Tree-motif anti-collapse masks

Integrate this into the mask-generation and mask-rewiring code for a sparse linear layer W in an MLP, attention projection, or MoE expert; operate on the binary support mask G=1[W != 0], not on activations. First normalize each row to a fixed nonzero count if the baseline uses row-balanced sparsity. Detect candidate motifs by sampling root columns j_star, collecting their neighboring rows i_l, then collecting m child columns from each row. Retain candidates whose child-column neighborhoods outside the root rows are approximately disjoint; exact disjointness is checked with set intersections. For every candidate, construct the paper witness v by setting v[j_star]=1 and v[c_{l,a}]=-1/m for unit-magnitude weights, or use v[c_{l,a}]=-W[i_l,j_star]/(m W[i_l,c_{l,a}]) followed by normalization for weighted matrices. Estimate the certificate q=d/sqrt(m), and add either a mask penalty equal to the sum of q^2 over candidates or a rewiring rule that removes one edge from the largest-q motif and adds it to a low-degree row or column pair. Also count 4-cycles using common-neighbor intersections and optionally constrain their maximum incidence. The exact paper computation is the witness bound q; empirical quantities are motif counts, sampled minimum singular values, gradient norms, and Jacobian condition estimates. Start with a 2-layer sparse MLP on CIFAR-10 or a 6-layer Transformer on a small language corpus, comparing random fixed masks, magnitude pruning, and the anti-collapse mask at identical parameter count and FLOPs. Success means fewer sampled submatrices with s_min below 1e-3, lower gradient anisotropy, slower loss spikes, and equal-or-better validation accuracy at the same sparsity.