Neural Picture Alchemy: TMLR paper recasts deep learning as equations solved by backprop

CatAstro_Piyush · x · 2026-10-31

• Cybercat Institute published a blog post and companion TMLR paper, "An Invitation to Neural Picture Alchemy," using string diagrams to describe the semantics of deep learning — the relation between objectives and trained model behavior — rather than the usual syntax of architectures and backprop.
• Premise: neural networks are variable maps and objectives are equations governing them; deep learning becomes a kind of representation theory where function-composition algebras replace groups and continuous maps replace linear maps. The pitch: characterize behavior as equations and let backprop find the implementation.
• The quoted tweet adds that gradient descent works surprisingly well on non-commutative, non-distributive, even non-associative algebras — arbitrarily invented algebraic rules still yield exact solutions in 100 iterations.

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