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EMG Tokenization Preserves Movement Information at a Fraction of the Bitrate

Raul C. Sîmpetru, Amin Olamazadeh, Devon Rohlf, Vlad Cnejevici, Alessandro Del Vecchio

arXiv:2610.32674v1eess.SPcs.HCcs.LG

TL;DR

Wireless sEMG wearables must balance electrode coverage against transmission bandwidth, and compact representations could retain information useful for movement decoding. This paper evaluates two pose-label-free EMG tokenizers against continuous features. Tokenization substantially reduces payload with small changes in decoding error in the reported settings, while separating wearable encoding from receiver-side pose decoding.

  • Problem

    Wireless sEMG wearables trade electrode coverage against transmission bandwidth, motivating compression that retains information useful for movement decoding.

    Source: §I · p. 1

  • Method

    The study compares a causal spectral-reconstruction encoder and an engineered SPAR tokenizer, both fitted without pose labels, against their continuous features using paired decoder procedures.

    Source: §I · p. 1

  • Results

    Tokenization changed mean error by +0.01 mm for SPAR and +0.45 mm for the learned representation, with both pooled increases below the 1 mm bound.

    Source: §IV · p. 10

  • Takeaways & Limitations

    Tokenization provides a compact interface for movement decoding while allowing receiver-side pose decoders to change without changing the wearable encoder or transmitted representation.

    Source: §V · p. 10

    The main HD-EMG results are personalized and within-session; validity across sessions, electrode re-donning, clinical populations, and closed-loop wearable control remains to be tested.

    Source: §IV · p. 10

Abstract

from arXiv · show

Wireless electromyography (EMG) interfaces must balance electrode coverage against transmission bandwidth. Here, we show that compact EMG tokens substantially reduce payload while retaining information for three-dimensional hand-pose decoding. We evaluate two causal tokenizers fitted without pose labels: an encoder pretrained to reconstruct EMG spectra and one based on SPAR, an engineered spectral-spatial representation of neighbouring electrodes. In personalized, within-session experiments with 320-channel EMG from nine participants, we compare tokenized and continuous features using matched decoder architectures and training procedures. Averaged across decoders, tokenization changed mean error by +0.01 mm for SPAR (95% confidence interval: -0.12 to 0.14) and +0.45 mm for the learned representation (0.10 to 0.82). Both increases met a 1 mm non-inferiority criterion. Stored token arrays reduced payloads 41-fold relative to raw EMG and 36-fold relative to continuous SPAR features. On sampled windows of the public emg2pose benchmark's test partition, absolute differences in mean error between learned tokens and continuous features were below 0.05 mm across 176 participants and in the subset of 20 participants unseen during training. Electrode coverage, calibration, and unseen recordings affected SPAR decoding more than quantization did. In a computational benchmark, optimized SPAR generated tokens for 63 channels within 20 ms on a Cortex-M55 microcontroller. These findings support tokenization as a compact interface between wearable sensing and movement decoding, allowing decoders to be updated while the wearable encoder and transmitted representation remain fixed.

I. INTRODUCTION

Wireless sEMG wearables trade electrode coverage against transmission bandwidth, motivating compact representations that retain information useful for movement decoding. The paper compares two pose-label-free tokenizers and introduces their data, evaluation, and learned spectral-tokenizer design.

I. INTRODUCTION

  • Wireless sEMG wearables trade electrode coverage against transmission bandwidth, while muscle activity can differ across regions of one muscle.Compressing multichannel recordings could reduce bitrate while retaining information useful for movement decoding.Source: §I · p. 1
  • The study compares pose-label-free learned spectral and SPAR tokenizers with continuous features using matched decoder architectures and training procedures.It evaluates personalized, within-session decoding on high-density EMG synchronized with 3D hand kinematics from nine participants, plus learned tokens on emg2pose.Source: §I · p. 1

A. Dataset and acquisition

  • The recordings pair surface EMG from 320 electrodes across five grids with markerless 3D hand tracking during finger movements, grasping, and pinches.Nine participants were analyzed for decoding; four additional participants were used only for tokenizer fitting.Source: Figure 1 · p. 2, A. Dataset and acquisition · p. 2

