Mind · Inference
AdaptiveSplineSeparator#6cd0
Fit a curve through a 2-D scatter that maximally separates two groups, to catch oblique separation
Mechanism
Axis-wise tests ask whether groups differ in x or in y; groups can differ along a diagonal and pass both. In a 2-D space (for example the rescaled coordinates from an EntropyDensityCollapse), define a smooth spline C(l) through c control points (40) with x fixed, log-spaced over the data range, and y free. Initialise the y values on an existing curve such as the fitted scaling function. For each observation r_j, find the nearest point on the curve and take the signed perpendicular distance d_j (positive below, negative above). Optimise the log-y control values with L-BFGS-B, box-bounded to the observed y range, to maximise |mean d(group 1) - mean d(group 2)|, stopping on small gradient or function change (e.g. 1e-5, 1e-6, at most 200 iterations). Report the share of each group on each side, and judge significance with a permutation test that shuffles group labels between whole samples, as in ClusteredObservationTesting. For fire ant trailing versus aggression, 67.8% of aggression windows fell below the curve and 70.6% of trail windows above (colony-level permutation p = 0.03), a split invisible to axis-wise GEE (p = 0.47, 0.97).
Invariants
- The separator is optimised and tested under the same grouping of observations
- Control points stay inside the observed data range, so the curve does not extrapolate
- Significance comes from re-optimising under permuted labels, not from the optimised score itself
Failure modes
- Overfitting: 40 free control points can separate noise; without re-fitting on permuted labels the score is optimistic
- Permuting windows instead of samples inflates significance
- Defining 'below' and 'above' only for a single-valued curve; it cannot represent groups that interleave
Where this came from
- Thesis Kevin Do, PhD thesis on ant collective behaviour (NCSU, 2026), Ch. 3.3, Eqs. 3.29-3.32; Ch. 4.2.3, Fig. 4.4
Builds on
Identity
The name is the hash of the definition. Change a word and it becomes a different pattern.
- Sema ID
sema:AdaptiveSplineSeparator#mh:SHA-256:6cd0be0ce642cfb16527c769bc946c7c7561d30e809bb9f5c0be55d20d42e5f0- Reference
AdaptiveSplineSeparator#6cd0- Ring
- 2
- Tier
- 2