Canonical orbit search for symmetric pruning masks

Integrate this into a discrete structured-pruning or architecture-search evaluator before expensive fine-tuning. Let indices 1 through n denote exchangeable channels in one hidden layer, or exchangeable experts in one MoE layer. First construct the exact symmetry group: for a simple MVP, use all permutations of channels within one homogeneous layer; for several groups of equivalent components, use the product of their permutation groups. Represent a candidate retained set S as a sorted integer tuple. Implement is_canonical(S) by applying every g in G, sorting the resulting tuple, and comparing it with S using the first differing element; retain S only if it is lexicographically smallest. Enumerate recursively from the empty set by appending an index larger than the current maximum, and call is_canonical on every child before recursing. Pseudocode: dfs(S): evaluate(S) if len(S)==k; for i in range(max(S)+1,n): T=sort(S+[i]); if is_canonical(T): dfs(T). The predecessor formula guarantees that canonical children have canonical parents, so this does not discard an orbit's only representative. Estimate the group size and orbit count empirically; the canonicality test is exact for the supplied permutations. For larger groups, use a stabilizer-chain or graph-canonical-labeling implementation, validated against exhaustive enumeration for small n. The first experiment should use a width-12 MLP on MNIST or CIFAR-10, enumerate all masks retaining k=6 channels, and compare exhaustive mask evaluation against canonical search using channel permutations. Measure evaluated masks, wall-clock search time, and best validation accuracy after identical one-shot-supernet scoring. Success is a reduction near the number of symmetry orbits with unchanged best accuracy; for a fully exchangeable layer, the 924 masks can collapse to one representative.