Flow Mismatching · semicircle toy, Appendix B.1

Bias-variance trade-off across ODE time

t = 0.02
per-t mismatch, this step only
cumulative mismatch, w(t)=t²-weighted up to current t
0.0 (low mismatch)
1.0 (high mismatch)
t = 0.02

Drag the slider to step through ODE time t. Left: the anomaly-score landscape from this single t alone -- at small t, interpolated states are dominated by source noise, so the low-mismatch region is a broad blob covering the manifold's interior (bias, poor localization); at large t, it localizes tightly to the manifold but is visibly speckled (variance). Right: the running w(t)=t²-weighted combination of every step up to the current one -- by the final step this equals the paper's actual detector output, both sharp and smooth.

Accumulated mismatch score

Running w(t)=t²-weighted integral of the mean per-t heatmap value, up to the current scrub position.