B. Learned spectral tokenizer

  • The learned tokenizer is a causal VQ-VAE encoder pretrained to reconstruct EMG spectra and applied independently to each channel.It is shared across channels and electrode layouts and is trained without kinematic labels.Source: B. Learned spectral tokenizer · p. 2
  • Each 20 ms update maps a 256-dimensional encoder output to its nearest of 1,024 codebook vectors, producing a packed 10-bit token.The encoder uses 160 ms windows and four causal residual blocks for a 480 ms receptive field; the first complete-context token follows 500 ms calibration plus 480 ms context, excluding computation.Source: B. Learned spectral tokenizer · p. 2
  • Tokenizer pretraining reconstructs the log-power spectrum of each window in 64 nonzero-frequency bins up to 400 Hz, without kinematic labels.Pretraining uses high-density recordings and emg2pose, with decoding validation and test windows excluded.Source: B. Learned spectral tokenizer · p. 2

C. SPAR: spectral–spatial features and tokenization

SPAR represents each electrode through local spectral–spatial features from a four-electrode patch, then quantizes those features with a participant-specific codebook. Boundary handling zeros couplings for absent neighbours after the matrix logarithm.

C. SPAR: spectral–spatial features and tokenization

  • SPAR computes local spectral–spatial features describing each electrode’s spectrum and coupling to nearby electrodes.Its four-electrode patch contains a centre, auxiliary electrode, and horizontal and vertical neighbours; the auxiliary affects the cross-spectral matrix but contributes no features directly.Source: C. SPAR: spectral–spatial features and… · pp. 2–3
  • Each causal 160 ms window yields a 4 × 4 cross-spectral matrix in six frequency bands, with regularization and an eigenvalue floor supporting the matrix logarithm.The matrix uses seven overlapping 64 ms Hann segments spaced 16 ms apart.Source: C. SPAR: spectral–spatial features and… · p. 3
  • Each logarithmic matrix contributes the centre electrode’s diagonal entry and real couplings with its right and lower neighbours, yielding 18 features per electrode.Missing-neighbour features are fixed at zero; at boundaries, an opposite-side electrode substitutes for a missing neighbour, but its coupling is zeroed after the matrix logarithm.Source: C. SPAR: spectral–spatial features and… · p. 3, Figure 3 · p. 3
  • Participant-specific k-means codebooks quantize standardized 18-component SPAR vectors into 1,024 centroids fitted without kinematic labels.The codebook is shared across electrodes within a participant, and the receiver restores the centroid and reapplies structural zeros; a 64-centroid, 6-bit option is also evaluated.Source: C. SPAR: spectral–spatial features and… · p. 3

D. Evaluation protocol

The evaluation uses within-participant, within-session decoding and a separate emg2pose test subset, pairing tokenized representations with continuous counterparts under matched decoder procedures. It also benchmarks communication and computation and uses retrieval and visualization analyses to examine representation structure.

D. Evaluation protocol

  • Each participant contributes 64 training, 16 validation, and 16 test windows across eight movement tasks, with pose-decoder scoring on the final second of each window.Windows are divided chronologically within each task recording, with at least one second separating the training, validation, and test blocks.Source: D. Evaluation protocol · p. 4
  • The main experiments assess personalized, within-session decoding; the learned representation is separately tested on emg2pose windows covering 176 participants, including 20 unseen during training.Learned-tokenizer pretraining excluded decoding participants’ validation and test windows, while SPAR fitting used each participant’s training windows.Source: D. Evaluation protocol · p. 4

E. Decoders and baseline comparisons

  • Tokenized and continuous inputs are compared using separately fitted decoders with the same architecture and training procedure, isolating the effect of quantization within each pair.Continuous learned features are the same encoder’s pre-quantization outputs; continuous SPAR uses standardized features without quantization.Source: E. Decoders and baseline comparisons · p. 4
  • The decoder comparisons include raw-waveform CNN references, matched-size architectures, a compact spatial CNN + TCN, frozen Qwen3 controls, and frozen TabPFN.The causal TCN, Transformer, and matched waveform CNN have approximately 7.5 million parameters and the same training budget; the compact spatial decoder has about 0.7 million parameters.Source: E. Decoders and baseline comparisons · p. 4

F. Communication and computational requirements

  • Token payload rate is channel count multiplied by update rate and bits per token; communication estimates assume 1.4 Mbit/s BLE 2M application throughput and exclude application headers.Microcontroller timing tests the 20 ms token-generation budget, while decoder size and FP32 latency are measured separately.Source: F. Communication and computational… · p. 4

