tracel-ai/burn ? reverse-engineered prompt

Build me a Rust library for tensor math and deep learning that feels simple to use but is still fast and flexible.

I want it to let me create tensors, do basic math, build neural network layers, and train a small model with automatic differentiation. It should support both training and inference in the same code, with a clean API that feels friendly like PyTorch but stays idiomatic Rust. If you can, include a CPU backend first, and make the design easy to extend later for other backends.

Please also add a few runnable examples, like a tiny MLP on fake data or a simple image classifier demo, plus clear docs so someone can understand how to use it quickly. Keep the code organized, well tested, and practical enough that I could actually build on it. If you need to check current Rust docs or best practices online, go ahead.