Algebra coverage.

Coalgebras and Automata

Lattice theory and algebraic models for deep convolutional learning based on mathematical morphology

We develop a rigorous algebraic framework for deep convolutional architectures, CNNs, ResNets, and encoder--decoder networks such as UNet, grounded in lattice theory and mathematic…

I Wanted To Build AI. Instead I Met Linear Algebra

When I first started learning machine learning, I was genuinely confident. In my head ML was...…

Group-Algebraic Tensors: Provably-optimal Equivariant Learning and Physical Symmetry Discovery

We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an archite…

How Alexander Grothendieck Revolutionized 20th-Century Mathematics

Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. But what were his actual mathematical contributions? The post Ho…

Using algebra to verify a flight-plan bug fix in Lean

The linear Diophantine system N = 25A and 12B, where p ≡ 1 (mod q)

This paper analyses the linear Diophantine system N = 25A + 12B, where p ≡ 1 (mod q) — the exact algebraic condition for clock behaviour. - A19dammer91/the-exact-algebraic-conditio…

An Algebraic Exposition of the Theory of Dyadic Morality

This paper provides an algebraic exposition of the theory of dyadic morality (TDM), a psychological model of moral judgment grounded in a simple two-node template: an intentional a…