Normalized Linear Model - AdamW Toy Example (Noise + Precise Theory)

```html Normalized Linear Model - AdamW Toy Example (Noise + Precise Theory)

Normalized Linear Model: y = Wx / ||Wx|| (Teacher–Student, AdamW)

Student weights \(W\) learn to match a fixed teacher on Gaussian inputs using AdamW, with added gradient noise. Outputs are normalized: \(y = \frac{Wx}{\|Wx\|}\).
Solid lines = empirical; dashed lines = predicted equilibrium values using the more precise \(W_\infty\) formula from the blog (no dependence on \(W_0\)). Moving sliders re-bases the dashed lines.

Learning rate:

Weight decay:

β₁:

Speed (steps/frame):

Iterations: 0

```