GASF-image CNN single-sample discriminator (frozen-BatchNorm, python-at-score)

Single-sample within-cohort discriminator (family M, image/invariance) that turns each specimen's per-sample robust-CLR (rCLR) profile into a Gramian Angular Summation Field (GASF) image (Wang & Oates, 2015) and scores it through a small convolutional network with FROZEN BatchNorm. Following the canonical Wang & Oates pipeline, the length-\(p\) frozen-order rCLR profile is first PAA-reduced to a FIXED length \(L = \min(p, \mathrm{image\_size})\) (default image_size = 128) so a specimen maps to a single-channel \(L \times L\) GASF image of bounded size regardless of the feature count; a small Conv-BN-ReLU-MaxPool CNN with a global-average-pool logit head is trained end-to-end on the TRAINING images by binary cross-entropy, then FROZEN. A new specimen is scored by the logit of the frozen, eval-mode CNN on its GASF image. Larger = more case-like.

Python-at-score contract (no live pointer). Unlike the BatchNorm-free trained-torch siblings (proto-net, lrt-deepmaha) which export weights to a pure-R forward, a CNN with Conv2d/MaxPool/BatchNorm has no compact pure-R forward, so this scorer follows the PROVEN PYTHON-AT-SCORE pattern of fit_tabicl / fit_tabpfn: the fitted model stores ONLY plain R-side state – the CNN state_dict as named float64 numeric arrays (every conv/BN/linear parameter, INCLUDING the BN running_mean, running_var, num_batches_tracked), the architecture config, the frozen per-feature GASF min/max bounds, the feature universe, and the seed/hp. There is NO live python pointer on the model. At SCORE, the identical CNN is rebuilt in python from that R state, load_state_dict loads the exported weights, net.eval() puts BatchNorm in FROZEN mode (running stats, not per-batch stats), and each query's GASF image is forwarded ONE ROW AT A TIME. Because the R-side state is fully serialisable, the default model_digest is a stable deterministic snapshot suitable for singlesample_assert_row_equivariant.

Frozen BatchNorm + forced row-by-row = exact single-sample equivariance. Two ingredients make the canonical gate hold EXACTLY. (1) net.eval() freezes BatchNorm to its training running statistics, so a query's normalisation depends only on the FROZEN stats – never on the other rows in the scored batch. In net.train() mode BatchNorm would compute per-batch statistics and COUPLE the rows, breaking single-sample deployability; eval mode is therefore mandatory and is asserted by a dedicated test (§7.10). (2) On a TRAINED net the float32 conv accumulation across the batch dimension makes a 1-row forward differ from the same row inside an \(n>1\) batch by \(\sim 2\times 10^{-7}\) (a tiling/accumulation artefact, not a cross-row coupling). To remove even that, this scorer forwards in float64 and ONE ROW AT A TIME, so the \(n=1\) path is used uniformly and a row's logit is bit-identical whether scored alone or in any batch (single-row score == batch score EXACTLY 0). float64 also makes the same image in a batch of 1 vs a batch of 32 agree to \(\sim 4\times 10^{-16}\) (the frozen-BN eval-mode proof).

GASF transform (deterministic, single-sample-safe via FROZEN bounds). For a specimen's universe-aligned per-sample rCLR vector \(v\) (length \(p\), frozen feature order): (1) min-max scale to \([-1, 1]\) using FROZEN TRAINING per-feature bounds \((\mathrm{lo}_j, \mathrm{hi}_j)\) computed once at fit, \(\tilde v_j = \mathrm{clamp}(2(v_j - \mathrm{lo}_j)/(\mathrm{hi}_j - \mathrm{lo}_j) - 1, -1, 1)\); (2) angular \(\phi_j = \arccos(\tilde v_j)\); (3) \(\mathrm{GASF}[i, j] = \cos(\phi_i + \phi_j) = \tilde v_i \tilde v_j - \sqrt{1 - \tilde v_i^2}\sqrt{1 - \tilde v_j^2}\), a single-channel \(p \times p\) image. Because the bounds are FROZEN (training-derived), a query is scaled by training bounds – never its own min/max – so the image depends ONLY on the query and the frozen bounds, making it single-sample. The transform is implemented in python (numpy) at fit and score; a pure-R .img_gasfcnn_gasf reimplements the closed form and is used only by a §7 test to independently verify the python 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 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 GASF 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 but is a VALID specimen: it yields a valid GASF and is scored normally (NOT floored) – the empty-support test is on the ORIGINAL abundances, NOT on all(z == 0).

References

Wang Z, Oates T. (2015) Imaging Time-Series to Improve Classification and Imputation. Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI), 3939-3945. arXiv:1506.00327.

Ioffe S, Szegedy C. (2015) Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. ICML.