L1 · Fit, validation, and residual phase
Fitting searches for a delay that explains the chirp observations, then we compare its predictions with the zero-delay initial model. The search bounds and optimizer start are chosen before running; neither validation data nor the true delay selects them.
| Split | Excitation | Used by fitting? | Question |
|---|---|---|---|
| Fit | chirp | yes | Can public observations identify the timing effect? |
| Validation | held-out reversal waveform | no | Does the fitted delay predict another motion? |
Compare position and velocity for Oracle, Initial, and Identified curves. A small fit error is expected after fitting, but the stronger evidence is lower held-out validation error for the Identified Student. The default report's metrics record both models so the comparison is inspectable rather than a single success score.
How to read the residuals
The report defines residuals as model - observed for the selected quantity.
Repeating positive and negative lobes around reversals can be a timing clue:
the Initial response is ahead of or behind the delayed Oracle. For a small
time shift, position residual is approximately proportional to velocity, so
the residual-versus-velocity view can also reveal phase mismatch. It does not
identify friction by itself: delay and velocity-dependent effects can produce
correlated patterns, and controlled experiments are needed to distinguish
them. In this matched ideal benchmark, a near-zero Identified
residual supports recovery of the configured effective delay; it does not prove
that delay is the only effect on a real servo.
The machine playback is a replay of recorded states. Scrubbing it must not re-simulate or re-fit. Oracle and Identified lines keep distinct labels and styles even when their arrays coincide.
Checkpoint questions
- Why would fit error alone be weak evidence?
- What does lower Identified validation error show about the held-out command?
- If validation error stayed high, what repeat-from-another-start test would separate optimizer trouble from a missing model effect?
Suggested answers: fit-only scoring cannot reveal poor generalization; lower held-out error shows prediction improved on a motion withheld from fitting; and repeating from an independent optimizer start checks convergence before adding another physical effect.