G. Representation visualization and pose retrieval

  • The SPAR visualization embeds current and past representations without labels or poses during fitting, but its display later uses movement labels and pose-derived phase.Because groups are repositioned to avoid overlap, distances between groups are not interpretable.Source: G. Representation visualization and… · pp. 4–5
  • Pose retrieval and direction classification test pose information and opening-versus-closing distinctions using one SPAR representation per update, without UMAP or concatenated history.Pose retrieval excludes the query’s own and adjacent cycles and averages measured poses from the five closest remaining cycles.Source: G. Representation visualization and… · p. 5

H. Robustness analyses

Across decoders, tokenization increased mean error by less than the 1 mm non-inferiority bound; robustness analyses also show that recording conditions and representation choice matter beyond quantization.

H. Robustness analyses

  • Robustness analyses tested simulated noise and electrode loss, calibration mismatch and refitting, and SPAR performance on recordings and movements not used for fitting.The analyses included evaluation without refitting under changed calibration and evaluation of unseen recordings not used to fit the SPAR pipelines.Source: H. Robustness analyses · p. 5

I. Outcomes and statistical analysis

  • Mean Euclidean landmark error was averaged within participants and then across participants with equal weight; paired token-minus-feature differences were the basis for quantization comparisons.The analysis used participant-level paired tests, with a 1 mm non-inferiority bound and Holm correction across four comparisons; procedures assumed independent participants and symmetric differences.Source: §I · p. 5

A. Averaged across decoders, quantization adds less than a millimetre of error

  • +0.01 mm for SPAR and +0.45 mm for the learned representation were the tokenization-related mean-error increases; both met the 1 mm bound.The 95% confidence intervals were −0.12 to +0.14 mm for SPAR and +0.10 to +0.82 mm for the learned representation.Source: A. Averaged across decoders,… · p. 5, Figure 4 · p. 6
  • On emg2pose, learned tokens and continuous features had mean errors of 28.00 and 28.04 mm across 176 test participants, a difference of −0.04 mm.The difference was +0.02 mm (95% confidence interval −0.16 to 0.21) among 20 participants unseen during tokenizer pretraining and decoder training; these benchmark errors are not directly comparable with HD-EMG errors.Source: A. Averaged across decoders,… · p. 5
  • With the proposed spatial CNN + TCN, SPAR tokens achieved 10.8 mm and continuous SPAR features 10.9 mm; SPAR tokens had 2.4 mm lower error than learned tokens.The SPAR-versus-learned difference had a 95% confidence interval of 1.7 to 3.1 mm and Holm-adjusted p = 0.016.Source: A. Averaged across decoders,… · p. 5
  • The proposed decoder combined lower mean error with fewer parameters than matched temporal models, and waveform, temporal, and Qwen3 decoders were below the 20 ms inference interval.TabPFN reduced error by a further 0.37 mm relative to the proposed SPAR-token decoder but required more than two minutes per complete-pose prediction.Source: Figure 4 · p. 6, A. Averaged across decoders,… · p. 7

B. SPAR tokens retain hand pose across repetitions

SPAR tokens retain pose-related structure across repetitions, although retrieval depends on how token similarity is measured. Token histories also vary with hand closure, and retain opening-versus-closing information at matched closure.

B. SPAR tokens retain hand pose across repetitions

  • Codebook-vector retrieval increased pose error by 0.09 mm with 1,024 codes and 0.22 mm with 64 codes versus continuous SPAR, while direct token-ID matching increased it by 0.92 mm.For 1,024-code tokens, both matching methods used the same transmitted IDs; codebook-vector matching accounted for distances between vectors, unlike Hamming matching.Source: B. SPAR tokens retain hand pose across… · p. 7, Figure 6 · p. 8
  • In participant 1’s token-history trajectories, hand closure varied over time, and movement direction was classifiable at matched closure with 70% accuracy for dequantized tokens versus 71% for continuous SPAR.The majority-direction control was 55%.Source: B. SPAR tokens retain hand pose across… · p. 7

C. Communication cost and embedded feasibility

Stored token arrays substantially reduce payload, and optimized SPAR tokenization fits the tested 20 ms interval for 63 channels. Robustness tests indicate that degradation, calibration, and unseen recordings can affect SPAR decoding beyond quantization.

