Scope
A novel formulation of machine learning, based not on minimizing loss functions, but driven by failures of compositionality.
Start here
Begin here if you know basic category theory and want the clearest statement of structural diagnosis and repair across learning, causality, reasoning, and trustworthy foundation models.
Chapter outline
Part ICategorical Foundations
p. 31
- A Working Language of Compositionalityp. 33
- Axioms of Structural Learningp. 59
- Learning by Repairp. 75
- Learning Sketches and Factorization Obstructionsp. 83
- Tangent Learning Sketchesp. 91
- Infinitesimal Causalityp. 101
- Infinitesimal Categorical Databasesp. 111
- Infinitesimal Decisionsp. 123
- Deep Learning in Non-Compositional Sketchesp. 133
- Quotients, Localization, Repair, and Admissionp. 143
- Reasoning by Structural Repairp. 153
Part IIApplications
p. 163
- Geometric Causal Discoveryp. 165
- Repairing Kan-Extension Structurep. 173
- Composable Neural Adaptersp. 181
- Skills over Lie Algebroidsp. 187
- Infinitesimal Reinforcement Learningp. 193
Part IIIRelational Learning and Reasoning
p. 201
- Learning from Structured Preferencesp. 203
- Relational Manifold Recoveryp. 209
- Sheaf-Based Distributed Learningp. 215
- Infinitesimal Argument Repairp. 223
- Trustworthy Foundation Modelsp. 229
Part IVSynthesis
p. 241
- A Pattern Language for LINCS Systemsp. 243
- Frontiers of Infinitesimal Learningp. 247