Decomposing motor units through elimination for real-time intention driven assistive neurotechnology
Authors: Nicholas Tacca
Bryan R. Schlink
Jackson T Levine
Mary K. Heimann
Collin Dunlap
Sam Colachis IV
Philip Putnam
Matthew A. Zeglen
Daniel J. Brobston
Austin M Bollinger
José L. Pons
Lauren Wengerd
Eric Christopher Meyers
David A. Friedenberg
Venue: NeurIPS 2025 poster ()
Keywords: neurotechnology
motor unit decomposition
assistive technology
electromyography
Primary area: neuroscience_and_cognitive_science
TL;DR: We introduce MUelim, an algorithm for efficient motor unit decomposition that uses approximate joint diagonalization with a subtractive approach to rapidly identify motor units for advanced neuroprosthetic control.

Abstract: Extracting neural signals at the single motor neuron level provides an optimal control signal for neuroprosthetic applications. However, current algorithms to decompose motor units from high-density electromyography (HD-EMG) are time-consuming and inconsistent, limiting their application to controlled scenarios in a research setting. We introduce MUelim, an algorithm for efficient motor unit decomposition that uses approximate joint diagonalization with a subtractive approach to rapidly identify and refine candidate sources. The algorithm incorporates an extend-lag procedure to augment data for enhanced source separability prior to diagonalization. By systematically iterating and eliminating redundant or noisy sources, MUelim achieves high decomposition accuracy while significantly reducing computational complexity, making it well-suited for real-time applications. We validate MUelim by demonstrating its ability to extract motor units in both simulated and physiological HD-EMG grid data. Across six healthy participants performing ramp and maximum voluntary contraction paradigms, MUelim achieves up to a 36$\times$ speed increase compared to existing state-of-the-art methods while decomposing a similar number of high signal-to-noise sources. Furthermore, we showcase a real-world application of MUelim in a clinical setting in which an individual with spinal cord injury controlled an EMG-driven neuroprosthetic to perform functional tasks. We demonstrate the ability to decode motor intent in real-time using a spiking neural network trained on the decomposed motor unit spike trains to trigger functional electrical stimulation patterns that evoke hand movements during task practice therapy. We show that motor unit-based decoding enables nuanced motor control, highlighting the potential of MUelim to advance assistive neurotechnology and rehabilitation through precise, intention-driven neuroprosthetic systems.

Decomposing motor units through elimination for real-time intention driven assistive neurotechnology
Nicholas Tacca'
Bryan R. Schlink'
Jackson T. Levine Mary K. Heimann'
Collin Dunlap'
Samuel C. Colachis IV Philip Putnam' Matthew A. Zeglen
Daniel J. Brobston Austin M. Bollinger José L. Pons
Lauren Wengerd
Eric C. Meyers
David A. Friedenberg'
Battelle Memorial Institute Shirley Ryan Abilitylab Northwestern University
University of Texas at Dallas
The Ohio State University
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Abstract
Extracting neural signals at the single motor neuron level provides an optimal control signal for neuroprosthetic applications. However, current algorithms decompose motor units from high-density electromyography (HD-EMG) are time- consuming and inconsistent, limiting their application controlled scenarios in a research setting. We introduce MUelim, algorithm for efficient motor unit de- composition that uses approximate joint diagonalization with subtractive approach to rapidly identify and refine candidate sources. The algorithm incorporates an extend-lag procedure to augment data for enhanced source separability prior to diag- onalization. By systematically iterating and eliminating redundant noisy sources, MUelim achieves high decomposition accuracy while significantly reducing com- putational complexity, making it well-suited for real-time applications. We validate MUelim by demonstrating its ability to extract motor units in both simulated and physiological HD-EMC grid data. Across six healthy participants performing ramp and maximum voluntary contraction paradigms, MUelim achieves up to a 36 speed increase compared existing state-of-the-art methods while decomposing a similar number of high signal-to-noise sources. Furthermore, we showcase a cal-world application of MUelim in clinical setting in which an individual with spinal cord injury controlled an EMG-driven neuroprosthetic to perform functional tasks. We demonstrate the ability to decode motor intent in real-time using a spiking neural network trained on the decomposed motor unit spike trains to trigger functional electrical stimulation patterns that evoke hand movements during task practice therapy. We show that motor unit-based decoding enables nuanced motor control, highlighting the potential of MUelim advance assistive neurotechnology and rehabilitation through precise, intention-dria driven neuroprosthetic systems.
