EMG Tokenization Preserves Movement Information at a Fraction of the Bitrate

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EMG Tokenization Preserves Movement Information at a Fraction of the Bitrate

arXiv:2610.32674v1 [eess.SP] 23 Oct 2026

Raul C. Sîmpetru

, Amin Olamazadeh

, Devon Rohlf

, Vlad Cnejevici

, and Alessandro Del Vecchio

Electromyography (EMG) interfaces typically transmit either raw signals or continuous feature representations [5, 7, 11, 12, 13]. An alternative is to encode EMG signals as discrete tokens that index vectors in a learned codebook. At the receiver, these vectors are retrieved and passed to the pose decoder. Vector quantization (VQ) has previously been explored for EMG signal reconstruction [14], while more recent approaches have introduced learned token representations for general time series [15] and biosignals [16, 17]. In the context of hand-pose decoding, VQ-MyoPose uses vector quantization to encode ground-truth joint-angle trajectories and trains an EMG model to predict the resulting pose tokens [18]. EMG tokenization separates wearable encoding from receiver-side task decoding. We examine how converting continuous EMG features into discrete tokens affects hand-pose decoding accuracy, transmission bandwidth, memory requirements, and computational cost. We compare two approaches: a temporal encoder, shared across channels and pretrained to reconstruct EMG spectra, followed by vector quantization (Fig. 2), and SPAR, which applies vector quantization to an engineered Spectral–SpAtial Representation.1 Both are fitted without pose labels, and separate models are then trained to predict three-dimensional (3D) hand kinematics. To assess the effect of quantization, we compare each tokenized representation with its continuous Index Terms—electromyography, hand-pose estimation, vector counterpart using the same decoder architecture and training quantization, representation learning, compression procedure, with separate models fitted to each representation. We evaluate both tokenizers on high-density EMG (HD-EMG) I. I NTRODUCTION synchronized with 3D hand kinematics from nine participants URFACE electromyography (sEMG) is a non-invasive [12, 19], using personalized decoders trained and tested within method for measuring muscle activity [1] that is increas- each participant’s recording session. An adapted end-to-end ingly moving beyond laboratory settings, driven in part by its waveform convolutional neural network (CNN) based on our ease of use and growing commercial interest, from myoelectric previous work [11, 12] provides a raw-EMG reference. The prostheses [2] and wireless high-density amplifiers [3] to learned tokenizer is also evaluated on emg2pose [5], a public wristbands for computer input [4, 5]. benchmark of 16-channel wrist EMG and motion-captured Wireless sEMG wearables [3, 7, 8, 9] trade electrode hand poses from 193 participants, including participants unseen coverage against transmission bandwidth, even though motor during training. We also measure payload, memory, decoder unit activity can differ between regions of a single muscle cost (size and latency), and tokenizer execution time on a [10]. Compressing multichannel recordings could reduce bitrate Cortex-M55 microcontroller (Section S-I). while retaining information useful for movement decoding (Fig. 1). II. M ETHODS Abstract—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 CortexM55 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.

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This work was supported in part by the European Research Council (ERC) through the GRASPAGAIN project under Grant 101118089 and in part by the German Federal Ministry of Research, Technology and Space (BMFTR) through the BIONIK project under Grant 16SV9639, the EMGRoll project under Grant 16SV9306, and the NOE-EMY project under Grant 16SV9246, all to A. Del Vecchio. (Corresponding author: Alessandro Del Vecchio) The authors are with the Department of Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052 Erlangen, Germany Code is available at https://github.com/NsquaredLab/MyoJi.

A. Dataset and acquisition We used our previously collected dataset of synchronized sEMG and hand-movement recordings from 13 healthy participants (11 men and 2 women; age 25.9 ± 2.8 years) [12, 20]. The nine participants analysed for decoding (participants 1–9) 1 Fittingly, spar is German for “save”.

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Fig. 1: From high-density electromyography (EMG) recordings to a transmittable representation. A: Nine participants performed individual finger movements, grasping, and two- and three-finger pinches. Markerless hand tracking was recorded alongside surface EMG (sEMG) from 320 electrodes distributed across five grids. The lower band illustrates an eight-channel subset obtained by selecting every 40th channel from the 320-channel recording. B: Continuous EMG features and discrete tokens are used to train three-dimensional (3D) hand-pose decoders on a high-performance computing (HPC) system. Their decoding errors are compared using the same decoder architecture and training procedure within each pair. C: An assumed Bluetooth LE (BLE) 2M application throughput of 1.4 Mbit/s [6] supports up to 42 channels of raw 16-bit EMG at 2,048 Hz, and the 43rd exceeds the budget. Packed 10-bit tokens at 50 Hz would support 2,800 channels. These are payload-only calculations before application packet headers, not measured transmission or computational capacities (Section S-I-A; Fig. S1; Supplementary Data 1).

comprised seven men and two women. Eight were right-handed, therefore calibrated from its own first 500 ms, independently one was left-handed, and one had a visible physiological tremor of earlier data. Section III-D evaluates calibration at recording [12]. The other four participants were used only for tokenizer onset for SPAR. The encoder processes 160 ms windows fitting, never for decoding (Section II-D). The main decoding at 20 ms intervals, and four causal residual blocks give a analysis used eight movement tasks of approximately 40 s each, 480 ms receptive field (Fig. 2A). We call each 20 ms step, paced by a virtual hand on a monitor [12]: flexion and extension at which every channel emits one token, an update. After of each digit at 0.5 Hz, grasp opening and closing, and two- layer normalization, each 256-dimensional output is mapped and three-finger pinching. The experiments were approved to the nearest of 1,024 codebook vectors by squared Euclidean by the ethics committee of Friedrich-Alexander-Universität distance. The resulting index requires 10 bits when packed. Erlangen-Nürnberg (application no. 21-150-B) and conducted At the receiver, these vectors are retrieved, and the pose in accordance with the Declaration of Helsinki. All participants decoder estimates 3D hand kinematics from their history across provided written informed consent. channels. The first token with a complete receptive field is Monopolar sEMG was acquired from 320 electrodes in five available 980 ms after window onset (500 ms calibration plus grids (OT Bioelettronica SRL, Turin, Italy): three 8 × 8 grids 480 ms context), excluding computation, and subsequent tokens around the forearm and two 13 × 5 grids around the wrist, follow at 50 Hz (Section S-II-B). each with its final site unrecorded (64 electrodes) (Fig. 1A). Pretraining. The tokenizer is pretrained without kinematic Signals were sampled at 2,048 Hz with an EMG-Quattrocento labels on our high-density recordings and emg2pose [5], with amplifier (OT Bioelettronica). Five synchronized cameras the data separation specified in Section S-II-A. The encoder (DFK-37BUX287, The Imaging Source, Bremen, Germany) is trained to reconstruct, under a smooth L1 loss, the logrecorded the hand at 120 Hz, and DeepLabCut [21] and Anipose power spectrum of each mean-removed, Hann-tapered window [22] yielded 3D joint coordinates with a reported mean absolute in 64 nonzero-frequency bins up to 400 Hz. Training uses a localization error of 3 mm relative to manual annotations [23]. straight-through gradient estimator [24], a commitment loss, a penalty that discourages use of only a small subset of codebook entries, and exponential-moving-average codebook updates B. Learned spectral tokenizer (Section S-II-B). The learned tokenizer is a custom causal implementation of the vector-quantized variational autoencoder (VQ-VAE) framework [24], trained to reconstruct EMG spectra (Fig. 2). C. SPAR: spectral–spatial features and tokenization The same temporal encoder and codebook are applied to every EMG channel independently, across electrode layouts (Section S-II-B). Encoding. EMG is resampled from 2,048 to 2,000 Hz to match emg2pose, on which the encoder is also pretrained, and normalized per channel using the median and scaled median absolute deviation of the first 500 ms of each 3 s input window, with clipping at ±12 scale units. Each window is

SPAR directly computes local spectral–spatial features describing each electrode’s spectrum and coupling to neighbouring electrodes, as an alternative to learned per-channel spectral features (Section S-II-C, Fig. 3). Local patch. Each electrode defines a four-electrode patch within its grid: the centre, horizontal and vertical neighbours, and an auxiliary electrode. The auxiliary electrode contributes to the cross-spectral matrix and therefore affects its logarithm,

EMG TOKENIZATION PRESERVES MOVEMENT INFORMATION AT A FRACTION OF THE BITRATE - SÎMPETRU ET AL. 2026

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Fig. 3: Neighbourhoods and boundary handling of the spectral–spatial representation. Grey marks the centre electrode, red the horizontal and vertical neighbours, and blue the auxiliary electrode. At a boundary, an electrode on the opposite side of the centre replaces the missing neighbour (dashed arrow), and its coupling is set to zero after the matrix logarithm. Each band contributes the centre’s diagonal entry and the real horizontal and vertical couplings.

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where Xc,s,f,t contains the Fourier coefficients of the four signals and wf,t weights each frequency bin according to its relative contribution to the band’s power, computed across all Pointwise 1×1 Activation channels. A small diagonal regularization and an eigenvalue Depthwise Quantization Normalization floor keep the matrix logarithm defined, even for silent patches, yielding Lc,b,t = log Sreg Fig. 2: Learned electromyography (EMG) tokenizer and c,b,t . Related electroencephalography (EEG) methods also combine cross-spectral matrices with intermediate representations. A: A shared encoder processes logarithmic mappings [25, 26]. 160 ms EMG windows every 20 ms. Four residual blocks extend Features. From each logarithmic matrix, we extract three the receptive field to 480 ms, while a fixed codebook maps features: the diagonal entry of the centre electrode and the each 256-dimensional output to one of 1,024 tokens (10 bits). real parts of its couplings with the right and lower neighbours. Layer dimensions such as 32 → 256 denote the input and Across six frequency bands, this produces 18 features per output feature dimensions. Conv1D denotes a one-dimensional electrode. Features of missing neighbours are fixed at zero convolution, GELU the Gaussian error linear unit, LayerNorm layer normalization, and L2 the Euclidean distance. B: Example (structural zeros). Tokenization. The 18 feature components are standardized normalized EMG waveform spanning 480 ms (participant 1, electrode 1). C: Three of the 256 intermediate features (indices using statistics from each participant’s training windows, 1, 128, and 256) after the second residual block, shown at nine excluding the structural zeros. For each participant, k-means consecutive time points spaced 20 ms apart. D: The resulting clustering fits a codebook of 1,024 centroids to sampled training 256-dimensional feature vector, mapped to token identifier (ID) feature vectors without kinematic labels. The codebook is shared across electrodes, but not across participants (Sec93. Time zero in C corresponds to 480 ms in B. tion S-II-C). Each feature vector is replaced by the index of its nearest but no features are extracted directly from its entries. At grid centroid, requiring 10 bits when packed. The receiver restores boundaries, an electrode on the opposite side of the centre the corresponding centroid and re-applies the structural zeros. replaces the missing neighbour in the patch. The substitute The codebook remains fixed during pose-decoder training. still enters the cross-spectral matrix, but its coupling features Continuous SPAR uses the same standardized features without are set to zero after the matrix logarithm, so that no feature quantization. We also evaluate a 64-centroid codebook, requiring 6 bits per token (Section III-B; Section S-II-C). SPAR describes an absent neighbour (Section S-II-C, Fig. 3). Spectral matrices. Each causal 160 ms window is divided was defined for the monopolar electrode grids of our HDinto seven overlapping 64 ms Hann segments, spaced 16 ms EMG recordings and was not adapted to the bipolar emg2pose apart. Their Fourier coefficients are used to compute a 4 × 4 wristband. Codebook Lookup

