TopoAlign: A Framework for Aligning Code to Math via Topological Decomposition

arXiv:2510.11944 · cs.CL, cs.AI · Submitted 2025-10-13 · Read on arXiv

cs.CL, cs.AI

Submitted: 2025-10-13

Updated: 2026-09-01

Code: https://github.com/huawei-noah/TopoAlign

Terminology

• Benchmark — 12× in this paper · explained in 2 episodes
• Alignment — 6× in this paper · explained in 1 episode
• Natural Language — 6× in this paper
• Consistency — 5× in this paper · explained in 3 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Fine-Tuning — 4× in this paper · explained in 5 episodes
• Ablation — 3× in this paper · explained in 1 episode
• Large Language Models (LLMs) — 3× in this paper · explained in 6 episodes
• Transfer Learning — 3× in this paper · explained in 10 episodes
• Ablation Studies — 2× in this paper · explained in 1 episode
• Catastrophic Forgetting — 2× in this paper · explained in 5 episodes
• Formal Languages — 2× in this paper
• Hallucination — 2× in this paper · explained in 3 episodes
• International Conference on Learning Representations — 2× in this paper
• Ablation study — 1× in this paper · explained in 1 episode
• Alignment Methods — 1× in this paper · explained in 1 episode
• Downstream Tasks — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Semantic Similarity — 1× in this paper · explained in 2 episodes
• Synthetic Data Generation — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Verifier — 1× in this paper · explained in 2 episodes

Sources

• Lean-ing on Quality: How High-Quality Data Beats Diverse Multilingual Data in AutoFormalization
• Evaluating Large Language Models Trained on Code
• Autoformalize Mathematical Statements by Symbolic Equivalence and Semantic Consistency
• ATLAS: Autoformalizing Theorems through Lifting, Augmentation, and Synthesis of Data
• StarCoder 2 and The Stack v2: The Next Generation
• GFLean: An Autoformalisation Framework for Lean via GF
• Reliable Evaluation and Benchmarks for Statement Autoformalization
• Mathematical Reasoning via Self-supervised Skip-tree Training
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning
• First Experiments with Neural Translation of Informal to Formal Mathematics

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