RG Spectral Feature Gate

1. Integration point: apply the gate to the feature dimension of a transformer MLP output, convolutional channel activation, or embedding table before the next linear projection. During calibration, collect a rolling matrix X of centered activation vectors from N samples, compute the correlation matrix C, and eigendecompose C = U diag(lambda_1,...,lambda_P) U^T. Do not simply keep the largest eigenvalues. 2. Pseudocode: X <- centered activation batch; C <- corr(X); lambda,U <- eigh(C); form logarithmic or quantile spectral bands B_r; z_r <- X U[:,B_r]; kappa4_r <- mean(z_r^4) - 3 mean(z_r^2)^2; u4_r <- -kappa4_r/(mean(z_r^2)^2 + eps); d_r <- finite_difference(log(abs(u4_r)+eps), log(lambda_band+eps)); rc <- first r with a sign change in d_r that persists for two bands; mask[B_r] <- 1 for bands on the signal side of rc and 0 otherwise; h_next <- W(mask * U z). Use a straight-through estimator for the binary mask during training, or freeze the mask after calibration. 3. Compute the MP edges from q = P/N and estimate sigma^2 from the median bulk eigenvalue. Estimate u4_r and the crossing from minibatches, using an exponential moving average and bootstrap resampling to prevent unstable gates. 4. First experiment: use a 6-layer transformer on CIFAR-10 or a small language-model benchmark, insert the gate after every MLP, and compare dense training, fixed top-k PCA, and magnitude pruning at equal retained width. Measure validation accuracy, retained FLOPs, and mask stability across batches. Success means higher accuracy than top-k PCA at the same width, or at least 20 percent lower width at matched accuracy, with a persistent spectral crossing rather than a validation-tuned cutoff.