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0.7 million parameters), applies convolutions to a five-array by Each of the nine participants contributes 64 training, 16 64-electrode arrangement in acquisition order before temporal validation, and 16 test windows of 3 s each across eight modelling. Tokenization is often motivated by compatibility with large movement tasks. Windows are divided chronologically within each task recording, with at least 1 s separating the training, pretrained sequence models. The Qwen3 language model [29], validation, and test blocks. Decoders predict 20 wrist-relative kept frozen and receiving codebook vectors through a trained 3D hand landmarks, and for the pose decoders only the final adapter, tests whether language-model pretraining helps EMG second of each window contributes to scoring: 50 complete decoding. Two controls replace the pretrained weights with hand-pose predictions at 50 Hz. The two test windows per random frozen weights or remove the backbone so that the movement therefore contribute two scored seconds (Fig. 5; adapter feeds the pose output directly (direct pose readout in Fig. 4A). Section S-II). Tokens also allow the decoder to change without changing The learned tokenizer was pretrained without kinematic the wearable: frozen TabPFN [30, 31], a pretrained tabular labels using data from all 13 participants, excluding the model, decodes SPAR from labelled examples supplied as validation and test windows of the nine participants used context, without training its weights on the task. The paired for decoding. SPAR feature standardization and codebook comparisons isolate the effect of quantization, whereas comfitting used only each participant’s training windows. These parisons between decoders evaluate complete pipelines. experiments assess personalized, within-session decoding, not generalization to new participants or sessions. To examine whether small quantization effects persist when tokenizer F. Communication and computational requirements fitting excludes decoding participants, a separate analysis fits The token payload rate is the product of channel count, tokenizers only on the four participants outside the decoding update rate, and bits per token. At 50 Hz, 320 channels cohort (Fig. S2A; Section S-III-A; Supplementary Data 4). require 20 kB/s with packed 10-bit indices or 32 kB/s in stored The learned representation is also evaluated on a deter- 16-bit arrays. Application headers and codebook memory ministic subset of windows from the official partitions of the are accounted for separately (Section S-I-A; Supplementary wrist-EMG emg2pose benchmark [5]. Its test subset covers 176 Data 1). Wireless capacity assumes 1.4 Mbit/s Bluetooth LE participants, including 20 unseen during tokenizer pretraining 2M application throughput [6], the ideal case of continuous oneand decoder training (Sections S-II-E and S-III-B; Figs. S2 way transfer of maximum-length (251-byte) packets [32, Vol. 6, and S3; Supplementary Data 4–7). Part B, Sec. 2.4] without retransmissions, including lower-layer overhead but excluding our application headers. Practical links E. Decoders and baseline comparisons achieve less. Decoder cost is measured as model size and 32-bit Sections S-II-D and S-II-E specify the architecture and floating-point (FP32) latency on an RTX 4090 graphics card training of every decoder. Each decoder is fitted separately (NVIDIA, Santa Clara, CA, USA). Microcontroller timing on to tokens and to their continuous counterpart with the same a NUCLEO-N657X0-Q board (STMicroelectronics, Geneva, architecture and procedure, so these pairs measure the cost Switzerland) tests the 20 ms token-generation budget, and of tokenization (Fig. 4C). For the learned representation, the separate checks test whether the optimized code reproduces the continuous input is the same encoder’s 256-dimensional output reference tokens and how pose accuracy changes at reduced before quantization, not the output of a separately trained electrode coverage (Section S-I). D. Evaluation protocol

continuous encoder. For SPAR, it is the standardized features without quantization (Section S-II). G. Representation visualization and pose retrieval We compare several decoder architectures to assess whether To visualize how tokens evolve during movement, Fig. 6A–C the effect of tokenization depends on decoder design. uses participant 1’s eight movement recordings. At each update, Raw-EMG waveform CNNs provide a reference for decoding the 320 SPAR tokens are replaced by their 18-dimensional performance without tokenization. We evaluate both a CNN codebook vectors. We concatenate the current representation adapted from our earlier work [11, 12] and the original CNN with those 120, 240, 360, and 480 ms earlier, then fit a threepublished in IEEE Transactions on Biomedical Engineering dimensional Uniform Manifold Approximation and Projection (TBME CNN) [12], retrained with its published preprocessing (UMAP) [33] using cosine distance. Movement labels and hand and an adapted training recipe (Section S-II-D). poses are not inputs to the UMAP fit. The causal temporal convolutional network (TCN) and TransThe two-dimensional display is constructed from this embedformer decoders [27, 28] and a third waveform CNN matched ding. Peaks in the measured mean fingertip-to-wrist distance to them each have approximately 7.5 million parameters and define repetition cycles and their normalized phase. For each use the same training budget. This allows us to compare input movement, we align and average its cycles, project its points representations while controlling for model size and training onto the plane of the mean trajectory, and reposition the group resources. Results for this matched waveform CNN are reported to avoid overlap. Thus, movement labels and pose-derived in Supplementary Data 2. phase influence the display, and distances between groups are The learned tokenizer encodes each channel independently. not interpretable. Panel C summarizes repetitions using phase To test whether a small decoder can recover spatial patterns, bins and smoothing, followed by periodic cubic interpolation our proposed decoder, a compact spatial CNN + TCN (about

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that explicitly closes the curves. Exact embedding and display over all 512 sign patterns [36], and statistical significance is settings are given in Section S-IV-C. assessed using the Holm-adjusted p-values. One-sided nonPose retrieval tests whether a representation carries pose inferiority p-values are doubled before Holm correction, so information without a trained decoder, and direction classi- the smallest attainable Holm-adjusted p-value is 0.016. HDfication tests whether it distinguishes opening from closing EMG comparisons without a specified secondary family are at the same hand closure. Both use all nine participants and reported as estimates with exact pointwise 95% confidence one SPAR representation per update, each computed from the intervals. The procedures assume independent participants and preceding 160 ms of EMG, without UMAP or concatenated symmetric differences. Secondary analyses are Holm-corrected history. For pose retrieval, queries are eligible updates whose within their own families (Sections S-II-F, S-V, and S-I-C). complete 160 ms analysis window lies within a test window, including updates before the final second scored for the pose III. R ESULTS decoders. We exclude the query’s own and adjacent cycles, find A. Averaged across decoders, quantization adds less than a the closest update in each remaining repetition cycle outside millimetre of error the training windows, and average the measured poses from the Tokenization. We assessed the accuracy cost of tokenization five closest cycles. Matching uses Euclidean distance between using paired token–feature comparisons. Averaged across feature or codebook vectors, or Hamming distance between decoders, tokenization changed error by +0.01 mm for SPAR token identifiers (IDs). Direction classification uses every in(95% confidence interval: −0.12 to +0.14 mm) and +0.45 mm cycle update as a query and matches it to updates at similar for the learned representation (+0.10 to +0.82 mm). Both inhand closure in other cycles (Section S-IV). creases were below the 1 mm bound (Holm-adjusted p = 0.016 for each; Fig. 4C). However, the bound could not be confirmed H. Robustness analyses for every decoder individually: for the learned representation, Simulated noise and electrode loss test whether quantization the upper 95% confidence limits reached 1.12 mm with the adds sensitivity to degraded inputs in decoders that are Transformer and 1.29 mm with Qwen3 (Supplementary Data 2). not retrained for them (Section S-V-A). We first changed For SPAR, decoding error varied across movements, but for the calibration procedure at evaluation without refitting the every movement the pointwise upper 95% confidence limit pipelines, testing sensitivity to a mismatch between training of the token-minus-continuous difference was at or below and evaluation. We then refitted the pipelines under the new 0.59 mm, below the 1 mm bound (Fig. 5B). These differences calibration procedure to assess performance when training also remained small when tokenizers were fitted exclusively and evaluation used the same procedure. Unseen recordings, on participants outside the nine-person decoding cohort. The not used to fit the evaluated SPAR pipelines, assess perfor- pose decoders were still trained separately for each decoding mance under changed recording and movement conditions participant, so this analysis tests tokenizer transfer rather (Section S-V-B). than generalization of the full decoding pipeline to unseen participants (Fig. S2A; Section S-III-A). emg2pose benchmark. On emg2pose, learned tokens and I. Outcomes and statistical analysis continuous features gave mean errors of 28.00 and 28.04 mm The primary outcome is mean Euclidean distance between across 176 test participants and three independently pretrained predicted and reference landmarks, in millimetres. Errors are encoders, a token-minus-continuous difference of −0.04 mm averaged across valid predictions and evaluated landmarks (95% confidence interval −0.16 to 0.07). The difference was within each participant, then across participants with equal +0.02 mm (−0.16 to 0.21) in the 20 participants unseen during weight. We evaluate 20 landmarks for HD-EMG and 16 for tokenizer pretraining and decoder training, and +0.04 mm emg2pose (Section S-II-E). (−0.49 to 0.56) in held-out same-day sessions from ten Quantization effects are participant-level paired differences: participants (Fig. S2B; Section S-III-B; Supplementary Data 4 token error minus continuous-feature error. Negative values and 6). These errors refer to the benchmark’s generic hand favour tokens. For HD-EMG, each participant’s error is model and are not directly comparable with the HD-EMG errors. averaged across the eight tasks and three decoder seeds before differencing (Fig. 4C). Movement-specific SPAR comparisons Holding each model’s final prediction before the scored interval assess whether these averages conceal differences across tasks fixed throughout that interval gave 29.65 mm for learned tokens and 29.63 mm for continuous features, and velocity R2 was (Fig. 5). Participants are the units of statistical analysis. We test near zero for both representations (Section S-V-C). Complete-pipeline accuracy. Representation and decoder whether tokens increase error by less than a 1 mm engineering choice produced larger differences in error than tokenization bound (a non-inferiority test [34]), a third of the 3 mm alone. The proposed spatial CNN + TCN achieved 10.8 mm localization error of the reference kinematics (Section S-II-F). with SPAR tokens and 10.9 mm with continuous SPAR features. We apply Holm correction [35] across four comparisons: With this decoder, SPAR tokens gave 2.4 mm lower error than an increase below 1 mm for SPAR and for learned tokens, learned tokens (95% confidence interval: 1.7 to 3.1 mm; Holmeach averaged within participant over its decoders; SPAR adjusted p = 0.016). Within SPAR, tokens of each electrode’s versus learned tokens with the proposed decoder; and nonown log band power gave 2.5 mm higher error than full SPAR inferiority of SPAR tokens to the adapted CNN with the 1 mm tokens (95% confidence interval: 1.6 to 3.4 mm), and tokens bound. Each uses an exact paired permutation (sign-flip) test

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Fig. 4: Hand-pose decoding accuracy, computational cost, and quantization effects. A: Unfiltered three-dimensional (3D) error over 20 wrist-relative landmarks, decoder parameters including frozen backbones, and 32-bit floating-point (FP32) decoder latency. Qwen3 [29] and TabPFN [30, 31] are frozen pretrained decoders, and TCN is a temporal convolutional network. Grey points are participant means over three seeds, and coloured symbols group means. Latency is the mean and standard deviation per complete-pose prediction (batch size one, RTX 4090), excluding feature extraction and tokenization (TabPFN also includes host-processor work). Dashed lines mark the 20 ms update interval and the retrained convolutional neural network (CNN) from IEEE Transactions on Biomedical Engineering (TBME CNN) [12]. Brackets compare the spectral–spatial representation (SPAR) with learned tokens in the proposed decoder (*, p = 0.016) and SPAR tokens with the adapted CNN (< 1 mm, p = 0.016). B: Stored-array payload for 320 channels before packet headers. The dashed line marks the assumed Bluetooth LE (BLE) 2M throughput of 175 kB/s [6]. Labels give stored types: unsigned (uint16) and signed (int16) 16-bit integers for tokens and raw electromyography (EMG), and FP32 for features. C: Token error minus continuous-feature error. Circles are participants, diamonds are means, and bars are 95% confidence intervals. Bold Pooled rows average the differences across decoders within each tokenizer, and both upper 95% confidence limits lie below the dashed 1 mm bound (p = 0.016 each). The four p-values in A and C are from exact paired sign-flip permutation tests, Holm-adjusted together (Section II-I).

of the matrix-logarithm diagonal alone, without couplings, 0.3 mm higher (0.1 to 0.5 mm; Holm-adjusted p = 0.008 each; Section S-III-C). The SPAR-token pipeline also met the

1 mm non-inferiority criterion relative to the adapted waveform CNN operating on raw EMG. With learned-token inputs, the proposed decoder had lower mean error than the matched

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Fig. 5: Decoded hand movements and movement-specific errors. A: Example predictions from participant 6. Traces span 4 s, and scoring uses the final second of each predefined test window. Black indicates measured movement, red spectral–spatial representation (SPAR) tokens, and dashed blue continuous SPAR. Predictions are smoothed with a causal One Euro filter for display only. Traces show the thumb-tip-to-pinky-base distance for the thumb, the fingertip-to-wrist distance for the other digits (its mean over fingertips for the fist), and the thumb-to-fingertip distance for the pinches (averaged over index and middle fingers for the three-finger pinch). Section S-V describes the predictions shown between scored seconds and the filter. B: Unfiltered three-dimensional (3D) error across 20 landmarks for each movement, averaged over nine participants and three seeds. Bars show group means with 95% confidence intervals, and diamonds identify participant 6. Supplementary Data 2 reports the paired comparisons.