C. Communication cost and embedded feasibility

  • At 320 channels, stored token arrays required 32 kB per second, a 41-fold reduction versus raw EMG and a 36-fold reduction versus continuous SPAR features.Ideal 10-bit packing would reduce payload to 20 kB/s; the learned encoder’s continuous output was 512 times larger than its stored tokens.Source: C. Communication cost and embedded… · p. 8
  • Optimized SPAR processed 63 channels within 20 ms on the Cortex-M55, whereas the optimized learned tokenizer took 96 ms for one channel.The benchmark timed token generation and excluded acquisition, radio transmission, and pose decoding.Source: C. Communication cost and embedded… · p. 9, Figure 7 · p. 9

D. Sensitivity to noise, electrode loss, calibration, and unseen recordings

  • Severe noise and electrode loss affected SPAR more strongly than the learned representation, with or without quantization; the largest upper confidence limit for the token-minus-feature increase was 0.93 mm.Three tested degradation conditions showed smaller increases with tokens.Source: D. Sensitivity to noise, electrode… · p. 9
  • Without refitting, onset calibration increased error by approximately 0.9 mm; after refitting under onset calibration, errors were 10.3 mm with tokens and 10.4 mm with continuous SPAR.On unseen 1.5 Hz digit recordings, SPAR reached approximately 18 mm versus 10 mm on 0.5 Hz test windows, with a token-minus-continuous difference of +0.18 mm; pace and training-window status were confounded.Source: D. Sensitivity to noise, electrode… · p. 9

IV. DISCUSSION

Tokenization substantially reduced stored payload while keeping average pose-error increases below the 1 mm bound, and learned tokens closely matched continuous features on emg2pose. The results also show that representation, coverage, calibration, and recording conditions matter, while decoder updates can be separated from the wearable representation.

IV. DISCUSSION

  • +0.01 mm for SPAR and +0.45 mm for the learned representation were the average error changes across decoders, both below the 1 mm bound; stored tokens reduced payload 41-fold versus raw EMG and 36-fold versus continuous SPAR.On emg2pose, learned-token versus continuous-feature mean-error differences stayed below 0.05 mm across 176 test participants, including 20 unseen during training.Source: §IV · pp. 9–10
  • Representation choice, electrode coverage, calibration, and unseen recordings affected accuracy more than tokenization across the evaluated pipelines.The main HD-EMG results used personalized within-session decoders for nine participants.Source: §IV · p. 10
  • With clean inputs, SPAR tokens had lower mean error than learned tokens and met the 1 mm noninferiority criterion against the adapted raw-waveform CNN, while learned features performed better under severe signal degradation.The tokenizer-fitting data, input processing, and decoder training differed between the pipelines, so their relative performance cannot be attributed to spatial features alone.Source: §IV · p. 10
  • Decoder complexity brought no consistent accuracy advantage; the compact spatial CNN + TCN had lower mean error and fewer parameters than the TCN and Transformer with learned-token inputs.TabPFN reduced error by a further 0.37 mm relative to the proposed SPAR-token decoder, but required over two minutes per pose when reprocessing training context.Source: §IV · p. 10
  • Nearest-neighbour retrieval error changed little when continuous features were replaced by codebook vectors, whereas Hamming-distance matching of token IDs produced larger errors.Opening and closing were distinguishable at matched hand closure.Source: §IV · p. 10

V. CONCLUSION

  • Changing calibration increased error, while refitting standardization, codebooks, and decoders improved both representations; unseen recordings raised absolute errors while token-versus-feature differences stayed small.The conclusion supports tokenization as a compact interface for hand-pose decoding, with decoder updates possible while the wearable encoder and transmitted representation remain fixed.Source: §IV · p. 10, §V · p. 10

A. Payload and memory accounting

The supplement accounts for payload and computational costs alongside decoding accuracy. Optimized SPAR met the 20 ms token-generation budget at 63 channels, while reduced-coverage comparisons show accuracy depends on the full pipeline and its electrode count.

