A Deterministic Task-Discriminant Token Ladder: When and Why Multi-Token Quantization Pays for Edge Decisions

Abstract

A Deterministic Task-Discriminant Token Ladder: When and Why Multi-Token Quantization Pays for Edge Decisions Randolph James Ferlic, M.D., and Kimberly Kate Ferlic — Fieldstone Analytics, LLC Correspondence: randolphf@fieldstoneanalyticsllc.com Preprint · Zenodo DOI: 10.5281/zenodo.22003179 · CC-BY 4.0 Abstract A single class-discriminant token — a features to discriminant-subspace to codebook-index encoding — can carry a decision from a signal window at roughly eight bits, but on multichannel streams one token pays an accuracy tax: it must funnel every channel through a single code. We characterize the deterministic, closed-form remedy — a token ladder that partitions the input channels into M groups, encodes each with an independent class-discriminant codebook, and fuses the M tokens with a naive-Bayes head (M = 1 recovers the single token) — and ask, across fifteen public datasets in seven domains, precisely when and why it pays. Three findings anchor the paper. First, the ladder reliably beats the single token where the stream is genuinely multichannel (twenty-seed gains of +0.02 to +0.09 macro-AUC, all p < 0.05), and we localize the cause by ruling out the alternatives: adding centroids, supervised (LVQ) centroid placement, and residual quantization of the shared embedding all fail — only partitioning the channels helps, so the single-token tax is a channel bottleneck, not a resolution limit. Second, the ladder is fault-tolerant: because the single token is a single point of failure, it collapses under channel dropout and additive noise, whereas the ladder's independent tokens localize the damage — the advantage grows to +0.10 to +0.35 AUC when a quarter of the channels drop or the input is noised. Third, the benefit tracks a clean applicability envelope — multichannel, a real single-token tax, and a learnable base task — which we confirm on twelve-lead ECG (PTB-XL: +0.04 accuracy, +0.07 under distribution shift, +0.07 lead-dropout tolerance) and whose boundaries we mark with cases that each fail one condition. The ladder is competitive with a task-trained neural vector-quantizer at equal bits — dominating it in the small-data regime where the neural codec overfits — while requiring no gradient training. All results use real public data with pre-registered outcome bands, and we report the honest negatives. Highlights • On multichannel streams a single decision token is a channel bottleneck; a deterministic token ladder (channel-partition product quantization with a naive-Bayes fusion head) recovers the tax — twenty-seed gains of +0.02 to +0.09 macro-AUC, all p < 0.05 — while M = 1 exactly recovers the single token. • The mechanism is isolated to the channel split: adding centroids, supervised (LVQ) centroid placement, and residual quantization of the shared embedding all fail; only partitioning the channels helps, and any partition (contiguous, random, correlation-clustered) works equally well. • Fault tolerance: because the single token is a single point of failure, it collapses under channel dropout and additive noise while the ladder localizes the damage — the ladder's advantage grows to +0.10 to +0.35 AUC as a quarter of the channels drop or the input is noised. • A clean applicability envelope — multichannel, a real single-token tax, and a learnable base task — confirmed on twelve-lead ECG (+0.04 accuracy, +0.07 under fold-split drift, +0.07 lead-dropout tolerance) and bounded by cases that each fail one condition (single-channel signals; a near-chance task). • The deterministic ladder is competitive with a task-trained neural vector-quantizer at equal bits, dominating it in the small-data regime where the neural codec overfits — with no gradient training, no hyperparameter search, and bit-exact reproducibility. What this record contains • The manuscript (PDF). • A reproducibility archive (`PAPER_37_ZENODO_ARCHIVE.zip`): deterministic runners for every experiment (the rate-accuracy dial, the four mechanism controls, the partition and head ablations, twenty-seed significance, the fault-tolerance and drift studies, the learned-vector-quantizer baseline, the projection-versus-codebook decomposition, and the twelve-lead-ECG clinical study), the per-run JSON result summaries behind every figure and table, and the figures. All datasets are public (UCI Robot Execution Failures and Human Activity Recognition; the UEA multivariate archive; the CWRU Bearing Data Center; the ROSMA da Vinci Research Kit; and PhysioNet PTB-XL). No raw subject data is redistributed; loaders fetch the public sources. Cite as R. J. Ferlic and K. K. Ferlic, "A deterministic task-discriminant token ladder: when and why multi-token quantization pays for edge decisions," Zenodo, 2026, doi: 10.5281/zenodo.22003179. License and patent notice Released under CC-BY 4.0. Consistent with Section 2(b) of that license, no patent, patent-application, or other intellectual-property right of the authors is licensed, waived, granted, or otherwise conveyed by this publication or by any reuse of it; the encoding methods described herein — including the single-token and the multiple-token (product-quantization / channel-partition) embodiments — are the subject of pending U.S. patent applications. Companion deposits Part of the single-token class-discriminant codebook family on Zenodo (community: spiral-domain-encoder-campaign), which includes the encoder-method deposit and the rate-accuracy comparison of the single token against general-purpose compression codecs. Keywords product quantization, task-aware compression, coding for machines, edge inference, multichannel sensing, fault tolerance, class-discriminant codebook, sufficient statistic, vector quantization, condition monitoring, electrocardiography, human activity recognition, bearing fault diagnosis, pre-registration.