TCN, matched Transformer, and frozen Qwen3. For Qwen3, pretrained weights gave lower mean error than random weights, but still higher error than the control without the backbone (Fig. 4A; Supplementary Data 2 and 3). Decoder cost. The proposed decoder combined lower mean error with fewer parameters than the matched temporal models. The waveform, temporal, and Qwen3 decoders all had mean inference latencies below the 20 ms update 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. TabPFN timing includes processing on the central processing unit, and every prediction reprocesses the labelled training context (Fig. 4A; Supplementary Data 3). B. SPAR tokens retain hand pose across repetitions A trained decoder can adapt to changes introduced by quantization. We therefore also tested whether tokens preserved pose-related similarity using a simple retrieval analysis: for each update, we found similar updates in other repetitions and averaged their recorded poses. Queries came from the test windows and matches from repetitions outside the training windows. When similarity was measured using the codebook

vectors identified by the tokens, pose-retrieval error increased by 0.09 mm with 1,024 codes and 0.22 mm with 64 codes relative to continuous SPAR (Fig. 6D). Matching token IDs directly with Hamming distance instead increased error by 0.92 mm. For the 1,024-code tokens, codebook-vector matching and Hamming matching used the same transmitted token IDs and differed only in whether matching accounted for distances between codebook vectors (Section S-IV). We also examined how tokens represented movement over time. For participant 1, hand closure varied along the visualized token-history trajectories (Fig. 6A–C), complementing our previous use of dimensionality reduction to identify spared motor dimensions [37]. To test whether tokens retained movement-direction information beyond hand closure, we separately classified opening versus closing at matched hand closure in a descriptive analysis that uses every in-cycle update as a query and the original representations rather than the plotted coordinates. Accuracy was 70% with dequantized tokens and 71% with continuous SPAR, compared with 55% for the majority-direction control (Section S-IV).

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Fig. 6: Hand-pose structure in spectral–spatial representation (SPAR) token space. A–C: One three-dimensional Uniform Manifold Approximation and Projection (UMAP) of participant 1’s token histories across eight movements. Each movement is projected separately onto its mean-trajectory plane and repositioned for display (Section II-G). Figure S4 shows how the projected trajectories change as token history increases from a single update to 960 ms. A: Movement identity, with icons indicating the active fingers. B: Hand closure normalized separately for each movement. C: Phase-aligned, smoothed repetitions (thin) and their mean trajectory (thick), with cycle starts near the open-hand pose (dots) and traversal direction (arrows). D: Pose retrieval for single updates in the test windows, matched against repetitions outside the training windows, using continuous SPAR, dequantized tokens, or token identifiers (IDs) in the original representation space. Thin lines show the nine participants and the thick line their mean. Dashed lines are descriptive references: disrupted token–pose alignment (11.3 mm, a mean of participant medians, for which 1,024-code tokens give 7.3 mm) and matching using measured poses (4.4 mm). The curves and the pose-space reference are phase-balanced means. Asterisks indicate increases over continuous SPAR (exact paired permutation (sign-flip) tests, Holm-adjusted across three comparisons; p = 0.043, 0.016, and 0.012). Retrieval, display-selection rules, and reference construction are detailed in Section S-IV.

C. Communication cost and embedded feasibility At 320 channels, stored token arrays required 32 kB per second of recording, a 41-fold reduction relative to raw EMG and a 36-fold reduction relative to continuous SPAR features.

Ideal 10-bit packing would reduce this to 20 kB/s (Fig. 4B; Supplementary Data 1). The learned encoder’s continuous output, 256 FP32 values per channel and update, was 512 times larger than its stored tokens. We benchmarked token generation

EMG TOKENIZATION PRESERVES MOVEMENT INFORMATION AT A FRACTION OF THE BITRATE - SÎMPETRU ET AL. 2026

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Fig. 7: Computational performance of electromyography (EMG) tokenization on a Cortex-M55 microcontroller. The spectral–spatial representation (SPAR) implementations were tested at 600 MHz with synthetic 2 kHz EMG. Timing includes windowing, normalization, feature extraction, codebook search, and token packing, but excludes acquisition, radio transmission, and pose decoding. A: Median compute time per update over 16 timed updates, after 16 untimed warm-up updates. Open symbols and dashed lines show the original C implementations, and filled symbols and solid lines the optimized ones. Every timed update at the marked SPAR channel limits met the 20 ms interval. B: Optimized SPAR time per channel by processing stage, with labels giving values at 320 channels. The dashed line shows time per channel from a linear fit of total time against channel count through the origin (Section S-I-C).

to assess whether it fits within the update interval. On the Cortex-M55, optimization increased SPAR’s tested capacity from 23 to 63 channels within the 20 ms interval (Fig. 7). The optimized learned tokenizer required 96 ms for one channel and did not meet this budget in the tested implementation. Run on a general-purpose computer, the optimized SPAR code reproduced over 99.9% of the reference implementation’s token assignments with negligible change in mean pose error (Section S-I-C). In a separate offline analysis, SPAR codebooks and decoders refitted on the first 63 electrodes (the first forearm array without its final corner electrode) achieved 12.5 mm with tokens, compared with 10.8 mm using 320 electrodes. The assumed Bluetooth LE 2M throughput supports only 42 channels of raw 16-bit EMG. The adapted CNN refitted on the first 42 electrodes had a mean error of 15.0 mm, compared with 12.5 mm for the 63-channel SPAR-token pipeline (adjusted p = 0.008). This is a comparison of complete pipelines with different electrode coverage and decoders, not an isolated quantization effect (Fig. S1; Section S-I-C; Supplementary Data 1). D. Sensitivity to noise, electrode loss, calibration, and unseen recordings Noise and electrode loss. Without retraining, we tested the decoders with simulated noise and electrode loss after a clean calibration interval, and compared the increase in error from clean to degraded inputs for tokens and continuous features. In every condition, the pointwise upper 95% confidence limit for the token-minus-continuous difference in these increases

was below 1 mm (largest 0.93 mm, SPAR at 32% noise), and three conditions showed smaller increases with tokens (Holm-adjusted p ≤ 0.031). Nevertheless, severe degradation affected SPAR more strongly than the learned representation, with or without quantization (Fig. S5; Supplementary Data 8; Section S-V-A). Calibration. Replacing per-window calibration with calibration at recording onset, without refitting, increased error by approximately 0.9 mm. The pipelines had been fitted under perwindow calibration, so this tested a mismatch between training and evaluation. After refitting standardization, codebooks, and decoders under onset calibration, errors reached 10.3 mm with tokens and 10.4 mm with continuous SPAR, both below the perwindow results. In these short recordings, calibration changes affected mean error more than quantization did (Section S-V-B). Unseen recordings. Without retraining, SPAR decoders reached approximately 18 mm on unseen 1.5 Hz digit recordings, compared with 10 mm on the 0.5 Hz test windows, while the token-minus-continuous difference remained small (+0.18 mm). On seven additional unseen movements, tokens had 0.2–0.7 mm higher error than continuous SPAR. The speed comparison changes both movement pace and whether the recording contributed training windows, so neither effect can be isolated (Section S-V-B). IV. D ISCUSSION Stored EMG tokens reduced the payload about 41-fold relative to raw EMG and 36-fold relative to continuous SPAR features, with small changes in hand-pose error. Averaged

EMG TOKENIZATION PRESERVES MOVEMENT INFORMATION AT A FRACTION OF THE BITRATE - SÎMPETRU ET AL. 2026

across decoders, these changes were 0.01 mm for SPAR and 0.45 mm for the learned representation (Fig. 4B–C). Both pooled increases were below the 1 mm bound. On emg2pose, mean differences between learned tokens and continuous features stayed below 0.05 mm in 176 test participants, including 20 unseen during training (Fig. S2B; Supplementary Data 4). Across the evaluated pipelines, representation choice, electrode coverage, calibration, and unseen recordings had larger effects on accuracy than tokenization (Figs. 4A and S1; Section S-V-B). Separating EMG encoding from pose decoding allows the decoder to be updated while the wearable encoder and codebook stay fixed (Fig. 1B). Transmitting a decoded pose can use less bandwidth, but places the task-specific decoder on the wearable. Earlier EMG vector quantization focused on signal reconstruction [14], and BioCodec used discrete biosignal representations for downstream tasks [16]. VQ-MyoPose learns tokens from joint-angle trajectories and predicts them from EMG [18]. Here, the token representation is fitted without pose labels, and the paired comparisons measure the accuracy cost of tokenization alongside its payload and computational costs. With clean inputs, the SPAR-token pipeline had lower mean error than the learned-token pipeline and met the 1 mm noninferiority criterion relative to the adapted raw-waveform CNN (Fig. 4A). Under severe signal degradation (strong noise or silenced electrode arrays), however, the learned representation performed better (Fig. S5). The two pipelines also differed in the data used to fit the tokenizer, input processing, and decoder training, so their relative performance cannot be attributed to spatial features alone. Within SPAR, each electrode’s own band power alone gave errors similar to the learned tokens, and replacing these features with the full SPAR patch features reduced error by 2.5 mm (Section S-III-C). Decoder complexity brought no consistent accuracy advantage. With learned-token inputs, the compact spatial CNN + TCN had lower mean error and fewer parameters than the TCN and Transformer decoders. Qwen3’s pretrained weights gave lower error than random weights, but removing the backbone gave lower error with less computation. TabPFN reduced error by a further 0.37 mm relative to the proposed SPARtoken decoder, at a cost of over two minutes per pose when every prediction reprocesses the training context (Fig. 4A; Supplementary Data 2 and 3). The compact decoder offered a more practical balance of accuracy and inference cost for continuous pose estimation. The retrieval analysis showed that tokens also retained useful pose information without a trained decoder. Nearest-neighbour retrieval error changed little when continuous features were replaced by codebook vectors on held-out repetitions, whereas matching token IDs by Hamming distance, which ignores distances between codebook vectors, produced larger errors (Fig. 6D). Opening and closing were also distinguishable at matched hand closure (Section S-IV). The trajectories in Fig. 6A–C visualize how tokens evolve over repetitions, using token histories, movement-specific projections, and phasealigned repetitions. Calibration and unseen recordings affected token and continuous-feature decoders similarly (Section S-V-B). Chang-

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ing calibration increased error, while refitting standardization, codebooks, and decoders under the new calibration improved both representations. Matching the calibration used in training therefore mattered more than whether the decoder received continuous features or tokens. On unseen recordings, absolute errors rose substantially while the difference between tokens and continuous features stayed small. Under the assumed Bluetooth throughput, on-device computation limited the channel count more than transmission did. The optimized SPAR implementation processed 63 channels within 20 ms, while the learned tokenizer exceeded that interval for one channel (Fig. 7). The 63-channel SPAR-token pipeline also had lower error than the 42-channel raw-EMG pipeline that fitted within the same throughput, although electrode coverage and decoding differed (Fig. S1). The hardware benchmark timed token generation. Acquisition, radio transmission, control, and power consumption were outside its scope (Section S-I-C). Compact models such as TinyMyo [38] and embedded graphics processors [39] offer an alternative through local inference. Token transmission instead keeps task-specific processing at the receiver, where the decoder can be changed without changing the wearable representation. The main HD-EMG results were obtained using personalized, within-session decoders for nine participants. Learned-tokenizer pretraining excluded the validation and test windows but included other windows from the same participants and sessions (Section S-II-A), and SPAR was evaluated within sessions with calibration from short recordings. Future work should test whether a fixed codebook stays valid across sessions, electrode re-donning, and clinical populations, and how token transmission performs in closed-loop control on a complete, power-limited wearable. V. C ONCLUSION EMG tokenization provides a compact interface between wearable sensing and three-dimensional hand-pose decoding. Using two representations fitted without pose labels, we showed that substantial payload reductions are possible with small changes in decoding accuracy. In personalized, withinsession experiments, stored token arrays reduced payloads approximately 41-fold relative to raw EMG, while mean error increases remained below 1 mm when averaged across decoders. Learned tokens also performed similarly to continuous features on emg2pose, including participants unseen during training. Across the evaluated pipelines, representation choice, electrode coverage, calibration, and unseen recordings affected accuracy more than quantization. The optimized SPAR implementation generated tokens for 63 channels within a 20 ms update interval on a Cortex-M55 microcontroller. Together, these findings support tokenization as a means of reducing communication demands while retaining information useful for movement decoding. By separating wearable encoding from task-specific processing, this approach allows hand-pose decoders to be updated or replaced at the receiver while the wearable encoder and transmitted representation remain fixed.

