Unraveling the iterative CHAD

arXiv:2505.15002 · cs.PL, cs.AI, cs.LG, math.CT, math.LO · Submitted 2025-05-21 · Read on arXiv

cs.PL, cs.AI, cs.LG, math.CT, math.LO

Submitted: 2025-05-21

Updated: 2026-09-13

Comments: 66 pages

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Automatic Differentiation — 21× in this paper
• Combinatory Homomorphic Automatic Differentiation — 8× in this paper
• Abstraction — 1× in this paper · explained in 1 episode
• Axioms — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• $\omega$PAP Spaces: Reasoning Denotationally About Higher-Order, Recursive Probabilistic and Differentiable Programs
• Pseudomonads and Descent, PhD Thesis (Chapter 1)
• Freely generated $n$-categories, coinserters and presentations of low dimensional categories
• Logical Relations for Partial Features and Automatic Differentiation Correctness
• In Search of Effectful Dependent Types
• Denotational Correctness of Forward-Mode Automatic Differentiation for Iteration and Recursion

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