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GeoRVQ: Decoder-aware geometry for residual-token prediction in physiological signals

Bo Cui, Yaowen Zhang

arXiv:2609.27018v1cs.LG

TL;DR

Conventional masked RVQ prediction treats all incorrect tokens equally, although substitutions can have different decoded effects and residual levels have coarse-to-fine dependencies. GeoRVQ combines decoder-aware costs with coarse-to-fine prediction. In descriptive matched-condition comparisons, it improves decoded and event measures more than exact token accuracy, while decoder-induced cost better tracks realized cost on sampled substitutions.

  • Problem

    Standard masked-token prediction treats RVQ token errors equally despite differing decoded effects and the coarse-to-fine structure of residual levels.

    Source: §1 · p. 1

  • Method

    GeoRVQ uses a frozen codec's decoder-induced substitution costs for soft targets and expected distortion, with coarse-to-fine quantizer-causal prediction.

    Source: §1 · p. 1, §2.2 · p. 2

  • Results

    Exact token accuracy rose from .133 ± .004 to .143 ± .003 and decoded distance fell from .606 ± .006 to .393 ± .007; R-peak F1 rose from .784 ± .004 to .837 ± .008 versus one-hot cross-entropy, while held-out cost correlation was .85 versus .54 for Euclidean distance.

    Source: §4.1 · p. 2, §4.2 · p. 2

  • Takeaways & Limitations

    Across evaluated cohorts, descriptive gains in decoded distance and R-peak preservation exceeded the change in exact token accuracy, and decoder-induced cost was more informative than Euclidean distance on sampled pairs.

    Source: §5 · p. 4

    The context-averaged graph approximates a nonlinear decoder and may miss rare state-dependent substitutions.

    Source: §5 · p. 4

Abstract

from arXiv · show

Residual vector quantization (RVQ) turns physiological waveforms into compact token sequences, but conventional masked modeling treats every incorrect token as equally costly. We propose GeoRVQ, a coarse-to-fine masked token model whose objective reflects the local response of a frozen waveform decoder. Decoder-induced costs define geometry-aware soft targets and expected distortion, while quantizer-causal prediction follows residual dependencies from coarse to fine levels. In a descriptive aggregate over MIMIC-IV Waveform, VitalDB, and CODE-15\%, GeoRVQ increases exact token accuracy from $.133\pm.004$ to $.143\pm.003$, reduces decoded distance from $.606\pm.006$ to $.393\pm.007$, and increases R-peak F1 from $.784\pm.004$ to $.837\pm.008$ under matched model and training conditions. Across 45 held-out code substitutions, decoder-induced cost has a Spearman correlation of $.85$ with realized decoded cost, compared with $.54$ for Euclidean codeword distance. These results indicate that decoder-aware objectives can improve waveform and event preservation without requiring a large increase in exact token accuracy.

1. INTRODUCTION

Standard masked-token prediction treats RVQ errors as equally costly and predicts residual levels in parallel despite their coarse-to-fine structure. GeoRVQ uses decoder-induced costs and quantizer-causal prediction to address both properties, evaluated under matched codec, backbone, and RVQ depth.

1. INTRODUCTION

  • Decoder-aware costs distinguish substitutions by their decoded waveform effects, while RVQ levels progress from coarse waveform trajectory to finer residual detail.Cross-entropy treats token-ID errors equally, and parallel prediction may estimate fine details before resolving the coarse signal.Source: §1 · p. 1
  • GeoRVQ uses a frozen pretrained codec to measure substitution effects, form soft targets, and penalize predictions according to decoded consequences.Its quantizer-causal heads predict coarse RVQ levels first and condition deeper-level predictions on resolved coarse tokens, while temporal context remains bidirectional.Source: §1 · p. 1
  • The evaluation compares one-hot cross-entropy, label smoothing, Euclidean codeword geometry, and decoder-aware objectives under the same codec, backbone, and RVQ depth.It separately tests decoder-induced geometry and coarse-to-fine prediction, excluding adaptive rate routing to focus on those components.Source: §1 · p. 1

2. GEORVQ

GeoRVQ predicts residual tokens using context across time and modalities, then conditions finer-level predictions on coarser RVQ tokens. Its decoder-induced geometry estimates substitution costs in waveform space and uses them for soft targets and expected-cost training.

2.1. RVQ token prediction

  • The frozen codec encodes waveforms into latent frames represented by shared multilevel RVQ indices, with a modality decoder reconstructing the signal.A mask selects observed modality–time–level entries and prediction targets; an axial backbone exchanges temporal and cross-modal context.Source: §2.1 · p. 1
  • Quantizer-causal heads predict coarse RVQ levels before conditioning deeper-level predictions on resolved coarse tokens, while scheduled sampling exposes fine-level heads to predicted coarse tokens.The causal ordering applies across quantizer levels, not time.Source: §2.1 · p. 1

