nx_train_r2_gate.nx

nx_train_r2_gate.nx -- GATE for TRAIN-R2 (T6): tensor autograd. Proves, by RUNNING: A MLP GRADCHECK: loss = MSE(W2*relu(W1*x+b1)+b2, t), W1 2x2/b1 2/W2 1x2/b2 1 = 9 params (values off the relu kinks). Each param: analytic (reverse-mode) vs central finite diff (h=1/128), rel<1/32 floor 1/64. Exercises every identity (matvec x2, vadd x2, relu, mse) through a real nonlinear composition. B RECOVER AN AFFINE MAP: train W(2x2)+b(2) to recover y=A*x+c (A=[[3/2,-1/2],[1/4,1]], c=[-1/2,3/4]) from 8 deterministic samples; full-batch GD lr=1/10, 400 epochs. Assert loss<1/1000 AND every W,b elt within 1/16 of truth. (LINEAR model: zero-init is convex-safe; nonconvex needs an init strategy = next rung.) C BIT-EXACT: run Gate-B training twice from scratch -> identical final bits for all 6 cells. D AdamW: the same affine recovery via AdamW (m/v moments + bias correction + sqrt) also converges -- the optimizer the FNet/transformer models will actually use. Evidence -> knowledge/status/train_r2.log (TRAINR2GATE authored=organ ... verdict=GREEN). license_tier: ORIGINAL