Determinantal Exclusion Router

Integrate the mechanism at an MoE routing layer after computing token-to-expert logits z[b,e]. For each routing group, initialize a collision-free configuration eta from the top-N logits, where each occupied lattice position represents one routing slot. Run m discrete Gillespie-like updates. At every update, compute both rates for every occupied position using the sine-product formula, multiply each rate by exp(beta times the destination-logit minus the current-logit), mask destinations already occupied, sample one move proportional to the resulting rates, and update eta. Dispatch tokens according to the final occupied positions. Use sums of log absolute sine values rather than direct products, handle periodic distances explicitly, and add a small numerical floor to sine magnitudes. The paper supplies the exclusion geometry and transition rates; the logit bias, finite-step sampler, and token-grouping rule are neural adaptations. The first cheap test should use a small Switch-Transformer on WikiText-103 or CIFAR-100, with ordinary top-1 routing and top-k routing plus load-balancing loss as baselines at equal expert FLOPs. Record expert-load coefficient of variation, collision rate, validation loss, and routing entropy. The prediction is that collision rate is exactly zero, load variance decreases with update count m and repulsion scale w until logits dominate, and a crossover occurs when w divided by the standard deviation of logits is comparable to the inverse temperature beta. Locate this crossover and test whether it shifts by less than 20 percent across random seeds.