Anchor-aware giant-core regularization

Integrate this into a hypergraph neural network or grouped higher-order attention layer whose incidence tensor is A[e,i], where e indexes hyperedges and i indexes node or token incidences. Give every incidence a trainable anchor logit a[e,i], with anchor probability theta[e,i] = sigmoid(a[e,i]). During training, use the current binary or soft routing mask to estimate P(q) from node degrees and Q(m) from active hyperedge sizes. Estimate p_N as the mean node keep probability and p_H as the mean hyperedge keep probability. For fixed thresholds k and n, initialize W=V=0.5 and run 10-30 damped fixed-point iterations: W_new=F_W(V), V_new=F_V(W), then W=rho*W_new+(1-rho)*W and V=rho*V_new+(1-rho)*V, with rho between 0.2 and 0.8. Implement binomial sums with log-space binomial coefficients or precomputed tables, and clamp probabilities to [1e-6,1-1e-6]. Define the regularizer as -W*V, or preferably an estimated giant-core fraction computed from node and hyperedge survival probabilities. Add an anchor-budget penalty such as lambda_anchor times the mean theta so the model cannot mark every incidence as an anchor; optionally add the entropy penalty lambda_entropy times theta(1-theta) to encourage decisive roles. Backpropagate through the unrolled iterations, or use stop-gradient on degree histograms if histogram differentiation is unstable. At inference, threshold anchor scores and retain incidences whose cavity messages exceed 0.5, or use the score only to select a global pruning ratio. The fixed-point recursion is taken directly from the paper; the degree histograms and exact-core correlation must be estimated empirically. First test a 2-layer hypergraph neural network on synthetic hypergraph node classification with random incidence dropout and magnitude pruning. Compare no regularizer, degree-preserving pruning, and this regularizer at equal parameter count. Measure validation accuracy after dropout, exact (k,n)-core fraction, and accuracy variance across masks. Success means a larger retained core and lower accuracy variance at equal FLOPs without substantial clean-data accuracy loss.