A. Payload and memory accounting

  • Stored token arrays use 16-bit indices, while raw EMG uses 16-bit samples at 2,048 Hz and continuous SPAR uses 32-bit floating-point values.Token generation is at 50 Hz; the assumed application throughput is 1.4 Mbit/s, with a 9-byte update header adding 450 B/s.Source: A. Payload and memory accounting · p. 12
  • On emg2pose, learned-token transmission requires 1.45 kB/s including per-update headers, versus approximately 128 kB/s for raw FP32 EMG and 820 kB/s for FP32 continuous features.The roughly 2.3 kB calibration-and-electrode setup message is excluded from these rates.Source: A. Payload and memory accounting · p. 12
  • The Fig. S1 points relate mean 3D pose error to payload across electrode counts, and the dashed line marks the assumed 175 kB/s BLE application throughput.Payload excludes headers and uses ideal 10-bit token packing, 32-bit SPAR values, and 16-bit raw-EMG values.Source: Figure S1 · p. 12

B. Timing measurement scope

  • For HD-EMG decoder timing, inputs began in GPU memory and execution excluded fitting and loading; emg2pose end-to-end timing included processing through pose prediction but excluded acquisition and network transmission.The learned-token emg2pose path took a median 4.4 ms on a V100 GPU and 13.7 ms on four CPU threads, below the 20 ms update interval.Source: B. Timing measurement scope · pp. 12–13

C. Cortex-M55 and reduced-electrode validation

  • The optimized SPAR implementation met the 20 ms timing budget at 63 channels, whereas the optimized learned tokenizer required 95.7 ms for one channel.At 64 channels, SPAR took 20.28 ms; spectral feature extraction accounted for most processing time, followed by codebook search.Source: C. Cortex-M55 and reduced-electrode… · p. 13
  • The 63-electrode SPAR-token pipeline had 12.465 mm error and continuous SPAR had 12.368 mm, a paired difference of 0.097 mm; both had higher error than their 320-channel versions.The paired difference’s 95% confidence interval was [−0.081, 0.284] mm; Holm-adjusted p = 0.26.Source: C. Cortex-M55 and reduced-electrode… · p. 13
  • Within the same throughput, the 63-electrode SPAR-token pipeline had lower error than the 42-electrode raw-EMG CNN by 2.57 mm, although coverage and decoder differed.The Holm-adjusted p value was 0.008; the comparison concerns complete pipelines.Source: C. Cortex-M55 and reduced-electrode… · p. 13

S-II. IMPLEMENTATION AND TRAINING

The implementation uses different data-separation rules for learned-tokenizer pretraining and SPAR fitting, then trains a causal learned encoder to reconstruct EMG spectra without kinematic labels. Calibration, causal processing, and codebook training define the tokenizer’s operating conditions.

A. Data separation

  • Learned-tokenizer pretraining used recordings from all 13 participants but excluded evaluated participants’ validation and test windows; SPAR fitting used only each participant’s training windows.The emg2pose test subset included 176 participants, of whom 20 were unseen during tokenizer pretraining and decoder training.Source: A. Data separation · p. 13

B. Learned tokenizer

  • Each 3 s decoding window uses its first 500 ms to set channel baselines and scales, and decoding resampling uses a causal filter with a retained 20 ms delay.The normalization subtracts the lower median, divides by max(1.4826 MAD, 10−4), and clips at ±12 robust-scale units.Source: B. Learned tokenizer · p. 14
  • The causal encoder processes 160 ms of EMG every 20 ms and uses four residual blocks to produce 256-dimensional features over a 480 ms receptive field.A final nearest-vector search maps each feature to the 1,024 × 256 codebook.Source: B. Learned tokenizer · p. 14
  • Pretraining reconstructs mean-removed, Hann-windowed EMG log-power spectra with smooth-L1 loss, using 64 nonzero-frequency bins up to 400 Hz.Training alternated between high-density EMG and emg2pose data and proceeded through unquantized spectral reconstruction followed by quantized training.Source: B. Learned tokenizer · p. 14
  • Quantized training uses a straight-through estimator and commitment loss, while an entropy penalty discourages concentrating assignments in fewer than 256 codebook entries.The codebook is initialized with Lloyd’s k-means and updated by exponential moving average; entries with low moving-average counts are reinitialized.Source: B. Learned tokenizer · p. 14
  • Continuous-feature controls use features from the same VQ-trained encoder with quantization skipped, rather than a separately trained encoder.The comparison matches computation settings, with different storage precision and execution settings across the stated datasets and decoders.Source: B. Learned tokenizer · p. 14

C. SPAR feature extraction

SPAR extracts local spectral–spatial features from four-electrode patches, quantizes the standardized features, and supplies representations to matched pose-decoder comparisons. The decoder inputs and scoring protocol vary by decoder but use causal histories and held-out evaluation windows.