Introduction
Electromyography (EMG) provides a natural motor interface for humans to interact with machines, capturing the electrical activity of muscles to facilitate intuitive control. At the core of physiological motor control is the motor unit, the smallest functional unit of muscle activation, consisting of
single motor neuron and the fibers it innervates (Heckman and Enoka 2012). EMG signals recorded at the periphery consist of summation of motor unit action potentials and noise, with the input signal
originating from the central nervous system, providing direct link to neuromotor intent [Farina and
Negro 2015). As result, decomposing the physiological motor input to muscles via motor unit
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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activity may provide a more advanced and intuitive control signal for neuroproshetics
Tanzarell la
al. 2023
Chen et al. 2020 Kapelner et al. 2019].
Recently, there have been significant advances in motor unit decomposition from non-invasive high-
density EMG (HD-EMG), leveraging swarm contrastive decomposition (SCD) [Grison et al. 2025
convolutive blind source separation (BSS) [Negro et al. 2016 Holobar et al. 2014], convolutional
kernel compensation (CKC) HHolbaar and Zazula| 2007]. and deep learning- based approaches [Lin
ct al.
2024
Wen et al. 2023]. Open-source tools Grison et al. 2025 Avrillon et al. 2024 Formento
ct al.
2021
have made it possible for researchers to analyze motor unit activity in controlled research
settings during both isometric and dynamic movements [[sswald et al. 2025 Tanzarella et al. 2023
Chen et al. 2020). However, these methods remain computationaly intensive and inconsistent, often
requiring significant processing time or manual intervention [Del Vecchio et al. [2220] Negro et al.
2016 Farina et at.) 2014), prohibiting their use in real-time neuroprosthetic systems, where rapid and
reliable decoding of motor intent is essential.
Existing decomposition methods typically use blind source separation (BSS), such as independent component analysis, in which the contrast functions used for source separation measure sparseness of spike trains, rather than independence (Negro et al. 2016]. While effective, these higher-order statistical methods are computationally demanding and sensitive to noise [Congedo et al. 2008).
Second-order statistical (SOS) methods [Belouchrani al. 1997 Belouchrani and Amin 1998 offer a more efficient alternative by leveraging spectral and temporal signatures of sources through joint diagonalization. However, SOS methods face two key challenges, namely joint diagonalization, core component of SOS methods, has historically been computationally expensive, and SOS methods are constrained to decompose at most as many sources as there are recording channels [Congedo et al. 2008 Pham and Cardoso 2001 Pham 2001].
Recent advancements in joint diagonalization techniques have significantly improved computational efficiency (de Vlaming and Slob 2021 Ablin et al. 2018). making SOS methods more practical for real-world applications. To address the challenge of limited source separability, we propose
using strategies based on existing decomposition methods [Grison et 2025 Negro et al. 2016
and olectreencephalography data augmentation techniques [Carrara and Papadopoulo [024] add
time-delayed extensions prior to joint diagonalization. This augmentation increases the effective dimensionality and enhances source separability by capturing temporal dynamics, improving the conditioning of the source separation problem. Taking inspiration from compressive sensing [Candès) al. 2006 Donoho al., (2055), we further accelerate the identification of candidate sources by leveraging the sparsity of motor unit source activity contained within symmetric positive definite (SPD) matrices. By randomly sampling SPD matrices for joint diagonalization, we can perform an iterative BSS to find unique sources while significantly reducing computational overhead.
With these considerations in mind, we propose MUelim, motor unit decomposition algorithm that leverages approximate joint diagonalization to extract many candidate motor unit sources all at once and then eliminates suspected noise sources. We validate MUclim on both simulated and physiological HD-EMG datasets, demonstrating its ability to extract motor units with high accuracy and speed. Furthermore, we showcase application in a clinical setting, where it enables a spinal cord injury (SCI) participant to control a neuroprosthetic device in real time, highlighting its potential to advance assistive neurotechnology and rehabilitation.
2 Methods
2.1 Overview of EMG decomposition blind source separation problem
EMG signals represent the summation of motor unit action potentials (MUAPs) and noise (Figure [A].. These signals can be modeled as a linear instantancous mixture of sparse sources, where each source corresponds to the discharge timings of a motor unit. The observed EMG signals X E RCN,
where C' is the number of channels and N is the number of samples, can be expressed as:
((1) = HS(() + N(t).
(1)
where H E RBCM is the mixing matrix with M motor unit sources, S(() E M represents the spike trains, and ((1) additive noise, The goal of EMG decomposition to estimate the spike trains S(t) from the observed signals X(t).
2

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Motor unit decomposition can be framed as a BSS problem, where the objective is to estimate the separating matrix B IR MxC such that:
S(t) BX)
(2)
where (() the estimated motor unit source activity.
2.2
MUelim algorithm
2.2.1
Preprocessing and data augmentation
The imput EMG data is first divided into non-overlapping windows of size L for SPD matrix computation. The windowed data is represented Xtinned E R &RxCXL where W is the number of windows.
