Symmetric lexicographic symmetric-subset reverse search for the enumeration of circuits, cocircuits, and triangulations up to symmetry

What the math gives to ML

The paper provides a constructive way to enumerate combinatorial objects modulo a finite symmetry group without visiting every symmetric duplicate. Its key transferable asset is the canonical-augmentation property: if a subset is lexicographically minimal in its orbit, deleting its largest element preserves orbit-minimality, so a complete search can recursively expand only canonical nodes. This can turn discrete neural architecture or pruning searches from enumeration of all masks into enumeration of one representative per channel-permutation orbit. The approach is most useful when the model has exact exchangeable components and the search space is small enough that symmetry reduction, rather than gradient optimization, is the bottleneck.