Amplitude thresholds examined for bend eligibility

cZt;k=⟨Zt−k−Zt,Zt+k−Zt⟩∥Zt−k−Zt∥ ∥Zt+k−Zt∥.

This is not the cosine between Zt and Zt+k. A straight, continuing path gives cZ=−1, since the backward and forward displacements point oppositely. Larger values indicate a sharper local bend. The complete windows are evaluated on five-step checkpoint centers for lags k∈{5,10,15}. Each lag uses every center for which its own two neighbors exist; this need not reproduce identical edge trimming in every source plotting call.

An angle can emphasize a tiny late-training movement. We therefore also apply the source program’s factor-amplitude eligibility rule. Let mA be the larger of the preceding and succeeding input-factor displacement norms, and mB the corresponding output-factor quantity. A center is excluded only when both are below threshold η. The sweep is η∈{0,10−4,5×10−4,10−3,2×10−3,5×10−3}.

The threshold 0.002 appears in the inspected source plotting call. Reporting the entire sweep prevents it from becoming an after-the-fact selection of the most appealing transition time. Importantly, this eligibility rule uses factor amplitudes and is not itself invariant to arbitrary reciprocal factor rescaling. The effective-update metric is invariant; the inherited filter is not. This limitation is retained rather than describing the entire selection procedure as coordinate-free.

4.5 Numerical stability and PCA
[Context excerpt; full source linked.]

\eta \in {0,{10}^{-4},5\times {10}^{-4},{10}^{-3},2\times {10}^{-3},5\times {10}^{-3}}