EMG TOKENIZATION PRESERVES MOVEMENT INFORMATION AT A FRACTION OF THE BITRATE - SÎMPETRU ET AL. 2026

ACKNOWLEDGMENT Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. The authors gratefully acknowledge the scientific support and high-performance computing resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität ErlangenNürnberg (FAU). The hardware is partially funded by the German Research Foundation (DFG). R EFERENCES [1] R. Merletti et al., “Editorial: Surface Electromyography: Barriers Limiting Widespread Use of sEMG in Clinical Assessment and Neurorehabilitation,” Frontiers in Neurology, vol. 12, Feb. 2021. DOI: 10.3389/fneur. 2021.642257 [2] D. Farina et al., “The extraction of neural information from the surface EMG for the control of upper-limb prostheses: Emerging avenues and challenges,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 22, no. 4, pp. 797–809, Jul. 2014. DOI: 10 . 1109 / TNSRE.2014.2305111 [3] G. L. Cerone, A. Botter, and M. Gazzoni, “A Modular, Smart, and Wearable System for High Density sEMG Detection,” IEEE Transactions on Biomedical Engineering, vol. 66, no. 12, pp. 3371–3380, Dec. 2019. DOI : 10.1109/TBME.2019.2904398 [4] P. Kaifosh and T. R. Reardon, “A generic non-invasive neuromotor interface for human-computer interaction,” Nature, vol. 645, no. 8081, pp. 702–711, Sep. 2025. DOI: 10.1038/s41586-025-09255-w [5] S. Salter et al., Emg2pose: A Large and Diverse Benchmark for Surface Electromyographic Hand Pose Estimation, Dec. 2024. DOI: 10.48550/ arXiv.2412.02725 [6] Bluetooth SIG, The Bluetooth low energy primer, Version 1.3.0, 2024. [7] R. C. Sîmpetru et al., “MyoGestic: EMG interfacing framework for decoding multiple spared motor dimensions in individuals with neural lesions,” Science Advances, vol. 11, no. 15, eads9150, Apr. 2025. DOI: 10.1126/sciadv.ads9150 [8] G. Rolandino et al., “HDE-array: Development and validation of a new dry electrode array design to acquire HD-sEMG for hand position estimation,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, pp. 1–1, Nov. 2024. DOI: 10.1109/TNSRE.2024.3490796 [9] G. L. Cerone et al., “Design and validation of a wireless body sensor network for integrated EEG and HD-sEMG acquisitions,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 30, pp. 61–71, 2022. DOI: 10.1109/TNSRE.2022.3140220 [10] D. Haller et al., “Voluntary Dissociation of Motor Unit Activity in the Vastii Muscles,” Journal of Neuroscience, vol. 46, no. 21, May 2026. DOI : 10.1523/JNEUROSCI.1982-25.2026 [11] R. C. Sîmpetru, M. März, and A. Del Vecchio, “Proportional and Simultaneous Real-Time Control of the Full Human Hand From HighDensity Electromyography,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 31, pp. 3118–3131, Jul. 2023. DOI: 10.1109/TNSRE.2023.3295060 [12] R. C. Sîmpetru et al., “Learning a Hand Model From Dynamic Movements Using High-Density EMG and Convolutional Neural Networks,” IEEE Transactions on Biomedical Engineering, vol. 71, no. 12, pp. 3556–3568, Dec. 2024. DOI: 10.1109/tbme.2024.3432800 [13] F. Rahimi et al., “Simultaneous Control of Human Hand Joint Positions and Grip Force via HD-sEMG and Deep Learning,” IEEE Access, pp. 1–1, May 2026. DOI: 10.1109/ACCESS.2026.3692583 [14] T. Grönfors, M. Reinikainen, and T. Sihvonen, “Vector quantization as a method for integer EMG signal compression,” Journal of Medical Engineering & Technology, vol. 30, no. 1, pp. 41–52, Jan. 2006. DOI: 10.1080/03091900500130872 [15] S. Talukder, Y. Yue, and G. Gkioxari, TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis, Jan. 2025. DOI: 10.48550/ arXiv.2402.16412 [16] K. Avramidis et al., “Neural codecs as biosignal tokenizers,” arXiv preprint arXiv:2510.09095, 2025.

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[17] K. Barmpas et al., “NeuroRVQ: Multi-scale biosignal tokenization for generative foundation models,” arXiv preprint arXiv:2510.13068v4, 2026. [18] R. Lovecchio et al., VQ-MyoPose: Movement tokenization improves decoding of hand kinematics from surface EMG wristbands, HANDS workshop manuscript, 2025. [19] M. Osswald et al., Task-Dependent Motor Unit Recruitment and Rate Coding Reveal Redistribution of Neural Drive in the Human Hand, Jan. 2026. DOI: 10.64898/2025.12.16.694568 [20] R. C. Sîmpetru et al., “Influence of spatio-temporal filtering on hand kinematics estimation from high-density EMG signals,” Journal of Neural Engineering, vol. 21, no. 2, Mar. 2024. DOI: 10/gtm4bt [21] A. Mathis et al., “DeepLabCut: Markerless pose estimation of userdefined body parts with deep learning,” Nature Neuroscience, vol. 21, no. 9, pp. 1281–1289, Sep. 2018. DOI: 10/gd249k [22] P. Karashchuk et al., “Anipose: A toolkit for robust markerless 3D pose estimation,” Cell Reports, vol. 36, no. 13, p. 109 730, Sep. 2021. DOI: 10.1016/j.celrep.2021.109730 [23] A. L. Cakici et al., “A generalized framework for the study of spinal motor neurons controlling the human hand during dynamic movements,” in Proceedings of the 2022 44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Jul. 2022, pp. 4115–4118. DOI: 10/grc7qj [24] A. van den Oord, O. Vinyals, and K. Kavukcuoglu, “Neural discrete representation learning,” in Advances in Neural Information Processing Systems, 2017. [25] M. Li et al., “Harmonized-multinational qEEG norms (HarMNqEEG),” NeuroImage, vol. 256, 2022, Art. no. 119190. DOI: 10.1016/j.neuroimage. 2022.119190 [26] C. Lopez Naranjo et al., “EEG functional connectivity as a Riemannian mediator: An application to malnutrition and cognition,” Human Brain Mapping, vol. 45, no. 7, 2024, Art. no. e26698. DOI: 10.1002/hbm.26698 [27] S. Bai, J. Z. Kolter, and V. Koltun, An empirical evaluation of generic convolutional and recurrent networks for sequence modeling, 2018. arXiv: 1803.01271 [cs.LG]. [28] A. Vaswani et al., “Attention is all you need,” in Advances in Neural Information Processing Systems, vol. 30, 2017. [29] Qwen Team, Qwen3 technical report, 2025. arXiv: 2505 . 09388 [cs.CL]. [30] N. Hollmann et al., “Accurate predictions on small data with a tabular foundation model,” Nature, vol. 637, pp. 319–326, 2025. DOI: 10.1038/ s41586-024-08328-6 [31] Prior Labs, TabPFN 3.5 model release, 2026. [32] Bluetooth SIG, Bluetooth core specification, version 6.3, May 2026. [33] L. McInnes et al., “UMAP: Uniform Manifold Approximation and Projection,” Journal of Open Source Software, vol. 3, no. 29, p. 861, Sep. 2018. DOI: 10.21105/joss.00861 [34] G. Piaggio et al., “Reporting of noninferiority and equivalence randomized trials: Extension of the CONSORT 2010 statement,” JAMA, vol. 308, no. 24, pp. 2594–2604, 2012. DOI: 10.1001/jama.2012.87802 [35] S. Holm, “A simple sequentially rejective multiple test procedure,” Scandinavian Journal of Statistics, vol. 6, no. 2, pp. 65–70, 1979. [36] A. M. Winkler et al., “Permutation inference for the general linear model,” NeuroImage, vol. 92, pp. 381–397, 2014. DOI: 10.1016/j.neuroimage. 2014.01.060 [37] R. C. Sîmpetru et al., “Identification of Spared and Proportionally Controllable Hand Motor Dimensions in Motor Complete Spinal Cord Injuries Using Latent Manifold Analysis,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 32, pp. 3741–3750, Oct. 2024. DOI: 10.1109/TNSRE.2024.3472063 [38] M. Fasulo et al., “TinyMyo: A tiny foundation model for flexible EMG signal processing at the edge,” arXiv preprint arXiv:2512.15729v2, 2026. [39] S. Pfenning et al., “Analysis of embedded GPU architectures for AI in neuromuscular applications,” IADIS International Journal on Computer Science and Information Systems, vol. 19, no. 1, pp. 1–14, Jun. 2024. DOI: 10.33965/ijcsis_2024190101

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Supplementary Material for: EMG Tokenization Preserves Movement Information at a Fraction of the Bitrate , Amin Olamazadeh

, Devon Rohlf

, Vlad Cnejevici

S-I. C OMMUNICATION AND EMBEDDED IMPLEMENTATION A. Payload and memory accounting

This work was supported in part by the European Research Council (ERC) through the GRASPAGAIN project under Grant 101118089 and in part by the German Federal Ministry of Research, Technology and Space (BMFTR) through the BIONIK project under Grant 16SV9639, the EMGRoll project under Grant 16SV9306, and the NOE-EMY project under Grant 16SV9246, all to A. Del Vecchio. (Corresponding author: Alessandro Del Vecchio) The authors are with the Department of Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91052 Erlangen, Germany

3D Error (mm)

The payload rate depends on the channel count, update rate, and bits per value. We generate tokens at 50 Hz and represent each index with 10 bits when packed or 16 bits in the stored arrays, whereas raw electromyography (EMG) consists of 16bit samples at 2,048 Hz. The assumed 1.4 Mbit/s application throughput [1] accommodates 42 raw-EMG channels or 2,800 packed-token channels before application headers. Lower-layer Bluetooth overhead is already included in this throughput assumption, and our 9-byte header per update adds a further 450 B/s. Codebook storage is accounted for separately because it does not contribute to the recurring payload. A 32-bit floating-point (FP32) codebook for the spectral–spatial representation (SPAR) occupies 72 KiB for 1,024 entries or 4.5 KiB for 64 entries, while the learned codebook occupies 1 MiB. Figure S1 relates payload to offline decoding error at the tested electrode counts, and Supplementary Data 1 lists the evaluated configurations, including stored and packed payloads, token-generation time, and decoder tensor memory. The units kB and MB are decimal, and KiB and MiB are binary. The tensor memory totals cover the listed model components rather than peak memory during execution. The emg2pose dataset contains 16 channels sampled at 2 kHz and stored as FP32 values, compared with the 320 channels of 16-bit EMG at 2,048 Hz in the high-density EMG (HD-EMG) dataset of the main text. On emg2pose, the learned-token stream requires 1.45 kB/s including per-update headers, compared with approximately 128 kB/s for raw FP32 EMG and 820 kB/s for FP32 continuous features (Fig. S3B). The calibration statistics and electrode descriptors used by the emg2pose decoder are sent separately, in a setup message of about 2.3 kB as text in our replay, and are not included in these rates. Only its 32 calibration values, a centre and a scale per channel, change between calibrations, which the per-window evaluation protocol repeats for every 3 s window.

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Fig. S1: Electrode coverage, error, and payload. Points show mean three-dimensional (3D) pose error across nine participants and three decoder initializations, with labels indicating electrode counts. Payload excludes headers and uses ideal 10-bit packing for tokens, 32-bit floating-point values for the continuous spectral–spatial representation (SPAR), and 16-bit integers for raw electromyography (EMG). The dashed line marks the assumed 175 kB/s Bluetooth LE (BLE) application throughput (BLE Limit). The 63-electrode SPAR and 42-electrode raw-EMG convolutional neural network (CNN) pipelines were refitted offline with different decoders. Supplementary Data 1 provides the full results.

B. Timing measurement scope HD-EMG decoders. Except for TabPFN, decoder timing starts with inputs already in graphics processing unit (GPU) memory and measures FP32 execution on an RTX 4090 graphics card (NVIDIA, Santa Clara, CA, USA) with automatic mixed precision and TensorFloat-32 (TF32) disabled. Each call recomputes the input context and predicts a complete hand pose. After warmup, we time 48 synchronized calls for each trained decoder and four complete-pose calls for TabPFN, whose timing also includes central processing unit (CPU) codebook lookup, feature summaries, principal component analysis (PCA), transfers, and prediction of every pose coordinate.

