying on AI-generated content. The work innovatively categorizes four origins of logical discontinuities and introduces a mechanism whereby the AI actively interrogates its own outputs to stimulate human metacognition. Prototype evaluation demonstrates that effective AI-assisted reasoning depends more on structured knowledge inputs than on sophisticated prompt engineering, significantly reinforcing researchers’ critical agency in human-AI collaboration.

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Information Acquisition with $α$-Divergence Costs

May 27, 2026

This work proposes a cost model for information acquisition that balances analytical tractability with modeling flexibility. Building on the f-information framework, the authors introduce an α-divergence–driven cost function and derive its closed-form expression using Amari’s α-integral. By generalizing mutual information into a unified parametric family—encompassing the Kullback–Leibler divergence, reverse KL divergence, and Hellinger distance—they characterize the optimal information acquisition strategy, whose choice probabilities belong to the q-exponential family. This approach not only explicitly identifies the optimal information structure but also recovers classical corrected logit models as special cases, thereby offering a computationally tractable and flexible new paradigm for information design problems.

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Categorical generalization of spectral decomposition

Apr 24, 2025

Spectral decomposition lacks an abstract, axiomatic characterization in semiadditive $mathbf{CMon}$-enriched categories, where biproducts are not assumed a priori. Method: We introduce an axiomatization of spectral decomposition independent of biproduct existence. By proving an equivalence theorem between finite biproducts and morphism addition, we internalize spectral decomposition within the category’s semiadditivity and $mathbf{CMon}$-enrichment. We further define semiadditive $mathbf{CMon}$-functors preserving spectral decompositions, achieving a functorial generalization. Contribution/Results: This work provides the first fully abstract, axiomatic reconstruction of spectral decomposition in category theory. It uniformly encompasses canonical models from matrix algebras, Hilbert spaces, and quantum computation, and yields multiple equivalent axiomatizations. The framework establishes a novel categorical foundation for algebra, operator theory, and quantum structures, advancing the conceptual unification of spectral theory across mathematical disciplines.

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Shinohara Rock-Paper-Scissors

Mar 13, 2025

This paper studies the Shinohara variant of Rock-Paper-Scissors, where (n) players simultaneously compete against a fixed “Rock”-playing dealer; each player chooses only “Rock” or “Paper”, and if multiple players select “Paper”, all are eliminated—only the unique “Paper”-chooser wins. The central challenge is characterizing equilibrium structures under strategic interdependence among multiple agents. Method: The authors formulate the first subgame-perfect equilibrium model for this game and conduct rigorous analytical and stability analysis, complemented by robustness verification. Contribution/Results: They prove the existence and uniqueness of a symmetric equilibrium, deriving a closed-form equation for the equilibrium “Paper”-playing probability (p): ((1-p)^{n-1} + p^{n-1}/n = 1/n). They further identify infinitely many asymmetric equilibria and characterize the delicate balance between cooperation (coordinated “Paper” selection) and defection (unilateral deviation to “Rock”). The work provides a novel paradigm for finite-action, elimination-based multiplayer games.

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Recent publications

Latest Papers

Vibe Compiler: A Research-Logic Synthesis Tool That Runs without Prompt Engineering -Toward Enhancing Metacognition for Sustaining Agency in the Age of Generative AI-

Aug 05, 2026

This study addresses the risk that generative AI, when used to support research, may lead users to uncritically accept its outputs, thereby undermining human cognitive agency. To counter this, the authors propose a Synthesis-Analysis Reciprocity Model and implement it in the Vibe Compiler system, which translates researchers’ vague intuitions (“Vibes”) into rigorous logical structures via a 16-dimensional academic ontology. When logical gaps are detected, the system prompts users with reflective questions to autonomously complete the reasoning rather than relying on AI-generated content. The work innovatively categorizes four origins of logical discontinuities and introduces a mechanism whereby the AI actively interrogates its own outputs to stimulate human metacognition. Prototype evaluation demonstrates that effective AI-assisted reasoning depends more on structured knowledge inputs than on sophisticated prompt engineering, significantly reinforcing researchers’ critical agency in human-AI collaboration.

0 citationsRead paper

Information Acquisition with $α$-Divergence Costs

May 27, 2026

This work proposes a cost model for information acquisition that balances analytical tractability with modeling flexibility. Building on the f-information framework, the authors introduce an α-divergence–driven cost function and derive its closed-form expression using Amari’s α-integral. By generalizing mutual information into a unified parametric family—encompassing the Kullback–Leibler divergence, reverse KL divergence, and Hellinger distance—they characterize the optimal information acquisition strategy, whose choice probabilities belong to the q-exponential family. This approach not only explicitly identifies the optimal information structure but also recovers classical corrected logit models as special cases, thereby offering a computationally tractable and flexible new paradigm for information design problems.

0 citationsRead paper

Categorical generalization of spectral decomposition

Apr 24, 2025

Spectral decomposition lacks an abstract, axiomatic characterization in semiadditive $mathbf{CMon}$-enriched categories, where biproducts are not assumed a priori. Method: We introduce an axiomatization of spectral decomposition independent of biproduct existence. By proving an equivalence theorem between finite biproducts and morphism addition, we internalize spectral decomposition within the category’s semiadditivity and $mathbf{CMon}$-enrichment. We further define semiadditive $mathbf{CMon}$-functors preserving spectral decompositions, achieving a functorial generalization. Contribution/Results: This work provides the first fully abstract, axiomatic reconstruction of spectral decomposition in category theory. It uniformly encompasses canonical models from matrix algebras, Hilbert spaces, and quantum computation, and yields multiple equivalent axiomatizations. The framework establishes a novel categorical foundation for algebra, operator theory, and quantum structures, advancing the conceptual unification of spectral theory across mathematical disciplines.

0 citationsRead paper

Shinohara Rock-Paper-Scissors

Mar 13, 2025

This paper studies the Shinohara variant of Rock-Paper-Scissors, where (n) players simultaneously compete against a fixed “Rock”-playing dealer; each player chooses only “Rock” or “Paper”, and if multiple players select “Paper”, all are eliminated—only the unique “Paper”-chooser wins. The central challenge is characterizing equilibrium structures under strategic interdependence among multiple agents. Method: The authors formulate the first subgame-perfect equilibrium model for this game and conduct rigorous analytical and stability analysis, complemented by robustness verification. Contribution/Results: They prove the existence and uniqueness of a symmetric equilibrium, deriving a closed-form equation for the equilibrium “Paper”-playing probability (p): ((1-p)^{n-1} + p^{n-1}/n = 1/n). They further identify infinitely many asymmetric equilibria and characterize the delicate balance between cooperation (coordinated “Paper” selection) and defection (unilateral deviation to “Rock”). The work provides a novel paradigm for finite-action, elimination-based multiplayer games.

0 citationsRead paper