Homological Topological Quantum Field Theories

What the math gives to ML

The paper's transferable asset is not the TQFT invariant itself, but its representation of unordered collections of points as configuration spaces equipped with path-dependent local-system transport. A neural module can use the same separation between configurations and trajectories: permutation symmetry is enforced at the state level, while nontrivial braid or motion history is retained through a learned monodromy representation. This offers a principled alternative to ordinary pooling for multi-object sequences, where exchanging two objects can be distinguishable by the path taken even when the instantaneous set is unordered. The first implementation should be a small braid-aware recurrent layer for object-centric video or simulated particle data, compared against permutation-invariant pooling and ordinary object transformers.