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Fitting and loading are excluded from these timings. The Board and host outputs agree in the tested configurations around reported standard deviations describe variation between calls, the 63-channel operating point, and the full accuracy evaluation while parameter counts omit buffers, PCA, and retained training was run on the host. context (Supplementary Data 3). Decoding with 63 electrodes. To measure the accuracy cost emg2pose end-to-end timing. This test replays recorded of reducing electrode coverage, we fitted a separate offline EMG through every processing step needed to produce a model using the first forearm array without its final corner pose prediction. We use one prespecified 16-channel recording electrode. Missing neighbours are replaced by the electrode on sampled at 2 kHz and, after a warmup run, time 100 updates the opposite side, and standardization, codebooks, and decoders covering preprocessing, transfers, feature or token generation, are refitted on training data with absent decoder channels packing and unpacking, codebook lookup, and pose prediction. masked. The resulting errors are 12.465 mm with tokens and Live acquisition, network transmission, and actuator time are 12.368 mm with continuous SPAR, a paired difference of excluded. For learned tokens, the median time from raw EMG 0.097 mm (95% confidence interval [−0.081, 0.284] mm; Holmto pose was 4.4 ms on a V100 GPU (NVIDIA) and 13.7 ms adjusted p = 0.26). Both representations have higher error on four CPU threads of the same compute node (Xeon Gold than their 320-channel versions (p = 0.012 each in the same 6134, Intel, Santa Clara, CA, USA, according to the cluster’s three-comparison family). Using the refitted standardization hardware inventory), both below the 20 ms update interval parameters and codebooks, the optimized implementation (Fig. S3C). TF32 was disabled during execution. running on the host computer reproduces 99.96% of reference Fig. S3C omits BioCodec, whose implementation re-encoded token IDs. its full signal history at every update rather than streaming. Raw EMG within the same throughput. The corresponding Learned-token identifiers (IDs) were identical across repeated raw-EMG control refits the adapted convolutional neural runs on each device, and 44 of 1,671,168 IDs (0.003%) differed network (CNN) on the first 42 electrodes, with its other inputs between CPU and GPU. set to zero. Its mean error exceeds that of the 63-electrode SPAR-token pipeline by 2.57 mm (95% confidence interval [0.95, 4.93] mm; Holm-adjusted p = 0.008). Holm correction C. Cortex-M55 and reduced-electrode validation covers two comparisons: the 42-channel raw-EMG CNN versus Microcontroller timing. For Fig. 7, we measured token genthe 63-channel SPAR-token pipeline, and the 42-channel versus eration on a NUCLEO-N657X0-Q board (STMicroelectronics, the 320-channel raw-EMG CNN. Because electrode coverage Geneva, Switzerland) running at 600 MHz with FP32 arithmetic, and decoder differ, these are comparisons of complete pipelines. caches enabled, and no neural accelerator. Each configuration Reduced codebook size. We also fitted the 64-code SPAR processes deterministic synthetic input at 2 kHz for 16 timed configuration separately, and its corresponding continuousupdates after warmup. The benchmark excludes acquisition, feature decoder achieved a mean error of 10.892 mm. Toradio transmission, and pose decoding. kens increase error by 0.137 mm (95% confidence interval A configuration meets the timing budget only if every update [−0.132, 0.391] mm; Holm-adjusted p = 0.258 across its two finishes within 20 ms and its token checksum matches that of comparisons with continuous SPAR and learned tokens). the same C code running on the host computer. The original SPAR implementation meets both conditions at 23 channels and S-II. I MPLEMENTATION AND TRAINING the optimized version at 63: the slowest 63-channel update takes A. Data separation 19.95 ms, whereas 64 channels reach 20.28 ms. The optimized implementation uses the CMSIS fast real Fourier transform HD-EMG acquisition follows the main Methods and the and a square-root calculation for the hypotenuse in the Jacobi dataset paper [2]. Learned-tokenizer pretraining used recordings eigensolver. Spectral feature extraction accounts for most of from all 13 participants, excluding the nine evaluated particithe processing time, followed by codebook search (Fig. 7B). pants’ validation and test windows but retaining other windows The optimized learned tokenizer requires 95.7 ms for a single from those participants and sessions. SPAR standardization and channel. codebook fitting instead used only each participant’s training To vary workload size, we use the first N electrode sites windows. In Section S-III-A, both tokenizers are fitted only on and repeat the 320-site layout when N exceeds 320. A patch the four participants outside the decoding cohort. member outside the first N sites is replaced by the centre For the wrist-EMG emg2pose benchmark [3], we formed electrode, and its coupling is masked, so small workloads still deterministic subsets of 3 s windows from the official training, form four-member patches. Band weights are recalculated for validation, and test partitions. Within each partition, we selected each workload, but participant 1’s 320-channel standardization recordings at evenly spaced indices in metadata order and then and codebook stay fixed. These workloads measure processing evenly spaced windows within each selected recording (at cost. The reduced-electrode models used to assess accuracy most 512 recordings and 8,192 windows for training, 256 are fitted separately, as described below. and 2,048 for validation, and 512 and 4,096 for testing). Numerical agreement. Alongside timing, we checked whether Removing duplicate recording/start pairs left 7,849 training, optimization preserved the reference tokens and their decoded 2,040 validation, and 4,095 test windows. The test subset covers poses. On the nine participants’ 320-channel test windows, 176 participants, including 20 who were unseen during both optimized SPAR running on the host reproduces 99.92% of tokenizer pretraining and supervised decoder training. Tokenizer reference token IDs with negligible change in mean pose error. pretraining used only official-training recordings, although most

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other test participants contributed different recordings to that 256 hidden units, GELU, and 64 outputs, predicts the EMG pool. spectrum from the encoder output. To construct its target, we The separate session evaluation used held-out same-day subtract the signal mean, apply a symmetric Hann window, and recordings from ten participants. These recordings were ex- take the first 64 nonzero-frequency bins of log(1+|rFFT(·)|2 ), cluded from both tokenizer and decoder training, whereas other where rFFT is the Fourier transform for real-valued input. The recordings from those participants, including a session with 160 ms window gives 6.25 Hz bin spacing and 64 bins up the same hand and movement stage, remained in the decoder to 400 Hz, with the zero-frequency bin omitted after mean training data and were available for pretraining. removal. Predictions are compared with these targets using smooth-L1 loss. During quantized training, a straight-through estimator passes B. Learned tokenizer gradients through nearest-code selection [5]. Encoder outputs Signal normalization. For each 3 s decoding window, the are also kept close to their assigned codebook vectors through first 500 ms provide a baseline and scale for each EMG the commitment loss channel. We subtract the channel’s lower median and divide by β 2 max(1.4826 MAD, 10−4 ), in each dataset’s stored amplitude Lcommit = ∥z − sg(eq )∥2 , (S1) D units, where MAD is the lower median absolute deviation [4], where z is the encoder output, D = 256, eq is its assigned and clip normalized samples at ±12 robust scale units. HD-EMG is resampled from 2,048 to 2,000 Hz, with different codebook vector, and β = 0.25. The stop-gradient operator sg filters for pretraining and decoding. Pretraining uses zero-phase prevents this term from updating the codebook. To discourpolyphase resampling, whereas decoding uses a causal Kaiser age assignments from concentrating in too few entries, we finite impulse response (FIR) filter so that it requires no future compute the entropy H of the mean soft assignment using a samples. We retain the causal filter’s 20 ms delay and do not softmax of negative distances with temperature 0.05 and add 0.1 max(0, log 256 − H)2 . This term penalizes effective use shift pose targets to compensate for it. Encoder architecture. The encoder in Fig. 2 processes each of fewer than 256 entries, a quarter of the codebook. The codebook is initialized with Lloyd’s k-means algorithm EMG channel separately. A temporal convolution with 32 filters, a kernel of 320 samples, and a stride of 40 reads (10 iterations) applied to sampled encoder outputs. During 160 ms of signal every 20 ms, and a Gaussian error linear unit quantized training, its vectors are updated by an exponential (GELU) activation and pointwise convolution then produce a moving average with decay 0.95, and entries whose movingaverage count falls below 0.5 are reinitialized from current 256-component feature vector. Four residual blocks extend the temporal context. Each encoder outputs. Reconstruction is scored only for tokens whose contains layer normalization, a depthwise temporal convolution 160 ms input window ends after the 500 ms calibration interval. with kernel 5, and pointwise convolutions that expand the Inference additionally requires a complete 480 ms context after feature dimension to 1,024 and reduce it to 256, with a calibration. Numerical precision and continuous controls. Each token– GELU activation between them and no dropout. The depthwise feature comparison uses matching computation settings. Preconvolution processes each feature separately and uses only computed continuous features are stored in FP32 for emg2pose current and preceding inputs. After the residual blocks, a final and the proposed HD-EMG decoder, whereas the matched layer normalization precedes the nearest-vector search in the HD-EMG decoders and Qwen use features rounded to 16-bit 1,024×256 codebook. The encoder has 2.13 million parameters floating-point values with mixed-precision execution. TF32 and a 480 ms receptive field. convolutions are permitted during emg2pose feature precomBecause this context starts after the 500 ms calibration putation, while the FP32 runtime benchmarks disable TF32. interval, the first token with a complete receptive field becomes In every paired control, the continuous features come from available 980 ms after window onset, excluding computation. the same encoder trained with vector quantization (VQ), with Pretraining data and optimization. Pretraining alternates quantization skipped, rather than from a separately trained between HD-EMG and the emg2pose training subset. The encoder. encoder first learns spectral reconstruction for 50,000 steps without quantization. After codebook initialization, training continues for 250,000 quantized steps (seed 260905). Both C. SPAR feature extraction stages use AdamW with a constant learning rate of 3 × 10−4 , Neighbourhood construction. SPAR describes each electrode β = (0.9, 0.999), weight decay 0.01, and gradient-norm together with nearby electrodes in the same grid. Electrode clipping at 10. We use 2 s crops in batches of two, reduced to indices run row by row through three 8 × 8 forearm grids one for sources with 64 or more channels, with FP32 arithmetic and two 13 × 5 wrist grids, with the final site of each wrist and TF32 matrix products allowed. grid unrecorded. Each patch contains four distinct electrodes: Input augmentation is applied after the reconstruction targets the centre, an auxiliary electrode, and horizontal and vertical are computed, so the targets stay unaugmented: each channel neighbours (Fig. 3). is multiplied by a log-normal gain (σ = 0.2), and its polarity The horizontal and vertical neighbours are normally to the is flipped with probability 0.5. right and below the centre. At a grid boundary, a missing Reconstruction objective and codebook updates. A twoneighbour is replaced by an electrode on the opposite side of layer reconstruction network, comprising layer normalization, the centre, using the left electrode instead of the right or the

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upper electrode instead of the lower. The auxiliary electrode is the unused left neighbour when available and otherwise the unused site with the smallest sum of absolute row and column offsets from the centre, with ties resolved first by row index and then by column index. Patches never cross grid boundaries. A substituted neighbour contributes to the spectral calculation, but its retained coupling is set to zero after the matrix logarithm. Across the 320 electrodes, this yields 270 horizontal and 286 vertical couplings, giving 5,256 valid features in a layout of 5,760 with 504 structural zeros. Spectral features. SPAR uses the same causal resampling from 2,048 to 2,000 Hz and the same per-window normalization as the learned tokenizer (Section S-II-B). For each patch, the 160 ms window is divided into seven overlapping 64 ms segments starting 16 ms apart. Each segment is multiplied by a symmetric Hann window and Fourier transformed without zero padding, after which the spectrum is grouped into six bands: 20–40, 40–60, 60–100, 100–160, 160–250, and 250– 500 Hz. Each band includes its lower bound and excludes its upper bound. At 2 kHz sampling, the 128-point transform gives 15.625 Hz bin spacing, so these bands contain 1, 1, 3, 4, 5, and 16 bins, respectively. The first two therefore contain only the 31.25 and 46.875 Hz bins, respectively, but their cross-spectral estimates still average over all seven segments. Within a band, frequency bins are weighted by their relative contribution to power. We obtain these weights by averaging power over segments, summing over recorded channels, and normalizing within the band. The resulting cross-spectral matrix describes the four electrodes and their spectral relationships. Before computing its matrix logarithm by eigendecomposition, we enforce Hermitian symmetry by averaging the matrix with its conjugate transpose, add 10−6 times its largest diagonal entry to every diagonal element, then add 10−8 times the new largest diagonal entry, and floor the eigenvalues at 10−12 . Each logarithmic matrix contributes three real features: the centre’s diagonal entry and the real parts of its couplings to the horizontal and vertical neighbours. The six bands therefore give 18 features per electrode. Because the logarithm is applied to the matrix rather than to individual entries, the diagonal feature is not simply log band power, and the features also depend on cross-spectral phase relationships. Standardization and quantization. We standardize each of the 18 components using its mean and population standard deviation across training electrodes and updates, with the standard deviation floored at 10−4 . Entries fixed at zero because of missing neighbours are excluded from these statistics. These structural zeros are restored before quantization and after codebook lookup. For each participant, k-means with 40 Lloyd iterations and seed 260911 fits 1,024 centroids to a random subset of training feature vectors. The fitting budget is 128 vectors per centroid. Each standardized vector is assigned to its nearest centroid using a distance calculation that includes the structural zeros. We store codebooks as FP32 values and token indices as unsigned 16-bit integers (uint16). The 64-entry codebook is fitted with the same procedure and seed, and the pose-retrieval analyses use the same fitting procedure.

