1D wavelet-scattering single-sample discriminator (python-at-score, frozen head)

Single-sample within-cohort discriminator (family M, image/invariance) that maps each specimen's frozen-order per-sample robust-CLR (rCLR) profile to a 1D wavelet scattering transform (Mallat 2012; Anden & Mallat 2014) and scores the scattering coefficients through a FROZEN regularized-logistic head. A specimen of \(p\) universe features is laid out as a 1D signal along the frozen feature axis, zero-padded to \(\mathrm{shape} = \mathrm{next\_pow2}(p)\), scattered by a fixed cascade of wavelet convolutions + modulus + low-pass averaging (ScatteringTorch1D, kymatio), flattened to a fixed-length coefficient vector, standardized by FROZEN training statistics, and fed to a FROZEN ridge-logistic linear head. Larger = more case-like.

Python-at-score contract (no live pointer). Like the proven python-at-score siblings fit_img_gasfcnn / fit_tabicl (and unlike the export-to-pure-R trained-torch siblings proto-net / lrt-deepmaha), the scattering transform is computed in python at fit AND score, but the fitted model holds ONLY plain R-side state: the scattering CONFIG (J, Q, shape, max_order, the frozen feature universe), the FROZEN per-coordinate coefficient standardization (coef_mean, coef_sd), the FROZEN linear head (weights, intercept), and the seed/hp. There is NO live python pointer on the model. At SCORE the identical ScatteringTorch1D is REBUILT in python from the config each call, the coefficients are computed FORCED ROW-BY-ROW in float64, standardized with the frozen stats, and the frozen R-side linear head is applied in pure base R. Because every model field is a plain R object, the default model_digest is a stable deterministic snapshot suitable for singlesample_assert_row_equivariant.

Why this is inherently single-sample (no BatchNorm). The scattering transform \(S(x)\) is a FIXED cascade of wavelet convolutions, modulus, and low-pass averaging with NO learned parameters and NO cross-sample statistics – each specimen's coefficients depend ONLY on that specimen's own signal. There is no BatchNorm and no batch coupling. The only numerical wrinkle is float32 convolution accumulation across a batch dimension; this scorer computes the coefficients in float64 ONE ROW AT A TIME, so the \(n=1\) path is used uniformly and a row's coefficients (hence its score) are bit-identical whether scored alone or in any batch – single-row score == batch score EXACTLY 0. The coefficient standardization uses FROZEN training mean/sd (never the query's own), and the head is a frozen linear map, so the whole pipeline is single-sample-safe.

Signal construction (deterministic, frozen). For a specimen's universe-aligned per-sample rCLR vector \(v\) (length \(p = \) size of the FROZEN feature universe, in the FROZEN feature ORDER), the 1D signal is \(v\) laid out along the frozen feature axis, zero-padded to \(\mathrm{shape} = \mathrm{next\_pow2}(p)\) (FROZEN at fit from the training universe size). The scattering transform is ORDER-dependent along the feature axis: this is an intended, frozen design choice (the feature order is fixed at fit; there is NO claim of feature-permutation invariance). The row-equivariance harness permutes SAMPLES (rows), never features (columns) – exactly as for img-gasfcnn's GASF.

Single-sample transform. Each specimen is mapped to the self-contained per-sample robust CLR over its OWN strictly-positive support (geometric-mean centring on v > 0) in the FROZEN feature universe; this is exactly invariant to per-specimen positive scaling and uses no cross-row statistic. Universe features absent from a specimen carry the neutral rCLR value 0. The SAME rCLR transform feeds the scattering at fit and at score.

Degenerate-neutral. A query returns the neutral score 0 if fewer than hp$min_features universe features overlap the query columns (a column-overlap floor, batch-independent), or it has empty positive support over the frozen universe on the (pre-rCLR) aligned ORIGINAL abundances (!any(X_use[i, ] > 0)). A FLAT all-equal-positive composition maps to the rCLR origin (an all-zero signal) but is a VALID specimen: it yields valid (zero) scattering coefficients and is scored normally (NOT floored) – the empty-support test is on the ORIGINAL abundances, NOT on all(z == 0).

kymatio import workaround. kymatio 0.3.0's package init (import kymatio.torch) eagerly imports the 3D harmonic-scattering module, which calls scipy.special.sph_harm (REMOVED in scipy >= 1.15), so the top-level import RAISES ImportError. The 1D frontend is therefore imported DIRECTLY from kymatio.scattering1d.frontend.torch_frontend (verified working: float64, deterministic). The reticulate skip-guard probes torch AND that direct ScatteringTorch1D import (NOT import kymatio.torch).

References

Mallat S. (2012) Group Invariant Scattering. Communications on Pure and Applied Mathematics 65(10):1331-1398.

Anden J, Mallat S. (2014) Deep Scattering Spectrum. IEEE Transactions on Signal Processing 62(16):4114-4128.

Andreux M, Angles T, Exarchakis G, et al. (2020) Kymatio: Scattering Transforms in Python. Journal of Machine Learning Research 21(60):1-6.