2.2. Decoder-induced code geometry

  • Euclidean codeword distance omits decoder anisotropy and residual interactions, so GeoRVQ estimates context-averaged decoded costs for codeword substitutions.The cost combines normalized waveform, derivative, and event-neighborhood errors with fixed non-negative weights summing to one; contexts are sampled from the training split.Source: §2.2 · p. 1
  • The full cost row supplies expected-cost training, while the source code and its K nearest neighbors define the support for geometry-aware soft targets.The geometry term is expected decoded cost under predicted probabilities.Source: §2.2 · p. 2
  • The objective combines hard-label cross-entropy, soft-target cross-entropy, and expected cost, with hard targets anchoring code identity.The two geometry terms are ablated separately to distinguish useful structure from generic smoothing.Source: §2.2 · p. 2

3. EXPERIMENTS

Experiments use dataset-specific partitions and matched comparisons across reconstruction, translation, and synthesis tasks. Metrics are aggregated at the subject or case level, with three-run variability reported descriptively rather than as population-level subject uncertainty.

3.1. Datasets, splits, and preprocessing

  • Pretraining draws paired ECG–PPG windows from MIMIC-IV and VitalDB and ECG-only data from CODE-15%, with dataset-balanced sampling.MIMIC-IV uses a subject-disjoint 138/20/40 split; VitalDB and CODE-15% use case- and patient-disjoint 70/10/20 partitions, respectively, with normalization and geometry contexts fitted on training data.Source: §3.1 · p. 2

3.2. Comparisons and tasks

  • Comparisons hold the codec, mask schedule, backbone, parameter count, update budget, and active RVQ depth fixed across loss variants and prediction heads.Tasks include inpainting, paired ECG–PPG translation, and supported 25-to-100/250/500 Hz ECG synthesis; CODE-15% is limited to ECG-compatible evaluation.Source: §3.2 · p. 2

3.3. Metrics and statistics

  • Metrics include masked-token accuracy and likelihood, decoded waveform and PSD measures, and eligible event-level measures, averaged within subject or case before dataset aggregation.Three independent runs are reported with across-run standard deviations interpreted descriptively; geometry validity is Spearman correlation over 45 substitutions, 15 per evaluated RVQ level.Source: §3.3 · p. 2

4. RESULTS

Under matched conditions, GeoRVQ improves decoded fidelity and event preservation more than exact token accuracy. Its decoder-induced geometry tracks held-out substitution costs better than Euclidean distance, while ablations and fixed-depth results support contributions from both decoder geometry and coarse-to-fine conditioning.

4.1. Decoded fidelity improves more than token accuracy

  • Exact token accuracy rose from .133±.004 to .143 ± .003 while decoded distance fell from .606±.006 to .393±.007, a 35.2% reduction under matched conditions.PCC increased from .969 ± .003 to .989 ± .001, R-peak F1 from .784 ± .004 to .837 ± .008, and PSD error decreased from .083 ± .004 to .041 ± .002.Source: §4.1 · p. 2, Table 1 · p. 3

4.3. Geometry and quantizer causality are complementary

  • Removing decoder geometry raised decoded distance from .393±.007 to .502±.012 and reduced R-peak F1 from .837±.008 to .807 ± .004.Removing quantizer-causal conditioning raised decoded distance to .441 ± .015, reduced R-peak F1 by .020, and increased timing MAE from 9.2±0.2 to 9.7±0.1 ms.Source: §4.3 · p. 2, Table 2 · p. 4

4.2. The decoder graph predicts held-out consequences

  • Across 45 held-out substitutions, decoder-induced cost correlated .85 with realized waveform cost versus .54 for Euclidean codeword distance.The geometry comparison was independent of the masked predictor; matched objectives with similar token accuracy occupied different decoded-distance regimes.Source: §4.2 · p. 2, Figure 2 · p. 3

4.4. Fixed-depth and cross-dataset consistency

  • At q1, q1:2, and q1:3, GeoRVQ R-peak F1 was .797 ± .004, .827 ± .003, and .837 ± .007 versus .739 ± .003, .770 ± .003, and .784 ± .004 for one-hot cross-entropy.Dataset-specific decoded distances favored GeoRVQ on MIMIC-IV (.392 versus .614), VitalDB (.407 versus .628), and CODE-15% (.381 versus .576); no population-level inference is claimed from three-run SD.Source: §4.4 · pp. 3–4, Figure 2 · p. 3

5. CONCLUSION

GeoRVQ aligns masked RVQ-token learning with decoded substitution effects and residual codes’ coarse-to-fine dependency. Across evaluated cohorts, decoded-distance and R-peak-preservation improvements exceeded the change in exact token accuracy.

5. CONCLUSION

  • GeoRVQ aligns masked RVQ-token learning with decoded substitution effects and residual codes’ coarse-to-fine dependency.Its context-averaged graph approximates a nonlinear decoder and may miss rare state-dependent substitutions.Source: §5 · p. 4
  • Across evaluated cohorts, descriptive gains in decoded distance and R-peak preservation were larger than the change in exact token accuracy.Held-out substitution analysis was consistent with decoder-induced cost providing more informative local geometry than Euclidean distance on sampled pairs.Source: §5 · p. 4
  • The context-averaged graph may miss rare state-dependent substitutions.Source: §5 · p. 4

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