Fair warning: this one is deeply theoretical, written in the language of category theory rather than the usual loss functions and vectors. The authors describe machine learning problems as sketches, which are graphs carrying rules about which paths must agree and which shapes must combine in certain ways. Their focus is non-compositionality, which they define not as prediction error but as a diagram failing to fit together the way the structure demands.

The framework, LINCS, then asks a further question: if you nudge the model infinitesimally, do those compositional constraints still hold? They build this using tangent-category machinery, iterate the construction into a tower of problems, and prove a fixed point exists under certain conditions. They note experiments are still underway.

This is honestly a hard abstract to compress, and the practical payoff is not yet shown, so read the paper if the categorical framing is your thing.