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"A Mathematical Explanation of Transformers" is a recent paper in which the authors construct a rigorous mathematical model of the Transformer architecture and large language models.

The Transformer is presented as a discretization of a continuous integro-differential equation. Self-attention is described as a non-local integral operator, layer normalization as a projection onto a constrained set, and fully connected layers and activation functions are incorporated into the same mathematical framework.

The authors then use operator splitting and numerical discretization to derive the standard Transformer architecture and extend this approach to multi-head attention, Vision Transformers, and convolutional Transformers.

I have previously shared several materials on the mathematics of neural networks, Transformers, and large language models, but new and interesting developments are constantly emerging in this field.

https://arxiv.org/pdf/2510.03989

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Once you start visualizing your SQL schemas like this, there's no going back.

sqltoerdiagram.com

https://xn--r1a.website/DataAnalyticsX

If you're just starting to learn machine learning and want to delve deeper into the mathematics required for machine learning and deep learning, I recommend trying this platform. It's something like LeetCode for machine learning.

This is not an advertisement: I personally used it and decided to share it with you.

https://deep-ml.com

https://xn--r1a.website/CodeProgrammer

Pandas vs Polars — 14-section course cheatshee

https://xn--r1a.website/MachineLearning9

Have you seen the interactive explanation of the Transformer?

It's a really cool visualization of how the architecture works.

https://poloclub.github.io/transformer-explainer/

One of the best resources for SQL performance:

use-the-index-luke.com

https://xn--r1a.website/DataAnalyticsX