Custom Training Loop

This page will document the software training harness used by the ablation experiments.

The first target is Experiment 1A: a one-layer, no-bias, floating-point linear regression test with scale drift.

Design Goals

• Use Keras models for the trainable layers.
• Avoid model.fit.
• Own the update step explicitly.
• Flatten trainable parameters into one global vector theta.
• Flatten gradients into one global vector G.
• Compute the dynamic global throttle alpha(t).
• Apply the full update vector with one shared scalar throttle.
• Log every diagnostic needed to explain closed-loop stability.

Minimal Loop Shape

for step in steps:
    x_batch, y_batch = sample_batch()

    with GradientTape:
        y_hat = model(x_batch)
        loss = mse(y_batch, y_hat)

    grads = tape.gradient(loss, model.trainable_variables)

    theta = flatten(model.trainable_variables)
    G = flatten(grads)

    delta_raw = -eta * G
    alpha = controller(theta, G, theta_prev, G_prev)
    delta_actual = alpha * delta_raw

    apply_flat_update(model.trainable_variables, delta_actual)
    log_step(...)

First Model

$$y = Ax$$ $$\hat{y} = Wx$$

No bias is included in the first test. Bias is added only after the pure scale-drift Hessian story is validated.

First Controller

$$C(t) = \frac{ \lVert G(t) - G(t-1) \rVert }{ \lVert \theta(t) - \theta(t-1) \rVert + \varepsilon }$$ $$S(t) = \operatorname{EMA}(C(t))$$ $$\alpha(t) = \operatorname{clamp} \left( \frac{1}{1 + \beta S(t)}, \alpha_{\min}, 1 \right)$$

Diagnostics

The first implementation should log:

• loss,
• output error,
• ||theta||,
• ||G||,
• raw update norm,
• actual update norm,
• curvature proxy C(t),
• EMA signal S(t),
• alpha(t),
• effective learning rate alpha(t) * eta,
• true Hessian metrics where feasible,
• stability margin eta * lambda_max(H),
• throttled stability margin alpha(t) * eta * lambda_max(H),
• update cosine.

Notes

Keep this page updated with code snippets once the harness stabilizes.