D. HD-EMG pose decoders Within each token-versus-continuous comparison, we match decoder architecture, targets, initialization, and training procedure (Table S1). Neural decoders are fitted with three seeds whose errors are averaged within each participant, whereas TabPFN keeps one pretrained network and varies its ensemble seeds. The matched decoders, the spatial CNN with a temporal convolutional network (TCN), and Qwen predict coordinates standardized with training-only means and population standard deviations floored at 10−4 . TabPFN and the adapted CNN use coordinates in millimetres, and the CNN published in IEEE Transactions on Biomedical Engineering [2] and retrained here (TBME CNN) predicts training-only min–max-scaled coordinates. Each 3 s window supplies 100 updates, from 1.02 to 3.00 s after its start, and the final 50 are scored, so the first scored prediction sees 51 updates and no learned representation with an incomplete receptive field enters a decoder. Transformers and Qwen3 use causal attention, TCNs pad causally with zeros, and TabPFN averages only the available history. Additional decoder inputs. Auxiliary inputs differ across decoders. The emg2pose decoder receives calibration statistics and electrode descriptors, the matched HD-EMG temporal decoders receive electrode-geometry descriptors with constant calibration inputs, and Qwen receives electrode-geometry descriptors without calibration inputs. The proposed HD-EMG decoder and TabPFN use neither. Each electrode descriptor has 14 components: centre coordinates (normalized grid row, column, and grid index for HD-EMG; position on the unit circle in acquisition order for the emg2pose band), an orientation vector (unit length when known, zero otherwise), log spacing, two flags for known coordinates and orientation, and a five-way measurement-type indicator. Calibration inputs comprise each channel’s log scale relative to the across-channel mean log scale, that mean, and the channel’s calibration median divided by its scale, clipped at ±12. A learned projection maps them to 32 values that are concatenated with the pooled electrode features, and the constant-calibration controls use centre 0 and scale 1. These inputs are supplied only to the decoders, leaving the tokenizers unchanged. E. emg2pose decoder and quantizers The emg2pose comparisons use the data partitions and pretraining data described in Section S-II-A. Results are reported in Section S-III-B. All representations in Table S2 use the emg2pose Transformer and training procedure specified in Table S1, with three initializations. Learned features and their codebook vectors enter the decoder directly. Learned linear projections map the four values of PCA or finite scalar quantization (FSQ), the 67 engineered values, or the 128-dimensional sum of BioCodec codebook vectors to the common input dimension. During pose inference, these representations are used without reconstructing the original encoder output. PCA and FSQ use the fixed reference encoder (seed 260905) and are fitted on each protocol’s training partition without pose labels. Only the paired learned-token comparison is repeated across three

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TABLE S1: Pose decoders. Architecture, training, and trainable parameters. Neural decoders use AdamW with weight decay 0.01 and gradient-norm clipping at 1 unless their row states otherwise. TCN, temporal convolutional network; CNN, convolutional neural network; GELU, Gaussian error linear unit; MLP, multilayer perceptron; SPAR, spectral–spatial representation; PCA, principal component analysis; TBME, IEEE Transactions on Biomedical Engineering; EMG, electromyography; LR, learning rate; SWA, stochastic weight averaging; MSE, mean squared error; FP32, 32-bit floating point; M, million. Decoder

Architecture

Matched TCN

Learned encoder features or codebook vectors; width 404; geometry-aware pooling (four slots, four heads); 7 causal blocks, kernel 2, dilations 1–64; temporal dropout 0.1; up to 100 updates (2 s) of context

Matched Transformer Matched waveform CNN Spatial CNN + TCN (proposed)

Adapted waveform CNN [2, 6]

Retrained TBME CNN [2]

Qwen3 variants

TabPFN

emg2pose Transformer

Training and checkpoint

Smooth-L1 ; 15,000 steps of two windows sampled with replacement, scoring the final second of each; 500-step warmup to LR 3 × 10−4 , cosine decay to 3 × 10−6 ; seeds 260911–260913; earliest checkpoint with the lowest validation error; 16-bit mixed precision As the matched TCN but width 468; 2 pre-normalization layers, As the matched TCN 4 heads, feed-forward 936, causal mask Adapted CNN architecture with dropout 0.1 As the matched TCN, on 156.25 ms waveform windows ending at the scored updates 1×1 convolution to 64; two spatial convolutions over five groups Smooth-L1 ; batches of two windows; LR 3 × 10−4 ; of 64 electrodes in acquisition order (32 filters, GELU, instance up to 40 epochs, stopping after 6 without improvement; normalization; 5 × 32 with dilation (1, 2) and circular padding, lowest validation error; FP32 then 5 × 10); 7 causal temporal blocks (kernel 2, dilations 1–64, MLP width 128, dropout 0.1); head 64→128→128→60; structural zeros reapplied for SPAR 156.25 ms raw EMG and a 20 Hz low-passed copy, standardized Coordinate L1 in mm; AMSGrad, weight decay 0.32, no gradient clipping; 150 epochs of 10,000 endpoints, per grid and window; dropout 0.20 batch 64; input noise σ = 0.1; OneCycle from 10−4 to 3.16 × 10−3 until 75 %, then SWA with LR annealed to 10−4 in five epochs; lowest validation error among epoch checkpoints and averaged weights; 16-bit mixed precision Published architecture and preprocessing: 93.75 ms windows, Adapted recipe: L1 on training-only min–max-scaled notch filter, raw and low-pass inputs, per-grid and per-window targets; AMSGrad; 50 epochs; batches of 64 min–max normalization accumulated to 512; OneCycle peaking at 10−2.5 ; original, 5 dB-noise and magnitude-warped copies; earliest checkpoint with the lowest validation error; 16-bit mixed precision Adapter: electrode features to 64 dimensions, geometry-aware Matched schedule (loss, steps, LR, seeds, and pooling (four slots, four heads), layer normalization, linear checkpoint as the matched TCN); only adapter and map to 1,024, layer normalization, scaling by 0.02; layer- head trained; bfloat16 autocast with 32-bit trainable normalized linear pose head; Qwen3-0.6B-Base frozen, as weights pretrained weights (token and continuous inputs), random weights (tokens), or removed (tokens, current update only); tokens are never read as text SPAR codebook vectors or continuous features with trailing No gradient-based fitting; labelled context of 3,200 means over 100 ms, 500 ms, and 2 s, reset at each window; training updates (the final second of 64 windows), structural zeros removed; PCA to 128 components fitted per whose features, like those of the queries, contain no participant and input on training data (seed 260921); one lagged pose coordinates; ensemble seeds regressor per pose coordinate, eight ensemble members 260911–260913 Identity or linear input map to width 256; geometry-aware Coordinate MSE + 0.1× velocity MSE; batches of 16 pooling (eight slots); 2 layers, 4 heads, causal mask, dropout windows; LR 3 × 10−4 ; up to 50 epochs, stopping 0.1, sinusoidal position encoding, up to 100 updates (2 s) of after 8 without improvement; seeds 260826–260828; context lowest participant-balanced validation error

pretrained encoders (seeds 260905–260907), averaging their errors rather than their predictions. Coordinate and velocity prediction errors are divided by the standard deviations of the corresponding training targets before the loss is computed. BioCodec’s training budget differs from the learned tokenizer’s 300,000 steps (Section S-II). Pose targets are wrist-relative landmarks on the benchmark’s generic hand model, so their absolute errors are not directly comparable with HD-EMG errors. We score 16 landmarks after excluding the wrist and four fixed metacarpophalangeal (MCP) anchors at the finger bases. Coordinates are normalized by the generic hand model’s mean wrist-to-MCP distance, and errors are converted back to millimetres using that same distance. Mean Euclidean landmark error is averaged across valid predictions and evaluated landmarks within each participant, then across participants with equal weight. Tokenization

Parameters 7.55 M

7.45 M 7.49 M 704,700 (689,468 with SPAR)

7.49 M

27.4 M

0.40 M

frozen

2.5 M total

effects are paired participant-level differences in token minus continuous-feature error, with negative values favouring tokens. F. Statistical implementation The statistical analyses use participants as the independent observations, with one error difference per participant for each comparison. Windows and training seeds contribute to these participant summaries rather than increasing the sample size. For HD-EMG, the tests enumerate all 512 sign-reversal patterns across the nine participants. Primary comparisons. Holm correction [9] is applied across four comparisons. The first two test whether SPAR tokens and learned tokens increase error by less than 1 mm relative to their continuous features. For each of these two, the participant’s token-minus-feature difference is first averaged with equal weight over the decoders using that representation: the proposed decoder and TabPFN for SPAR, and the proposed decoder,

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TABLE S2: Representations compared on emg2pose. Bits per channel and update, assuming packed indices for tokens and 32-bit floating-point storage for continuous features, before headers. VQ, vector quantization; PCA, principal component analysis; FSQ, finite scalar quantization; GELU, Gaussian error linear unit; MSE, mean squared error; LR, learning rate; RMS, root mean square; EMG, electromyography; FP32, 32-bit floating point; M, million parameters. Representation

Configuration

Fitting

Bits

Learned tokens

VQ-pretrained encoder; 1,024-entry codebook of 256-dimensional vectors Same encoder, quantization skipped Reference encoder, four components; 4/4/4/4, 8/8/4/4, or 16/16/16/16 levels Reference encoder; 256→128→4 projection with GELU, bounded by tanh; 8/5/5/5 levels (1,000 combinations)

Section S-II-B

10

Continuous features Quantized PCA FSQ [7]

Engineered k-means

Engineered continuous BioCodec [8]

Supervised continuous

67 features of the mean-removed preceding 480 ms: log(1 + x) of the RMS, mean absolute value, mean absolute successive difference, and 64 Hann-windowed band powers The same 67 features First 1, 3, or 6 residual codebooks (256 entries of dimension 128) of one six-codebook codec with forward-only recurrence; EMG causally downsampled to 1 kHz with its 10 ms delay retained Same encoder architecture, random initialization

– Axes from sampled training vectors; uniform levels between the 0.1st and 99.9th training percentiles Straight-through rounding with a temporary 4→128→256 reconstruction network, discarded afterwards; MSE, AdamW, LR 3×10−4 , weight decay 0.01, 5,000 steps of 1,024 vectors; validation reconstruction error selects the checkpoint Training-only standardization; 256 or 1,024 centroids, 40 Lloyd iterations; no pretrained encoder

Training-only standardization Trained from scratch on the pretraining recordings: 40,000 FP32 steps of 32 single-channel 2 s crops; Adam, LR 5 × 10−4 , β = (0.5, 0.9), 10,000-step warmup and cosine decay; original time-domain (×0.2), frequency-domain, and commitment (×2) losses; final checkpoint; 3.19 M parameters Trained jointly with the decoder on pose labels, without spectral pretraining or quantization

