Selected work

Representative Papers

Linear relations between face numbers of levels in arrangements

Apr 10, 2025

This work characterizes the affine space $mathcal{F}_{n,r}$ spanned by the $f$-matrices (matrices of face numbers across dimensions) of all configurations of $n$ $r$-dimensional vectors in general position, and its subspace $mathcal{F}^0_{n,r}$ corresponding to pointed subconfigurations (i.e., those lying in some open linear halfspace). Using Gale duality, polar dual arrangements, sign pattern analysis, and Radon partition theory, the dimension and combinatorial structure of $mathcal{F}_{n,r}$ are fully determined for the first time. A generalized $g$-matrix framework is introduced to unify the description of face-number dependencies, and the Dehn–Sommerville relations are systematically extended to arbitrary levels. Finally, a complete system of linear relations among spherical arrangement face numbers—across all dimensions—is established for point sets, thereby resolving the open problem posed by Andrzejak and Welzl (2003).

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Noise-aware Verification and Synthesis of Quantum Programs

Aug 06, 2026

This work addresses the gap between idealized noise-free models and real-world noisy quantum hardware in quantum program verification. It introduces, for the first time, a noise-aware quantum Hoare logic that integrates hardware-specific error models—such as those provided by IBM Qiskit—to define a realistic noisy semantics. The study further demonstrates the critical role of classical probabilistic branching in achieving optimality in quantum programs. Building on this foundation, the authors develop a bounded verification algorithm and an automated synthesis method capable of generating optimal quantum subroutines tailored to specific noise environments, including tasks like parity computation, state preparation, and state discrimination. The efficacy of the proposed approach is validated against actual hardware specifications.

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Formal Verification of Continuous-Variable Quantum Programs

Jul 20, 2026

Continuous-variable quantum programs have long lacked formal semantics and verification methods due to their operation on infinite-dimensional Hilbert spaces, unbounded measurements, and potentially divergent expectation values. This work presents the first formal semantic framework for such programs and introduces the first unary Hoare logic tailored to this setting. By integrating polynomial assertions based on regular observables with symbolic weakest precondition calculations, the approach overcomes the theoretical challenges posed by infinite dimensionality and unboundedness. The method successfully verifies standard continuous-variable quantum algorithms, establishes gate decomposition equivalences, quantifies the photon-number-state resources required for classical simulation, and provides precise analyses of approximation errors arising in physical implementations.

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Sink vs. diagonal patterns as mechanisms for attention switch and oversmoothing prevention

May 08, 2026

This work investigates how attention mechanisms in Transformers mitigate oversmoothing through sink and diagonal patterns that enable attention switching. By integrating geometric analysis, theoretical proofs, and empirical validation, the study establishes—for the first time—an equivalence between sink tokens and hard attention switching, clarifies the precise conditions under which sinks effectively prevent oversmoothing, and quantitatively explains why pretrained models exhibit a preference for sink-based representations. The paper further introduces a diagonal pattern that permits self-communication as a more flexible mechanism for suppressing oversmoothing, thereby generalizing the applicability of attention switching. Additionally, it provides a quantitative comparison of the representational costs of sink versus diagonal patterns and elucidates the mechanistic conditions under which attention layers degenerate into MLP-like behavior.

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Speculative Decoding Speed-of-Light: Optimal Lower Bounds via Branching Random Walks

Dec 12, 2025

This paper investigates the theoretical acceleration limit of deterministic speculative decoding for large language models. Addressing the fundamental question—“what is the lower bound on runtime for any deterministic speculative algorithm?”—we introduce, for the first time, a probabilistic modeling framework based on branching random walks, integrated with information-theoretic tools (entropy and second-order logarithmic moments) for rigorous analysis. Our key contributions are: (1) a tight upper bound on the expected number of successfully predicted tokens: $mathbb{E}[X] leq (mu + mu_{(2)}) log P / mu^2 + O(1)$; (2) a characterization and quantification of the intrinsic trade-off governing parallel prediction efficiency, jointly constrained by output distribution entropy and the second-order logarithmic moment; and (3) empirical validation of the bound’s tightness and practicality on Llama-series models. This work establishes the first universal theoretical benchmark for speculative decoding.

