arXiv Computation and Language
Sep 11
Formalizing building-up constructions of self-dual codes through isotropic lines in Lean
arXiv:2604. 08485v2 Announce Type: replace-cross Abstract: The purpose of this paper is two-fold.
A machine-checked proof of the Dong-Yang classification of optimal (n,4) binary codes for BSCs
The article reports a machine‑checked Lean 4 formalization of Dong and Yang’s classification of optimal finite‑length $(n,4)$ binary block codes for binary symmetric channels. The authors used an AI tool to feed the paper’s proofs into Lean, verified the main theorem statements and accepted axioms, and documented corrections, simplifications, and discrepancies found during the formalization. The Lean code is publicly available on GitHub.
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arXiv AI
Jul 13
Lean-QIT: Towards a Formal Infrastructure for Quantum Information Theory
arXiv:2607. 09632v1 Announce Type: cross Abstract: Quantum information theory (QIT) characterizes the capabilities and fundamental limits of quantum information processing, underpinning quantum communication, computation, and error correction.
arXiv Machine Learning
Sep 1
Strengthening Recursive Constructions for Zero-Error Shannon Capacity
arXiv:2608. 30273v1 Announce Type: cross Abstract: The exact Shannon capacity is unknown for every odd cycle beyond the five-cycle $C_5$, making odd cycles a central open problem in zero-error information theory.
arXiv AI
Jul 28
Formalizing Flag Algebras in Lean
arXiv:2607. 23500v1 Announce Type: cross Abstract: Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming.
arXiv AI
Sep 18
Long-horizon autoformalization of a core theorem underlying MIP* = RE
FormalFlow is a system that coordinates AI proving agents under human supervision to tackle long‑horizon formalizations, using a shared blueprint for nested planning, proving, and review loops. The team used it to produce a machine‑checked Lean 4 proof of the quantum soundness of the classical low‑individual‑degree test, a core theorem underlying MIP* = RE, in 63 days. The resulting library contains 126,367 lines of Lean code, all generated by agents, and corrects side conditions while preserving the published error bound under corrected assumptions.
arXiv AI
Jun 24
Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution
arXiv:2606. 24808v1 Announce Type: cross Abstract: Quantum computers could outperform classical machines on important problems, but only if the errors that pervade quantum hardware can be corrected at scale.
arXiv Machine Learning
Jul 30
Field Codes for Distributed Coupling Samplers and Certified Empirical Transport
arXiv:2607. 27078v1 Announce Type: cross Abstract: In this paper, we formulate three communication tasks for empirical optimal transport: distributed coupling sampling, cost-evaluable coupling output, and scalar value-certified sampling.
arXiv AI
Jul 10
Multi-agent Autoformalization of Tensor Network Theory
arXiv:2607. 07857v1 Announce Type: cross Abstract: We build a team of specialized large language-model agents and present an agent-driven workflow for research-level formalization in theoretical physics, with the autoformalization of the fundamental theorem of matrix-product states as a demonstration.
arXiv AI
Jun 6
Evaluation of LLMs for Mathematical Formalization in Lean
arXiv:2606. 05632v1 Announce Type: new Abstract: Within the past few years, the ability of Large Language Models (LLMs) to generate formal mathematical proofs has improved drastically.
arXiv Machine Learning
Sep 16
Shuttling Compiler for Trapped-Ion Quantum Computers Based on Fine-Tuned Large Language Models
The paper reports on shuttling compilers for trapped‑ion quantum computers that are built using five large language models (LLMs) fine‑tuned on hand‑crafted shuttling schedules for linear and branched one‑dimensional trap architectures. For circuits up to 16 qubits, the fine‑tuned LLMs produce valid schedules on the training architectures, and in 12% of compilations the best of ten runs achieves up to 21% fewer operations than heuristic baselines after rule‑based post‑processing. A single run of one LLM also generates a valid schedule for a previously unseen four‑way branched architecture, providing preliminary evidence of cross‑architecture generalization, though no LLM succeeded on two other unseen architectures.
arXiv AI
3d ago
Coding Agents for Coding Theory
The authors report that a large‑scale experiment using a language‑model coding agent over five weeks produced new lower bounds for DNA‑barcode‑style codes. By restricting searches to codes with a prescribed symmetry, the agent improved the best known code of length 6 and minimum edit distance 3 from 114 to 120 words, and similarly raised lower bounds for lengths 6–9 and distances 3–6. The study also documents failures and the limitations of the verification protocol, noting that intermediate results were never rechecked and could lead to erroneous conclusions.
arXiv Machine Learning
Aug 3
Open-Source LLM-Driven Formal Verification: A Multi-Agent Pipeline for RTL Repair
arXiv:2607. 28877v1 Announce Type: cross Abstract: Verification consumes the majority of modern chip design effort, yet the formal verification tools that provide mathematical guarantees of correctness remain expensive and restrictively licensed.