TorchLean: Formalizing Neural Networks in Lean (leandojo.org)

TorchLean has been introduced as a groundbreaking framework that formalizes neural networks within the Lean 4 theorem prover, addressing critical challenges in the verification and analysis of AI models deployed in high-stakes environments. Traditional models often suffer from a disconnect between the code and the verification process, leading to potential safety risks due to implicit assumptions about model behavior, such as operator semantics and floating-point computations. By treating learned models as mathematical objects with consistent semantics for both execution and verification, TorchLean bridges this gap effectively. Significantly, TorchLean features a PyTorch-style verified API that supports both eager and compiled computation modes, ensuring a coherent integration of execution and proof verification. It employs explicit Float32 semantics and leverages advanced techniques like interval bound propagation (IBP) and CROWN/LiRPA for rigorous verification of model robustness and safety. Additionally, the framework has been validated across several applications, including certified robustness and control verification, and includes mechanized theoretical results such as a universal approximation theorem. This advancement represents a critical step toward achieving fully formal, end-to-end verification of AI systems, enhancing the reliability of neural networks in mission-critical applications.