Transversal encoded gates

Replace a standard gated MLP operation h=W_2(sigma(W_1x)) with an encoded multiplicative block. Produce two encoded streams A and B from the input using separate linear projections. Each stream is represented on a u-dimensional evaluation grid, with per-axis polynomial degrees bounded by r_i and s_i. Enforce r_i+s_i<ell_i by parameterizing coefficient tensors only within those degree ranges. Compute G=A*B elementwise at every grid coordinate, optionally corrupt G with an adversarial top-k coordinate perturbation, and postpone decoding until after one or two encoded gates. Pseudocode is: A=Encode(W_Ax); B=Encode(W_Bx); G=A*B; G=Corrupt(G,p); for sweep in 1..S: G=TensorPolynomialProject(G); y=W_O Decode(G). TensorPolynomialProject fits a degree-(ell_i-1) polynomial independently on each axis-parallel line and replaces that line with its fitted evaluations. During training, add L_code=lambda times the mean squared projection residual over all lines, encouraging the learned activations to remain in the code space. The paper provides the transversal multiplication identity and degree condition; the real-valued Vandermonde implementation, projection frequency, and corruption injection are empirical choices. Begin with a CIFAR-10 MLP and compare against SwiGLU, ordinary bilinear gating, and naive triplication at equal decoded width. Measure clean accuracy, accuracy under 5-20% coordinate corruption, projection cost, parameter count, and activation memory. Success requires robustness better than ordinary gating with less overhead than independent replication and clean accuracy within 1 percentage point of the baseline.