Depth-first analytic MLP scaling

Integrate this as an architecture-selection policy for coordinate MLPs, neural fields, smooth regression, or the per-node update in a graph neural network. The exact tensors modified are the hidden affine/ReLU blocks: use a width w and depth D instead of allowing a conventional width-dominant baseline to determine both. First normalize every scalar input to [-1,1]. For a parameter budget P, sweep depth candidates D in {4, 8, 16, 32, 64}, set w approximately equal to P divided by D times the hidden-layer parameter multiplier, and reject candidates with w below 16. The training loop is: build Linear(d,w), followed by ReLU, repeated D times; append Linear(w, output_dim); train every candidate with the same optimizer, learning-rate schedule, seed set, batch size, and FLOP budget; record validation error and wall-clock time. Use the paper's bound as the design prior: for apparently analytic targets, increase D before increasing w, because the theoretical error behaves like N^{-C L}. Estimate smoothness with a small Fourier or Chebyshev probe: fit coefficients c_k and compute r_m = ||c_{k>m}||_2 / ||c_{k<=m}||_2; select depth-heavy models when r_m decays rapidly. The first experiment should use 2D or 3D regression on exp(x_1+x_2), sin(x_1) exp(x_2), and smooth PDE solutions. Compare width-heavy and depth-heavy MLPs at equal parameters and equal training FLOPs. Success is lower gridwise error at equal budget, with log error decreasing more rapidly as depth increases until optimization instability dominates.