C. SPAR feature extraction

  • Each SPAR patch contains a centre electrode, horizontal and vertical neighbours, and an auxiliary electrode, with boundary substitutions and no patches crossing grid boundaries.Across 320 electrodes, the resulting layout has 5,256 valid features and 504 structural zeros.Source: C. SPAR feature extraction · pp. 14–15
  • SPAR divides each 160 ms window into seven overlapping 64 ms segments and estimates spectral relationships across six frequency bands.A regularized cross-spectral matrix is transformed by a matrix logarithm; each band contributes the centre diagonal and real couplings to horizontal and vertical neighbours.Source: C. SPAR feature extraction · p. 15
  • The six bands yield 18 features per electrode, standardized using training statistics with structural zeros excluded and restored around quantization.Participant-specific k-means fits 1,024 centroids to sampled training feature vectors without kinematic labels; the codebook is shared across electrodes, not participants.Source: C. SPAR feature extraction · p. 15

D. HD-EMG pose decoders

  • Within each token-versus-continuous comparison, decoder architecture, targets, initialization, and training procedure are matched, while auxiliary inputs differ among decoders.The emg2pose decoder receives calibration statistics and electrode descriptors; the proposed HD-EMG decoder and TabPFN use neither.Source: D. HD-EMG pose decoders · p. 15
  • HD-EMG scoring uses the final 50 predictions of each 3 s window, and tokenization effects are paired participant-level differences in token-minus-continuous-feature error.The scoring protocol evaluates 16 wrist-relative landmarks and averages landmark error within participants, then across participants with equal weight.Source: D. HD-EMG pose decoders · pp. 15–16
  • The emg2pose comparisons use a Transformer decoder and three initializations across the listed representations, with learned features and codebook vectors entering the decoder directly.The methods also include PCA, finite scalar quantization, engineered values, and BioCodec codebook-vector sums as representations.Source: D. HD-EMG pose decoders · p. 15

F. Statistical implementation

The primary comparisons test whether tokenization increases error by less than 1 mm, using participant-level differences and correction across four comparisons. Separate analyses examine tokenizer transfer, emg2pose performance, and alternative quantizers.

F. Statistical implementation

  • All four primary comparisons met the 1 mm non-inferiority bound (Holm-adjusted p = 0.016); with a 0.5 mm bound, the learned-token comparison was no longer significant (p = 0.71).The comparisons tested SPAR and learned tokens against continuous features, SPAR tokens against learned tokens, and SPAR tokens against the adapted waveform CNN.Source: F. Statistical implementation · pp. 16–17

A. Tokenizers fitted on separate participants

  • Tokenizers fitted exclusively on four participants were frozen before personalized decoders were trained for nine different participants, testing tokenizer transfer while retaining personalized pose decoding.The reported mean tokenization effects were small.Source: A. Tokenizers fitted on separate… · p. 17
  • Learned tokens and continuous features had mean errors of 28.00 and 28.04 mm across 176 emg2pose test participants, with small paired differences also observed in 20 unseen participants and held-out same-day sessions.The direction of the effect varied across the three pretrained encoders.Source: A. Tokenizers fitted on separate… · p. 18
  • At 10 bits, FSQ did not differ significantly from learned tokens, whereas quantized PCA and engineered k-means had higher errors (adjusted p < 0.01).The FSQ and PCA comparisons changed the quantizer while keeping the VQ-pretrained encoder fixed; BioCodec used 48 bits at its evaluated operating point.Source: A. Tokenizers fitted on separate… · p. 18
  • Held-out participant and same-day session tests covered the learned representation; SPAR was evaluated only under the within-session HD-EMG protocol.Other analyses used participant-level observations, with windows and training seeds summarized within participants rather than counted as independent observations.Source: F. Statistical implementation · p. 16, A. Tokenizers fitted on separate… · p. 18

C. SPAR feature ablation

The section tests what SPAR features contribute and whether representations preserve pose and movement-direction information. The results show that the matrix-logarithm diagonal carries most of the improvement over per-electrode power, while token-based retrieval and direction classification retain useful information.

