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I 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)”

  > There’s no mystery here.