Tensor-coded hidden states

Integrate the code at the output of an MLP block or Transformer feed-forward block. Choose u=2 or u=3 tensor axes, with n_i=|E_i| typically 2 or 3, and represent each scalar feature h_j by evaluations of a low-degree polynomial over the grid E_1 x ... x E_u. A practical real-valued prototype can use a Vandermonde evaluation matrix instead of finite-field arithmetic. First map h_j to polynomial coefficients theta_j, then construct Y[a_1,...,a_u] = sum_{r_1<ell_1,...,r_u<ell_u} theta_j[r_1,...,r_u] product_i a_i^{r_i}. At a fault boundary, corrupt a chosen fraction p of Y coordinates using replacement values, sign flips, or values copied from another example. Decode using alternating robust polynomial projection: initialize Y_hat=Y; for each axis i, fit a degree-(ell_i-1) polynomial independently to every line parallel to axis i using the capped loss rho(r)=min(r^2,tau^2); replace the line by fitted evaluations; repeat for 2-4 sweeps. Decode the repaired tensor back to h and continue the network. The paper supplies the code structure and distance rationale; the real-valued decoder, corruption model, and projection schedule are empirical adaptations. Test a width-256 two-layer MLP on MNIST or CIFAR-10 against an ordinary MLP and naive coordinate replication with matched decoded width and approximately matched FLOPs. Inject 0%, 5%, 10%, and 20% adversarial coordinate corruption at each hidden layer. Success means graceful accuracy degradation, clean accuracy within 1-2 percentage points, and substantially lower hidden-state reconstruction error than replication.