Weyl-conjugation layer regularization

Integrate this at a linear feature operator, not at nonlinear activations. The cheapest first target is a 2D convolution or a ViT patch-mixing/projection layer whose feature map has spatial dimensions H by W and channel dimension C. Store the trainable base operator A0. At every training step sample K phase-space perturbations (qk, pk), with qk drawn from a zero-centered discrete Gaussian over shifts and pk drawn from a zero-centered discrete Gaussian over modulation frequencies. For each sample construct Wk by circularly shifting the spatial feature map by qk and multiplying each spatial location by exp(i pk dot x / h); use real-valued features by implementing the complex operation as a two-channel real rotation, or initially use only signed cosine modulation. Compute yk = Wk inverse(A0(Wk(x))) and return y = (1/K) sum yk. Pseudocode: x -> for k: xk=W(qk,pk)x; uk=A0(xk); yk=W(qk,pk)^T uk; output mean(yk). The exact imported mathematics is unitary conjugation and expectation; q and p distributions, K, and h are engineering choices. Estimate no spectral quantities: verify numerically that each Wk preserves the feature norm and that sampled Ak has the same singular values as A0. Begin with CIFAR-10, a small ResNet-18, and a baseline with identical parameter count and FLOPs. Compare K=1 stochastic training, K=2 averaging, and no conjugation at equal training budgets. Success means improved corruption and translation robustness and validation accuracy, or reduced train-test gap, without exploding activation norms; report the extra wall-clock cost and test whether narrow noise beats ordinary additive feature noise.