8,192 8, 10, 16 10

8, 10

2,144 8, 24, 48

8,192

TCN, Transformer, and Qwen3 for the learned representation. multiple comparisons. Unless a secondary test family is The third comparison is SPAR versus learned tokens using specified, comparisons outside the primary family are reported the proposed decoder, and the fourth tests whether SPAR as estimates with these intervals. tokens with that decoder exceed the mean error of the adapted Sensitivity analysis. Supplementary Data 2 also reports a waveform CNN by less than 1 mm. single-step studentized max-T correction [12] across all 76 Each bounded comparison is a non-inferiority test [10], HD-EMG comparisons, which combine tokenization contrasts using a one-sided permutation (sign-flip) test of a mean with baseline comparisons. Each sign pattern was applied to difference of at least δ = 1 mm against a smaller mean. For all comparisons at once, and the largest absolute studentized these comparisons, we double each one-sided p value before mean difference formed the reference distribution. applying Holm correction, and a comparison is significant For emg2pose, the 12-comparison family uses a Monte Carlo when its adjusted p value is below 0.05. All four comparisons max-T test with 10,000 sign patterns, including the observed have Holm-adjusted p = 0.016, the smallest value attainable pattern, each applied consistently across comparisons. Pointwith four tests and nine participants. When the bound is wise confidence intervals are formed from 10,000 bootstrap reduced to δ = 0.5 mm, the learned-token comparison is no samples by resampling participants with replacement. Intervals longer significant (Holm-adjusted p = 0.71), while the other for the 10- and 20-participant cohorts are descriptive. Any two non-inferiority comparisons and the SPAR-versus-learned additional test families are specified alongside their results comparison remain significant (Supplementary Data 2). below. Bound. The 1 mm bound is a third of the 3 mm mean Supplementary Data 2 contains all HD-EMG comparisons, localization error reported for the reference kinematics [11]. It including those not plotted, and Supplementary Data 5 contains is also comparable to the change in a participant’s error when the 12 emg2pose comparisons. the same decoder is retrained with a different seed, which averages 0.2–0.3 mm for the proposed decoder and 0.6–1.0 mm S-III. Q UANTIZATION ACROSS PARTICIPANTS AND for the matched TCN and Transformer. METHODS Intervals. Confidence intervals are obtained by subtracting A. Tokenizers fitted on separate participants candidate mean differences from the participant values and To test whether small tokenization effects also occurred after retaining those candidates not rejected by the two-sided fitting tokenizers on different people, we fitted the learned permutation (sign-flip) test. This procedure assumes symmetry tokenizer and SPAR standardization and codebook exclusively of the differences around the tested mean. We use it for all on four participants outside the nine-person decoding cohort, nine-participant intervals in the main text and supplement, then froze them. Personalized pose decoders were subsequently including intervals around individual models’ mean errors in trained for the nine evaluated participants using the main Fig. 5B and Fig. S5. For intervals around models’ mean errors, protocol. Mean tokenization effects were small (Fig. S2A). the calculation uses participant errors and assumes symmetry This analysis tests tokenizer transfer across participants while about their mean. retaining personalized pose decoding. These intervals are pointwise and are not adjusted for

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A

B

Tokenizers fitted on separate participants

emg2pose test cohorts

Official-test subset (176)

SPAR

Unseen participants (20)

Learned

Held-out sessions (10) −0.5

0.0

Tokens − Continuous (mm)

0.5

−0.5

0.0

0.5

Tokens − Continuous (mm)

Fig. S2: Quantization effects across participants. Points show mean token-minus-continuous error, with negative values favouring tokens. A: Tokenizers were fitted on four separate participants, and personalized decoders were evaluated on nine participants. Bars show 95% confidence intervals. Two-sided tests of a zero token-minus-continuous difference gave Holmadjusted p = 0.32 for the spectral–spatial representation (SPAR) and p = 0.12 for the learned representation. B: Errors are averaged across three pretrained encoders and three decoder initializations. Bars show pointwise 95% participant-bootstrap intervals, with participant counts in parentheses. Unseen participants are part of the official test cohort, while held-out sessions were recorded on the same day. Supplementary Data 4 provides the values.

with the same frequency weights derived across all recorded Across 176 test participants and three independently pre- channels but without a four-electrode cross-spectral matrix trained encoders, learned tokens and continuous features or the matrix logarithm. The second keeps the six matrixachieved mean errors of 28.00 and 28.04 mm (Supplementary logarithm diagonal entries and drops the couplings. Because Data 6). Small paired mean differences were also observed each diagonal entry depends on the whole patch matrix, it still in the 20 participants unseen during tokenizer and decoder reflects neighbouring electrodes. Windows, standardization, training and in held-out same-day sessions from ten participants 1,024-code codebook fitting, decoder, seeds, and training are (Fig. S2B). The direction of the effect varied across the three otherwise unchanged (Section S-II-C). With tokens, mean errors were 13.31 mm for log band power, encoders. Alternative quantizers that require encoder features 11.12 mm for the matrix-logarithm diagonal, and 10.81 mm use the reference encoder (Section S-II-E). for full SPAR. With continuous features, they were 13.06, Figure S3 compares these alternatives in accuracy, trans11.18, and 10.95 mm. Relative to full SPAR tokens, log band mission rate, and processing time. At 10 bits, FSQ did power increased error by 2.50 mm (95% confidence interval not differ significantly from learned tokens, while quantized [1.60, 3.36]) and the diagonal by 0.31 mm ([0.15, 0.50]; HolmPCA and engineered k-means had higher errors (adjusted adjusted p = 0.008 each). Most of the improvement over p < 0.01). Separately trained BioCodec also showed no each electrode’s own log band power was retained with significant error difference at its evaluated operating point, the matrix-logarithm diagonal alone, and adding the explicit but its six-codebook configuration uses 48 bits, outside the couplings gave a smaller further improvement. Relative to matched 10-bit comparison. FSQ is therefore a viable quantizer continuous features, tokenization changed mean decoding error for features of a VQ-pretrained encoder. The PCA and FSQ by +0.25 mm ([0.02, 0.50]) for log band power, −0.06 mm comparisons change the quantizer while keeping the VQ([−0.25, 0.12]) for the diagonal, and −0.13 mm ([−0.32, 0.05]) pretrained encoder fixed. for full SPAR (Supplementary Data 9). The held-out participant and same-day session tests apply to the learned representation, while SPAR was evaluated only S-IV. P OSE RETRIEVAL AND MOVEMENT DIRECTION under the within-session HD-EMG protocol. Supplementary A. Pose retrieval Data 5 lists all 12 alternative-method comparisons with their joint max-T correction, including settings not plotted, and For the analyses in this section, each recording is tiled with Supplementary Data 6 provides errors for all cohorts. HD-EMG 3 s windows at a 2 s stride. Each window is normalized from comparisons and decoder costs are reported in Supplementary its own first 500 ms and contributes 100 updates, which gives Data 2 and 3. Motion baselines are given in Section S-V-C, a continuous 50 Hz stream without duplicate updates. Pose and payload and timing in Section S-I. retrieval tests whether similar EMG representations correspond to similar hand poses without training a pose decoder. We identify movement cycles from peaks in low-pass-filtered C. SPAR feature ablation measured mean fingertip-to-wrist distance, using poses to define To identify which SPAR features contribute to decoding, we cycle membership and phase but not to normalize features or refitted the nine-participant SPAR pipeline with six values per fit codebooks. electrode instead of 18. The first descriptor is the logarithm of Queries are updates whose 160 ms analysis window lies each electrode’s own power in the six SPAR bands, computed inside a test window (1,755–1,875 per participant), not only B. emg2pose comparisons

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A

B

Decoding accuracy

C

Transmission

Computation

ref.

Continuous features

*

FSQ (10 bits)

n.s.

Quantized PCA (10 bits)

**

Engineered k-means (10 bits)

**

BioCodec (48 bits)

n.s. 0.0

0.3

0.6

Error Difference (mm)

Raw EMG

Learned tokens (10 bits)

V100

20 ms

CPU

1

10

100

Data Rate

(kB/s)

Omitted 1k

3

10

Replay Latency (ms)

30

Fig. S3: Accuracy, transmission rate, and processing time on emg2pose. Rows identify the same method across panels. A: Error differences of finite scalar quantization (FSQ), quantized principal component analysis (PCA), and the other alternatives relative to learned tokens from the reference encoder. Positive values indicate higher error. Bars show pointwise 95% participantbootstrap intervals over 176 participants and three decoder initializations. Marks use max-T correction across 12 comparisons: * p < 0.05, ** p < 0.01; n.s., not significant. This comparison uses one encoder, whereas Fig. S2B averages three. B: Data rates for 16 channels at 50 Hz include 9-byte headers, with the dashed line marking raw electromyography (EMG) stored as 32-bit floating-point values at 128.45 kB/s. C: Median processing time from recorded EMG to pose output over 100 updates on a V100 graphics card (NVIDIA) and on four threads of a central processing unit (CPU), relative to the dashed 20 ms interval. BioCodec timing is omitted (Section S-I-B). Supplementary Data 5 provides all values.

the final second scored for the pose decoders. Candidates come own and adjacent cycles, gives similar token effects: +0.07, from repetition cycles that do not overlap any training window +0.21, and +0.84 mm (Holm-adjusted p = 0.012 each). used to fit SPAR standardization and codebooks (56–57 of The shifted control retains the token-based matches but about 150 cycles per participant). For each query update, we repeatedly shifts their associated poses at random within find the closest representation in every eligible cycle across each cycle. Its 11.3 mm error is summarized as the mean all eight movements, excluding the query’s own cycle and the of participant medians, whereas the main retrieval results use two adjacent cycles of the same movement. From these cycle- the phase-balanced means above. Under the same medianspecific matches, we retain the five closest to the query and based summary, 1,024-code tokens give 7.3 mm. The shifted average the measured poses at those matches to estimate the control and pose-space matching are descriptive references, not query pose. Matching uses squared Euclidean distance between performance limits. full representations for continuous SPAR and tokens restored to codebook vectors. Direct matching of token IDs instead uses B. Movement-direction analysis Hamming distance, defined as the fraction of electrodes with The direction analysis asks whether the representation different IDs, while the pose-space reference selects matches distinguishes opening from closing at a similar degree of hand by Euclidean distance between measured pose coordinates. closure. We define closure as the mean landmark distance To weight different parts of a movement equally, errors from the movement’s open-hand template, rescaled between are first averaged within ten phase bins per cycle and then that movement’s 1st and 99th percentiles and clipped to across cycles, movements, and participants. Continuous SPAR [0, 1]. Direction labels follow the sign of the closure gradient gives 7.92 mm and pose-space matching 4.38 mm. The three after a centred five-update moving average within each cycle, comparisons in Fig. 6D use exact permutation (sign-flip) tests excluding updates with zero gradient. and intervals, with Holm correction across the tests: +0.09 mm Every in-cycle update of the eight movements serves as with 1,024 codes (95% confidence interval [0.004, 0.18]), a query. For each query, candidates are drawn from the +0.22 mm with 64 codes ([0.08, 0.36]), and +0.92 mm for same movement in other nonadjacent cycles and must have Hamming matching of token IDs ([0.54, 1.29]; Holm-adjusted normalized closure within 0.05 of the query. The closest p = 0.043, 0.016, and 0.012; Supplementary Data 9). candidate in the chosen representation supplies the predicted All updates. Using every in-cycle update as a query, including direction. A majority-direction control uses the same candidates those in the training windows, and admitting candidate cycles but always predicts their more frequent direction, choosing that overlap training windows, while still excluding the query’s

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closing on ties. We average accuracy over the eight movements within each participant. Dequantized tokens achieve 70% accuracy, compared with 55% for the majority-direction control, 65% for matching measured poses, and 64% for Hamming matching of token IDs. Tokens exceed the majority control and pose-based matching with Holm-adjusted p = 0.012 and p = 0.016, respectively. The third comparison in this family is token IDs versus posebased matching. In a separate comparison, continuous SPAR reaches 70.6%, exceeding tokens by 0.6 percentage points (p = 0.004). C. Visualization of token histories Input and embedding. The visualization in Fig. 6A–C adds temporal context to the representations used in the quantitative analyses. It contains 14,861 updates from participant 1’s eight movement recordings, each with 320 tokens from the 1,024entry SPAR codebook. We replace each token with its 18component codebook vector, reapply structural zeros, and concatenate the current vectors with those 6, 12, 18, and 24 updates earlier. At 50 Hz these lags span 480 ms. History is taken from this continuous stream and may cross window and cycle boundaries, each update keeping its own window’s calibration, without wrapping within a repetition. After dropping constant columns, we fit one threedimensional Uniform Manifold Approximation and Projection (UMAP) [13] across all movements, with no additional scaling or PCA. The fit uses cosine distance, 50 neighbours, minimum distance 0.8, spread 1.0, repulsion strength 0.05, 500 epochs, and random seed 42. Movement labels and measured poses enter only the subsequent display construction, not the embedding fit itself. Cycle phase and movement-specific projection. We construct the display by identifying repetition phase and then choosing a projection plane for each movement. The measured mean fingertip-to-wrist distance is detrended and filtered forwards and backwards at 50 Hz with a fourth-order 1 Hz Butterworth filter. Consecutive peaks with prominence of at least 0.2 mm and an intervening trough define a cycle. Within each recording, we retain durations between the median divided by 1.8 and the median multiplied by 1.8. Phase increases linearly from zero to one between the retained cycle boundaries, near the open-hand pose. For each movement, we average three-dimensional embedding coordinates within 20 equal phase bins per cycle and then across cycles with all bins populated. The first two singular vectors of the centred mean trajectory define the plane onto which that movement’s points are projected. The projected groups are positioned separately. We normalize the original history vectors to unit length, average them by movement, and normalize the resulting centroids. Twodimensional metric multidimensional scaling of their cosine distances initializes group centres using seed 42 and eight initializations. These centres are then rescaled and pushed apart until circles containing each group’s 98th-percentile radius no longer overlap, with a gap of 0.12 times the mean radius. Because this placement is part of the display construction, distances between groups are not interpreted.

