What One Backprop Step Is and Is Not - Backpropagation, Exactly

The finale states the boundary for the flagship exact step. The arithmetic is exact and the broader claims are explicitly outside this render.

highlighted = computed this step

What is exact

This book computes one exact backprop step on the same small rational network. The key register includes dL/dw11=-2, dL/dw12=-4, and dL/db1=-2.

\frac{dL}{dw_{11}}=-2,\quad \frac{dL}{dw_{12}}=-4,\quad \frac{dL}{db_1}=-2

What is not claimed

This is about 10 parameters, not 100B. It is not training, not convergence, not learning, and no generalization claim is made.

\text{one exact step; not training or convergence}

Summary

This is one exact backprop step on a small rational toy network. ReLU's zero-or-one derivative keeps every gradient exact rational; it is not training, not convergence, not learning, and no generalization claim.

\text{backprop mechanics on toy rational data}