Quantum key distribution (QKD), whose security is derived from quantum mechanics rather than computational assumptions, is moving into standardization and commercial deployment. Yet its security guarantees rest on technically delicate proofs checked by hand. Formal verification closes this gap, establishing a two-factor assurance: unconditional security from physical principles, and machine-checked proofs against reasoning errors. We present FVQKD, a Rocq library for machine-checking QKD security proofs. Its first result is a complete, end-to-end machine-checked proof of composable, finite-key security for BB84. The mechanization reconstructs the complete proof infrastructure from first principles, including the smooth entropy framework, the entropic uncertainty relation, and the Quantum Leftover Hash Lemma. It uncovers necessary side conditions that the published argument leaves unstated, one of which reveals a missing proof branch, and it grounds the information-theoretic bound in a formal semantics of protocol execution, which the pen-and-paper analysis lacks. The proof is entirely admit-free, relying only on the Rocq kernel and standard foundational axioms. To our knowledge, this is the first end-to-end formal verification of a QKD security proof. Built on MathComp, MathComp-Analysis, and CoqQ, the development provides quantum-information infrastructure designed for reuse across broader QKD variants and quantum cryptography applications.
Ruixuan Deng, Xiaoyang Hu Brown University, Miles Gilberti University of Michigan - Ann Arbor, Shane Storks University of Michigan - Ann Arbor, Aman Taxali University of Michigan - Ann Arbor, Mike Angstadt University of Michigan - Ann Arbor, Chandra Sripada University of Michigan, Joyce Chai
We identify semantically coherent, context-consistent network components in large language models (LLMs) using coactivation of sparse autoencoder (SAE) features collected from just a handful of prompts. Focusing on concept-relation prediction tasks, we show that ablating these components for concepts (e.g., countries and words) and relations (e.g., capital city and translation language) changes model outputs in predictable ways, while amplifying these components induces counterfactual responses. Notably, composing relation and concept components yields compound counterfactual outputs. Further analysis reveals that while most concept components emerge from the very first layer, more abstract relation components are concentrated in later layers. Lastly, we show that extracted components more comprehensively capture concepts and relations than individual features while maintaining specificity. Overall, our findings suggest a modular organization of knowledge and advance methods for efficient, targeted LLM manipulation.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表