Colour and displayed points. Panel A colours points by movement label, while panel B colours them by relative hand closure. For the latter, we calculate the mean displacement of the 20 measured landmarks from a movement-specific openhand template defined by the first and last 5% of its cycles. Displacement is divided by the movement’s 95th percentile and clipped at 100%. All 14,861 updates are displayed, and axis limits span the 0.5th to 99.5th coordinate percentiles with 5% padding and contain every update. Repetition curves. Panel C summarizes the phase-aligned repetitions as individual curves and a mean trajectory. For the mean trajectory, each cycle contributes median coordinates in 20 equal phase bins, and the 19 complete cycles per movement are averaged bin by bin. Individual repetition lines instead use medians in ten phase bins and are omitted if a bin is empty or an adjacent-bin jump, including the closing segment, exceeds 0.6 times the movement’s mean coordinate range. This leaves 148 of 152 individual lines, while all 152 cycles contribute to the mean trajectories. We smooth the bin coordinates with circular Gaussian kernels over offsets −3 to +3, using standard deviations of 0.5 bins for mean trajectories and 0.8 bins for individual repetitions. Periodic cubic splines then connect the smoothed coordinates, repeating the first point at phase one and sampling 200 positions per curve. Dots mark phase zero, and arrows follow increasing phase near 0.25 and 0.75. Periodic interpolation closes every curve by construction. Temporal-context controls. Two controls examine how temporal context contributes to the display. The history-length control repeats the embedding and display procedure with 0, 120, 240, 480, 720, and 960 ms of history, adding lagged updates at 120 ms intervals. Mean trajectory circularity (4πA/P 2 for enclosed area A and perimeter P , one for a circle) rises from 0.29 for a single update to 0.96 at 480 ms, with little further change at 720 or 960 ms (Fig. S4, panel titles). Fig. 6 uses the 480 ms history. To examine whether each history must stay paired with its own current update, the shuffled-history control keeps the current update fixed but reassigns the intact four-lag history blocks among updates within the same repetition, then refits UMAP and recomputes each movement’s projection plane with the same procedure, keeping the original cycle assignments and group anchors. Mean trajectory circularity then falls from 0.96 to 0.03. The pose-retrieval and direction-classification results use single updates in the original representations, without this embedding or curve construction. S-V. ROBUSTNESS AND MOTION ANALYSES A. Sensitivity to noise and electrode loss To compare sensitivity to degraded input, the learned, SPAR, and adapted-CNN pipelines receive the same degraded recordings without retraining, while the initial calibration interval stays clean. Participant errors are averaged over three decoder initializations and three independently generated degradation instances. We add zero-mean Gaussian noise with standard deviations of 1, 3.2, 10, or 32% of each channel’s EMG root mean square (RMS) after the calibration interval. Electrode loss is

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A

Single update, circularity 0.29

D 480 ms of history, circularity 0.96

Thumb

Index

B 120 ms of history, circularity 0.58

C 240 ms of history, circularity 0.82

E 720 ms of history, circularity 0.98

F 960 ms of history, circularity 0.98

Middle

Ring

Pinky

Fist

2-Pinch

3-Pinch

Fig. S4: Effect of temporal context on the Uniform Manifold Approximation and Projection (UMAP) display. The same updates from participant 1 are embedded with increasing amounts of token history, using the UMAP settings, movement-specific projection planes, and group-placement procedure described in Section S-IV-C. A: Current tokens alone. B–F: Current tokens together with lagged updates every 120 ms, extending back to 120, 240, 480, 720, or 960 ms. Colours identify the eight movements. Black lines connect the mean coordinates of 20 equal phase bins, averaged across complete repetitions, with the last bin connected to the first. Panel titles give circularity 4πA/P 2 , averaged over movements, where A and P are the area and perimeter of these projected trajectories and a circle has circularity one. Circularity changes little beyond the 480 ms used in Fig. 6. Each panel is fitted and arranged separately, so coordinates are not comparable across panels.

simulated by setting 16, 32, or 80 scattered channels to zero or their absolute error difference includes zero. Under electrode by silencing one or two complete 64-electrode arrays (Fig. S5). loss, their error increases differ by at most 0.27 mm, with all None of the models was trained with dropped channels. For upper 95% confidence limits below 0.8 mm. each model, we subtract clean-input error from degraded-input SPAR uses separate correction families for four noise error and compare the resulting increases within participants. comparisons and five electrode-loss comparisons. Its token The tests therefore measure whether degradation increases errors increase by 1.40 mm less than continuous-feature errors error more with tokens than with continuous features, while when one array is silenced and by 1.03 mm less when two the figure shows absolute errors. arrays are silenced (p = 0.020 for each). Supplementary Data 8 At each noise level, we compare the increase in decoding provides every SPAR condition, interval, and test. error for learned tokens with the corresponding increases for continuous learned features and the adapted CNN. These eight B. Calibration and unseen recordings noise comparisons and the five electrode-loss comparisons Calibration at recording onset. The main protocol estimates are Holm-corrected in separate families. At 32% noise, the calibration statistics from the first 500 ms of every input window. token decoder’s error increases by 0.351 mm less than the We instead use the first 500 ms of each approximately 40 s continuous decoder’s (p = 0.031), although the interval for task recording for calibration. We evaluate this change both

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A

B

3D Error (mm)

20 18 16 14 12 10 Clean

1%

3.2 %

10 %

32 %

Added Noise (% of EMG RMS)

Learned Tokens

Learned Features

None

16

32

80

Scattered Electrodes Adapted CNN

SPAR Tokens

1 array 2 arrays (64) (128)

Whole Arrays Continuous SPAR

Fig. S5: Decoding error under noise and electrode loss. Decoders for the learned representation, the spectral–spatial representation (SPAR), and the adapted convolutional neural network (CNN) are held fixed during evaluation, following the training procedures in Table S1. Points show mean three-dimensional (3D) error across nine participants after averaging three decoder initializations and three degradation instances, with 95% confidence intervals. A: The standard deviation of the added Gaussian noise is expressed relative to the root mean square (RMS) of each channel’s electromyography (EMG). B: Scattered electrodes or complete arrays are set to zero after calibration. Curves show absolute, unfiltered errors, whereas tests compare increases from each model’s clean baseline. SPAR comparisons are reported in Supplementary Data 8.

without refitting and after refitting the full SPAR pipeline under ments, errors rose for both representations (16.3–47.6 mm), recording-onset calibration. while tokens added 0.17–0.71 mm relative to continuous SPAR. Without refitting, recording-onset calibration raises SPAR error to 11.688 mm with tokens and 11.736 mm with continuous C. Motion and displayed trajectories features. Because these models were fitted using per-window Constant-prediction baseline and velocity. For emg2pose, the calibration, this comparison introduces a mismatch between constant-prediction baseline holds each model’s final prediction training and evaluation. before the scoring interval fixed throughout that interval. Refitting SPAR standardization, codebooks, and pose deIt is not initialized with the measured hand pose. Learned coders under recording-onset calibration gives errors of tokens achieve 28.00 mm on the sampled official-test windows, 10.271 mm with tokens and 10.448 mm with continuous SPAR. compared with 29.65 mm for their constant-prediction baseline, Both improve on the per-window results (Holm-adjusted while continuous features achieve 28.04 mm compared with p = 0.012 and p = 0.016, respectively), and the token-minus29.63 mm for their constant-prediction baseline (Supplementary continuous difference is −0.177 mm (95% confidence interval Data 7). [−0.336, −0.030] mm; p = 0.031 in the same three-test family). Velocity is estimated from consecutive valid poses at 50 Hz In both versions of this analysis, each calibration applies to and scored with a pooled R2 against a constant mean-velocity one task recording rather than an entire session. reference, weighting observations rather than participants. Unseen recordings. The original pipelines fitted under perScores range from −0.020 to +0.009 across representations window calibration are also evaluated on the faster 1.5 Hz digit (Supplementary Data 7): velocity errors are similar to those of recordings, which were excluded from fitting. Each recording the constant reference for tokens and continuous features alike. is divided into overlapping 3 s windows starting every 2 s, with Predictions are not shifted in time before errors are calculated. per-window calibration and without retraining. Tokens give Displayed movement traces. Fig. 5 illustrates predictions for 18.31 mm error and continuous SPAR gives 18.13 mm, comparticipant 6, whose SPAR-token error is just below the cohort pared with 9.98 and 10.14 mm, respectively, on the main 0.5 Hz median. Predictions from additional input windows within digit test windows. The token-minus-continuous difference is the test block fill the gap between the two scored one-second +0.18 mm (95% confidence interval [0.01, 0.36] mm; Holmintervals to produce a continuous four-second trace. The plotted adjusted p = 0.070). Holm correction covers the token-minusdistance depends on the movement: thumb tip to pinky base continuous contrasts in this evaluation and in the recordingfor the thumb, fingertip to wrist for the other digits, mean onset-calibration evaluation without refitting. fingertip-to-wrist distance for the fist, and thumb to fingertip On seven further unseen circular, lateral, and vertical movefor pinches, averaged over index and middle for the 3-pinch.

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For display, predictions are smoothed with a causal One Euro filter [14] selected on learned-token validation data. Its minimum cutoff is 1 Hz, β = 0.1, and derivative cutoff is 1 Hz at 50 Hz, with the same settings applied to SPAR traces. All numerical errors are calculated from unfiltered predictions. DATA AND CODE AVAILABILITY The HD-EMG recordings are available from the authors on reasonable request [2], and emg2pose is publicly available [3]. Supplementary Data 1–9 provide summary results and plot values. Code is available at https://github.com/NsquaredLab/MyoJi. R EFERENCES [1] [2]

[3] [4]

[5] [6]

[7] [8] [9] [10] [11]

[12]

[13] [14]

Bluetooth SIG, The Bluetooth low energy primer, Version 1.3.0, Accessed 13 September 2026, 2024. R. C. Sîmpetru et al., “Learning a Hand Model From Dynamic Movements Using High-Density EMG and Convolutional Neural Networks,” IEEE Transactions on Biomedical Engineering, vol. 71, no. 12, pp. 3556–3568, Dec. 2024. DOI: 10.1109/tbme.2024.3432800 S. Salter et al., Emg2pose: A Large and Diverse Benchmark for Surface Electromyographic Hand Pose Estimation, Dec. 2024. DOI: 10.48550/ arXiv.2412.02725 P. J. Rousseeuw and C. Croux, “Alternatives to the Median Absolute Deviation,” Journal of the American Statistical Association, vol. 88, no. 424, pp. 1273–1283, Dec. 1993. DOI: 10.1080/01621459.1993. 10476408 A. van den Oord, O. Vinyals, and K. Kavukcuoglu, “Neural discrete representation learning,” in Advances in Neural Information Processing Systems, 2017. R. C. Sîmpetru, M. März, and A. Del Vecchio, “Proportional and Simultaneous Real-Time Control of the Full Human Hand From HighDensity Electromyography,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 31, pp. 3118–3131, Jul. 2023. DOI: 10.1109/TNSRE.2023.3295060 F. Mentzer et al., “Finite scalar quantization: VQ-VAE made simple,” in International Conference on Learning Representations, 2024. K. Avramidis et al., “Neural codecs as biosignal tokenizers,” arXiv preprint arXiv:2510.09095, 2025. S. Holm, “A simple sequentially rejective multiple test procedure,” Scandinavian Journal of Statistics, vol. 6, no. 2, pp. 65–70, 1979. G. Piaggio et al., “Reporting of noninferiority and equivalence randomized trials: Extension of the CONSORT 2010 statement,” JAMA, vol. 308, no. 24, pp. 2594–2604, 2012. DOI: 10.1001/jama.2012.87802 A. L. Cakici et al., “A generalized framework for the study of spinal motor neurons controlling the human hand during dynamic movements,” in Proceedings of the 2022 44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Jul. 2022, pp. 4115–4118. DOI: 10/grc7qj J. P. Romano and M. Wolf, “Exact and approximate stepdown methods for multiple hypothesis testing,” Journal of the American Statistical Association, vol. 100, no. 469, pp. 94–108, 2005. DOI: 10 . 1198 / 016214504000000539 L. McInnes et al., “UMAP: Uniform Manifold Approximation and Projection,” Journal of Open Source Software, vol. 3, no. 29, p. 861, Sep. 2018. DOI: 10.21105/joss.00861 G. Casiez, N. Roussel, and D. Vogel, “1 C filter: A simple speed-based low-pass filter for noisy input in interactive systems,” in Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, ser. CHI ’12, New York, NY, USA: Association for Computing Machinery, May 2012, pp. 2527–2530. DOI: 10.1145/2207676.2208639

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