Learning goal: ridge penalties and limited gradient-descent time filter eigendirections differently. The scale relation λ = 1/(2ηt) can align their characteristic strengths, giving risk curves that are close in some regimes. It does not make their parameters or paths identical. Both can hurt when their additional bias outweighs the reduction in variance.

Points: training data; dashed gray: truth; red: ridge; green: stopping at the corresponding time scale.

Population risk versus aligned λ (log); red: ridge; green: stopping with the approximate relation λ=1/(2ηt).

Observe: the two risk curves can nearly overlap here. At the default setting their values are about 0.0313 and 0.0308. With the time scale aligned, the green curve can change little as η changes in a small-step regime. This is approximate spectral behavior, not exact equivalence. The minimum for a particular configuration may lie at the weak-regularization boundary. Smaller samples or larger degree can change the optimum. At degree 2, both restrictions can increase risk across the displayed range. Choose them by the risk tradeoff, not by treating the two filters as identical.