Formalizing Neural Networks in Lean

TorchLean is a Lean 4 framework for writing, running, inspecting, and verifying neural-network programs. It provides typed tensors and model APIs, a shared graph IR, runtime/autograd support, finite-precision semantics, certificate checkers, CUDA/runtime boundaries, and examples across modern ML and scientific ML.

The detailed story lives in the project site, guide, API docs, and paper. This README is the quick entry point: build the repo, run the first examples, find the docs, and cite the project.

Quickstart

git clone https://github.com/lean-dojo/TorchLean.git
cd TorchLean
lake build
lake exe torchlean mlp --cpu --steps 10

TorchLean is pinned by lean-toolchain and currently builds with leanprover/lean4:v4.29.0.

First Things To Try

lake exe torchlean --help
lake exe verify --help
lake exe verify -- torchlean-ibp

For the maintained example surface:

lake build NN.Examples.Zoo

Documentation

• Project site: https://lean-dojo.github.io/TorchLean/
• Guide: https://lean-dojo.github.io/TorchLean/blueprint/
• API reference: https://lean-dojo.github.io/TorchLean/docs/
• Paper: TorchLean: Formalizing Neural Networks in Lean (arXiv:2602.22631)

Detailed tutorials, verification chapters, model walkthroughs, CUDA notes, and API-level reference material belong in the guide and generated docs rather than in this README.

Use TorchLean From Another Lean Project

TorchLean is a normal Lake package. You can depend on the Git repository directly:

require TorchLean from git "https://github.com/lean-dojo/TorchLean.git" @ "main"

Then run:

lake update
lake exe cache get
lake build

Most downstream model and training files should start from the public facade:

import NN.API.Public

Use the broader umbrella when you want the maintained specification, IR, proof, verification, examples, and widget surface:

import NN.Library

For local development against a checkout, use a path dependency instead:

require TorchLean from "../TorchLean"

Reservoir is not required for Git or path dependencies. It is only for package discovery and versioned require lines once the repository is indexed.

Repository Map

• NN/API: public facade for model, tensor, data, and training workflows.
• NN/Spec: mathematical tensor, layer, model, and dynamical-system definitions.
• NN/Runtime: executable autograd, optimizers, training loops, CUDA boundary, PyTorch import/export, and RL runtime support.
• NN/IR and NN/GraphSpec: graph IR, graph semantics, and typed architecture descriptions.
• NN/Proofs: tensor algebra, autograd correctness, analytic derivatives, runtime approximation, and bridge proofs.
• NN/Floats: finite-precision models, IEEE-style executable semantics, NeuralFloat formats, and error-bound infrastructure.
• NN/MLTheory: learning theory, robustness, CROWN/LiRPA, generative objectives, optimization theory, and related proof layers.
• NN/Verification: certificate checkers and CLI workflows.
• NN/Examples: quickstarts, model zoo commands, widgets, verification fixtures, and interoperability demos.
• blueprint/TorchLeanBlueprint/Guide: source for the public guide.
• home_page: project website sources.

Correctness and Boundaries

For correctness claims, trust assumptions, and third-party tooling:

• TRUST_BOUNDARIES.md
• AI_USAGE.md
• THIRD_PARTY_NOTICES.md
• CONTRIBUTING.md

Lean proofs, executable checkers, Lake builds, tests, and explicit trust-boundary documentation are the source of truth for what is proved, checked, or assumed.

Citation

For the current paper BibTeX, use the citation metadata on arXiv:

@misc{george2026torchleanformalizingneuralnetworks,
      title={TorchLean: Formalizing Neural Networks in Lean},
      author={Robert Joseph George and Jennifer Cruden and Xiangru Zhong and Huan Zhang and Anima Anandkumar},
      year={2026},
      eprint={2602.22631},
      archivePrefix={arXiv},
      primaryClass={cs.MS},
      url={https://arxiv.org/abs/2602.22631},
}

License

TorchLean is released under the MIT License. See LICENSE.