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[2602.22631] TorchLean: Formalizing Neural Networks in Lean
Summary
TorchLean is a framework that formalizes neural networks within the Lean 4 theorem prover, enabling precise semantics for execution and verification, addressing critical safety in AI applications.
Why It Matters
As neural networks are increasingly used in safety-critical applications, ensuring their reliability through formal verification is essential. TorchLean bridges the gap between model execution and verification, enhancing trust in AI systems by providing a unified framework for rigorous analysis and certification.
Key Takeaways
- TorchLean treats neural networks as first-class mathematical objects for rigorous verification.
- It integrates a verified API with both eager and compiled execution modes.
- The framework supports explicit Float32 semantics and verification through advanced techniques.
- End-to-end validation demonstrates its effectiveness in certified robustness and controller verification.
- TorchLean aims to close the semantic gap in neural network analysis and execution.
Computer Science > Mathematical Software arXiv:2602.22631 (cs) [Submitted on 26 Feb 2026] Title:TorchLean: Formalizing Neural Networks in Lean Authors:Robert Joseph George, Jennifer Cruden, Xiangru Zhong, Huan Zhang, Anima Anandkumar View a PDF of the paper titled TorchLean: Formalizing Neural Networks in Lean, by Robert Joseph George and 4 other authors View PDF HTML (experimental) Abstract:Neural networks are increasingly deployed in safety- and mission-critical pipelines, yet many verification and analysis results are produced outside the programming environment that defines and runs the model. This separation creates a semantic gap between the executed network and the analyzed artifact, so guarantees can hinge on implicit conventions such as operator semantics, tensor layouts, preprocessing, and floating-point corner cases. We introduce TorchLean, a framework in the Lean 4 theorem prover that treats learned models as first-class mathematical objects with a single, precise semantics shared by execution and verification. TorchLean unifies (1) a PyTorch-style verified API with eager and compiled modes that lower to a shared op-tagged SSA/DAG computation-graph IR, (2) explicit Float32 semantics via an executable IEEE-754 binary32 kernel and proof-relevant rounding models, and (3) verification via IBP and CROWN/LiRPA-style bound propagation with certificate checking. We validate TorchLean end-to-end on certified robustness, physics-informed residual bounds for PINNs, and Ly...
