TorchLean: Formalizing Neural Networks in Lean
leandojo.orgI guess the next step would be adding support for quantized arithmetic.
FYI float is already quantized. It isn't continuous nor infinite. Even the distribution of representable numbers isn't uniform (more dense in [-1,1]).
The standard definition of quantized arithmetic for neural networks is not the same as the one used for floating point or double floating point values in the IEEE standardization of "real" arithmetic: https://arxiv.org/abs/1712.05877
And the lower precision float variants.
How could this lend insight into why Fast Fourier Transform approximates self-attention?
> Because self-attention can be replaced with FFT for a loss in accuracy and a reduction in kWh [1], I suspect that the Quantum Fourier Transform can also be substituted for attention in LLMs.
[1] "Fnet: Mixing tokens with fourier transforms" (2021) https://arxiv.org/abs/2105.03824 .. "Google Replaces BERT Self-Attention with Fourier Transform: 92% Accuracy, 7 Times Faster on GPUs" https://syncedreview.com/2021/05/14/deepmind-podracer-tpu-ba...
"Why formalize mathematics – more than catching errors" (2025) https://news.ycombinator.com/item?id=45695541
Can the QFT Quantum Fourier Transform (and IQFT Inverse Quantum Fourier Transform) also be substituted for self-attention in LLMs, and do Lean formalisms provide any insight into how or why?
This is just standard Fourier theory of being able to apply dense global convolutions with pointwise operations in frequency space? There’s no mystery here. It’s no different than a more general learnable parameterization of “Efficient Channel Attention (ECA)”
Yes and no. Yeah, no mystery because for some reason there's this belief that studying math is useless and by suggesting it's good that you're gatekeeping. But no because there are some deeper and more nuanced questions, but of course there are because for some reason we are proud of our black boxes and act like there's no other way> There’s no mystery here.