C. SPAR feature ablation

  • With tokens, mean error was 13.31 mm for log band power, 11.12 mm for the matrix-logarithm diagonal, and 10.81 mm for full SPAR.Relative to full SPAR tokens, log band power increased error by 2.50 mm and the diagonal by 0.31 mm; adding explicit couplings gave a smaller further improvement.Source: C. SPAR feature ablation · p. 18

A. Pose retrieval

  • Pose retrieval used 160 ms EMG windows and matched each query against eligible cycles from all eight movements, excluding its own and adjacent cycles; the five closest matches supplied the estimated pose.For SPAR, matching used squared Euclidean distance between continuous representations or tokens restored to codebook vectors; token IDs were also matched using Hamming distance.Source: A. Pose retrieval · pp. 18–19
  • With 1,024-code tokens, pose retrieval was 0.09 mm worse than continuous SPAR; 64-code tokens were 0.22 mm worse, and Hamming matching of token IDs was 0.92 mm worse.Continuous SPAR error was 7.92 mm and pose-space matching error was 4.38 mm.Source: A. Pose retrieval · p. 19

B. Movement-direction analysis

  • Dequantized tokens achieved 70% direction accuracy, versus 55% for the majority-direction control, 65% for pose-based matching, and 64% for Hamming matching of token IDs.Continuous SPAR reached 70.6%, exceeding tokens by 0.6 percentage points.Source: B. Movement-direction analysis · p. 20

C. Visualization of token histories

The section examines temporal context in token-history displays and tests representation robustness to noise and electrode loss. The display’s trajectory circularity rises with history and changes sharply when histories are shuffled; degradation effects also differ between learned tokens and SPAR.

C. Visualization of token histories

  • With recording histories extending to 480 ms, mean trajectory circularity rose from 0.29 for a single update to 0.96, then changed little at 720 or 960 ms; shuffling histories reduced it to 0.03.Fig. S4 shows panels for increasing token history, with colours identifying eight movements; coordinates are fitted and arranged separately across panels and are not comparable.Source: C. Visualization of token histories · p. 20, Figure S4 · p. 21

A. Sensitivity to noise and electrode loss

  • At 32% noise, learned-token error increased 0.351 mm less than continuous-feature error; under electrode loss, the increases differed by at most 0.27 mm, with upper 95% confidence limits below 0.8 mm.These evaluations kept decoders fixed and compared increases from clean-input error.Source: A. Sensitivity to noise and electrode… · p. 20, A B C · p. 21
  • When one or two complete electrode arrays were silenced, SPAR token error increased 1.40 mm and 1.03 mm less than continuous-feature error, respectively (p = 0.020 for each).These comparisons used separate correction families for noise and electrode loss.Source: A B C · p. 21

B. Calibration and unseen recordings

The section tests recording-onset calibration and evaluates SPAR on unseen recordings, alongside emg2pose motion references. Refitting under recording-onset calibration improved both SPAR variants, while errors rose on faster unseen recordings and additional movements.

B. Calibration and unseen recordings

  • Without refitting, recording-onset calibration yielded errors of 11.688 mm with tokens and 11.736 mm with continuous features, under a mismatch with the per-window calibration used for fitting.Calibration in both analyses applied to one task recording rather than an entire session.Source: B. Calibration and unseen recordings · p. 22
  • After refitting under recording-onset calibration, SPAR error was 10.271 mm with tokens and 10.448 mm with continuous features; the token-minus-continuous difference was −0.177 mm.Both improved on per-window results, and the difference had a 95% confidence interval of [−0.336, −0.030] mm.Source: B. Calibration and unseen recordings · p. 22
  • On faster unseen digit recordings, token error was 18.31 mm and continuous SPAR error was 18.13 mm; on seven further unseen movements, errors rose to 16.3–47.6 mm, with tokens adding 0.17–0.71 mm.The faster recordings were evaluated without retraining.Source: B. Calibration and unseen recordings · p. 22

C. Motion and displayed trajectories

  • On sampled official-test windows, learned tokens achieved 28.00 mm error versus 29.65 mm for their constant-prediction baseline, while continuous features achieved 28.04 mm versus 29.63 mm for theirs.Velocity scores ranged from −0.020 to +0.009 across representations and were similar to the constant mean-velocity reference.Source: C. Motion and displayed trajectories · p. 22
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