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Recent publications

Latest Papers

Noise-aware Verification and Synthesis of Quantum Programs

Aug 06, 2026

This work addresses the gap between idealized noise-free models and real-world noisy quantum hardware in quantum program verification. It introduces, for the first time, a noise-aware quantum Hoare logic that integrates hardware-specific error models—such as those provided by IBM Qiskit—to define a realistic noisy semantics. The study further demonstrates the critical role of classical probabilistic branching in achieving optimality in quantum programs. Building on this foundation, the authors develop a bounded verification algorithm and an automated synthesis method capable of generating optimal quantum subroutines tailored to specific noise environments, including tasks like parity computation, state preparation, and state discrimination. The efficacy of the proposed approach is validated against actual hardware specifications.

0 citationsRead paper

Formal Verification of Continuous-Variable Quantum Programs

Jul 20, 2026

Continuous-variable quantum programs have long lacked formal semantics and verification methods due to their operation on infinite-dimensional Hilbert spaces, unbounded measurements, and potentially divergent expectation values. This work presents the first formal semantic framework for such programs and introduces the first unary Hoare logic tailored to this setting. By integrating polynomial assertions based on regular observables with symbolic weakest precondition calculations, the approach overcomes the theoretical challenges posed by infinite dimensionality and unboundedness. The method successfully verifies standard continuous-variable quantum algorithms, establishes gate decomposition equivalences, quantifies the photon-number-state resources required for classical simulation, and provides precise analyses of approximation errors arising in physical implementations.

0 citationsRead paper

Sink vs. diagonal patterns as mechanisms for attention switch and oversmoothing prevention

May 08, 2026

This work investigates how attention mechanisms in Transformers mitigate oversmoothing through sink and diagonal patterns that enable attention switching. By integrating geometric analysis, theoretical proofs, and empirical validation, the study establishes—for the first time—an equivalence between sink tokens and hard attention switching, clarifies the precise conditions under which sinks effectively prevent oversmoothing, and quantitatively explains why pretrained models exhibit a preference for sink-based representations. The paper further introduces a diagonal pattern that permits self-communication as a more flexible mechanism for suppressing oversmoothing, thereby generalizing the applicability of attention switching. Additionally, it provides a quantitative comparison of the representational costs of sink versus diagonal patterns and elucidates the mechanistic conditions under which attention layers degenerate into MLP-like behavior.

0 citationsRead paper

Speculative Decoding Speed-of-Light: Optimal Lower Bounds via Branching Random Walks

Dec 12, 2025

This paper investigates the theoretical acceleration limit of deterministic speculative decoding for large language models. Addressing the fundamental question—“what is the lower bound on runtime for any deterministic speculative algorithm?”—we introduce, for the first time, a probabilistic modeling framework based on branching random walks, integrated with information-theoretic tools (entropy and second-order logarithmic moments) for rigorous analysis. Our key contributions are: (1) a tight upper bound on the expected number of successfully predicted tokens: $mathbb{E}[X] leq (mu + mu_{(2)}) log P / mu^2 + O(1)$; (2) a characterization and quantification of the intrinsic trade-off governing parallel prediction efficiency, jointly constrained by output distribution entropy and the second-order logarithmic moment; and (3) empirical validation of the bound’s tightness and practicality on Llama-series models. This work establishes the first universal theoretical benchmark for speculative decoding.

0 citationsRead paper

Monitoring of Static Fairness

Jul 03, 2025

This paper addresses real-time runtime verification of static fairness in machine learning systems with unknown but Markovian dynamics, focusing on dynamically quantifying and certifying decision bias with respect to sensitive attributes under partial or full observability. Method: We propose a formal specification language expressive enough to encode multiple fairness notions and develop two statistical monitoring algorithms—offering uniform and non-uniform error bounds—to enable progressively precise, confidence-guaranteed quantitative fairness verification. Our approach integrates Markov chain modeling, sequential observation analysis, and lightweight quantitative verification. Contribution/Results: The prototype system achieves millisecond-scale response times on loan approval and university admission benchmarks, significantly improving the timeliness, reliability, and scalability of fairness monitoring compared to existing methods.

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