To incorporate temporal information, the data is extended using lagged versions of each channel. This augmentation creates an extended dataset Xext E R (C-R)x where R is the extension factor. The extend-lag procedure increases the ratio observations to sources, improving the conditioning of the source separation problem [Holobar and Zazula (007]. By embedding the data into a higher- dimensional space, this approach captures both spatial and temporal dependencies, which are critical for resolving sources with overlapping activity.
The extend-lag procedure inspired by the success in decoding from the tangent space of augmented covariance matrices [Carrara and Papadopoulo) 2024]. The augmented covariance matrix combines spatial covariance with temporal information, effectively embedding the original dataset into higher- dimensional space. This embedding enhances the separability of sources by capturing their nonlinear dynamics (Takens 2006
X (1) pinned (4), X bi r)..... X Xiinned (R 11)
where 7 is the lag parameter, and R is the extension factor.
2.2.2 Iterative blind source separation (BSS)
MUelim employs iterative BSS approach to identify and refine sources. The algorithm assumes that the sources are sparse in the transformed domain. The iterative process continues until a stopping criterion is met, such reaching the maximum number of iterations, finding the maximum number of sources, or failing to identify a minimum number of new sources.
SPD matrix computation In each iteration, the extended dataset is sampled (X for SPD matrix computation. Depending on the characteristics of the data and the assumptions about the sources, several types of SPD matrix estimators can be used. Simple covariance matrices, channelwise kernels, such as linear, polynomial, or laplacian kernels, and cospectral matrices can be used to capture nonlinear dynamics of the system [Congedo et al. 2008 Belouchrani and Amin 1998 Belouchrani et al. 1997].
In this study, cospectral matrices are used as the primary estimator due to their ability to capture both spatial and spectral dependencies. For each frequency the range - the Fast Fourier transform is applied to each window of the extended data to compute the cospectral matrix Cy:
W
Cj
X
(x) (M)
ex.
(4)
W
1=
where H denotes the Hermitian transpose. The diagonal elements of Cj represent the power (auto- spectra) of each channel, while the off-diagonal elements represent the in in-phase SOS dependency [Congedo et al. 2008
Whitening To improve the numerical conditioning of the SPD matrices, whitening is applied. Whitening ensures that the mean SPD matrix C has an identity covariance structure, simplifying the subsequent diagonalization step. This is achieved through eigenvalue decomposition:
W whiten VA V
Cyyhicen W whiten C, W whiten
(5)
where V and A are the eigenvectors and eigenvalues of C.
3

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Approximate joint diagonalization The separation of non nonnstationary signals can be achieved by joint diagonalization of a set of autocorrelation matrices [Belouchrami and Amin 1998 Belouchrani et al. 1997]. In the context of MUelim, we consider set of n SPD matrices (CI...., C ) of size p x p. where each matrix C, represents a whitened SPD matrix computed from the extended EMG data (Eq. 4.. The goal of joint diagonalization is to find matrix B E IRPx such that the transformed
BC,, B " } contains matrices that are as diagonal as possible. This is achieved by minimizing the following joint diagonalization criterion:
set {BC, B
C(B)
1 2n
[log det diag (BC,BT) log det (BC,B"))
(6)
where diag(-) extracts the diagonal elements of matrix, and det(-) denotes the determinant. This criterion, introduced by |hham [200T]. is derived as the negative log- ligeliiel of a source separation model for Gaussian stationary sources.
After solving the joint diagonalization problem, the forward and backward filters are computed. The forward filters W forward are used to project the extended EMG data into the source space, while the backward filters W backward are used to reconstruct the original signals from the source space. Let
W whiten and W whiten represent the whitening and inverse whitening filters, respectively. The forward and backward filters are computed as:
W forward
BW T
(7)
whiten:
W backward
W whiten B-1
(8)
Peak detection and source refinement After obtaining the forward filters from the joint diagonal- ization step, the full extended dataset is transformed into the source domain. For each source, the source power 7t (k) is computed as:
M (k)
( forward X )²
Peaks are detected in the source power to refine each source filter w, as the mean of the corresponding impulse indices:
Σ Xex((k)
W,
(10)
Ekepeaks (ex(k))
The updated filter is then orthogonalized and normalized with respect to the previously identified filters to ensure independence:
W Wj W forward W
Forward Wj),
(11)
W
(12)
2
This process is repeated iteratively until convergence, ensuring that the filters are optimized for the identified sources. During this improvement iteration step, k-means clustering is used separate signal peaks from noise peaks detected in the source power. The silhouette score (SIL.) for each source is then calculated from the detected peaks. Sources that do not converge or that have a low SIL are climinated from the final forward filters (W (Wrorwad)).
Unique source identification Newly identified spatial filters per BSS iteration compared with previously found filters to ensure uniqueness. Spatial similarity is assessed using the cosine similarity between filters. Temporal similarity between spike trains is evaluated based on the percentage of coincident spike timings between motor unit spike trains. Newly identified candidate sources that exceed predefined similarity thresholds are discarded.
