Mnist-Lean4 (github.com)

A new project named Mnist-Lean4 has been launched, featuring a complete and self-contained neural network that trains on the popular MNIST handwritten digit dataset, exclusively utilizing Lean 4 without any external dependencies. The project includes two models: a Multilayer Perceptron (MLP) with an architecture of 784 → 512 → 512 → 10 that achieves approximately 97% accuracy, and a Convolutional Neural Network (CNN) comprising multiple convolutional and pooling layers, which attains around 98% accuracy but takes significantly longer to train—about five hours on a 24-core Intel workstation. This development is particularly significant for the AI/ML community as it demonstrates the potential of Lean 4, a formal proof language, for developing machine learning applications, paving the way for more rigorous and verified implementations in the field. The project also highlights the challenges faced in data modeling for training efficiency, as well as the necessity for custom gradient computation methods, given current limitations in Lean’s autodiff system. Overall, Mnist-Lean4 serves as an innovative step towards integrating formal verification with machine learning practices, offering a practical resource for researchers and developers interested in this intersection.