Optionally, to remove the influence of already identified sources, existing sources can be peeled off from the data [Chen and Zhou 2015). This step may improve the detection of weaker sources in sub- sequent iterations by removing the contribution of already--ddentiff Algorithm for pscudocode and Supplementary Figure [ for overview of the algorithm.
sources. Refer to Supplementary

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2.2.3 Computational complexity
MUelim's computational complexity is primarily determined by the joint diagonalization step, which is performed on the extended data matrix. The data is extended using R lagged versions of each channel, resulting in R extended channels, where the extension factor. The per-iteration computational cost is O x R)² + (C x R))), where K is the number of matrices being diagonalized. For large C' x R. the (C' x R) term dominates, so the complexity is approximately (((C' R))) per iteration. This scaling arises because the most expensive operation is matrix multiplications of size (C x Rt) x (C x R). As channels or extension factor increases, decomposition time increases accordingly. However, MUelim's 's advantage becomes more pronounced with more motor unit sources, as it efficiently extracts many sources simultaneously rather than incrementally.
the number of original channels and is
2.3 Algorithm evaluation
To validate the proposed algorithm, we tested the decomposition method on simulated EMG data. The simulated EMG signals were generated using a Poisson neuron model to create spike trains, which were then convolved with a MUAP template to produce signals across multiple channels. Random noise and amplitude modulation were incorporated to mimic the variability and complexity of real physiological signals. We tested MUelim, SCD [Grsson et al. 2025], and MUEdit [Avrillon et al., 2024 identical simulated datasets to enable direct comparison of decomposition performance.
We evaluated two channel configurations spanning the physiologically realistic range for motor unit decomposition: 32 channels with 5, 10, and 15 motor unit sources, and 64 channels with 5, 10, 15, 20, 25, and 30 motor unit sources. These configurations test up to N/2 sources across all three methods. Signals were generated using a sampling rate of 1088H2 with average motor unit firing rate of 10H for 30s total. We assessed decomposition accuracy by comparing detected spike timings with ground truth within a 25ms window, and calculated false positive and false negative rates for each method.
To assess the feasibility of using the MUelim algorithm in application, we decomposed motor units from 8x8 HD-EMG grid (GR 10MM0808; 64 monopolar EMG channels) and Quattrocento amplifier (OT Bioclettronica) across different parameters. EMG signals were recorded from the flexor digitorum superficialis muscle in six healthy participants (N=6). Participants performed two experimental paradigms: ramped contraction for 45s, with the first 15s ramping up, the next 15s plateaued at approximately 30% of the maximum voluntary contraction, and the last 15s ramping down, and maximum voluntary contraction (MVC) sustained for 10s. EMG measurements were taken at sampling rate of 2,048H2. z. An initial bandpass filter for the incoming signal was set at 1 = for each recording, and then an offline filter of 20-500H was applied to the recordings. Force measurements were taken using digital hand dynamometer at 10H z and was synced with the EMG signal offline.
Following decomposition, we plotted spike trains superimposed over target and force trajectories. We extracted MUAP waveforms using around detected spike times to isolate the waveform associated with each motor unit. For each spike timing, we extracted a 30ms window centered on the spike impulse. To reduce pross-contamination we reconstructed the EMG signal from source space using the BSS inverse filters while suppressing other motor unit sources. Waveforms were aligned to their global maxima across channels to handle temporal jitter before averaging. We extracted waveforms from all channels and displayed results from the 5 most active channels based on signal amplitude. Individual traces show the average computed over a sliding window spanning one fifth of all detected MUAPs, with stride equal to one sixth of the window length. Subsequent inverse spatial filters were mapped to the 2D grid to visualize source activity dipoles.
averaging (STA), which averages the EMG signal
We conducted two tests to benchmark the number of decomposed sources and decomposition time across different parameters in a single representative participant. First, we assessed the influence of the extension factor and lag on decomposition performance. The extension factor was set between 1 and 6, with the lag between 1 and 10 for a total of 60 permutations. A cospectral estimator and bin size of 20ms was used across all permutations. In the second test, we evaluated the influence of the SPD estimator, as well as the variability in bin size to compute SPD matrices. We evaluated cospectral estimator and laplacian channelwise kernel over a range of bin sizes (10-2000ms) using For all cospectral matrices,
open-source methods from pyRiemann Barachant et al. 2025
5

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computed the FFT using a window size of 8 with 75% overlap between 0 and 20H². For this test, we held the extension factor and lag constant at extensions and lag samples, respectively. For both tests, we ran each decomposition permutation over 5 seeds to determine the consistency of the algorithm with the given set of parameters. The average number of sources decomposed and decomposition time + standard error of the mean are reported. A SIL threshold of 0.85 was used to determine high signal-to-noise sources. We found sources over 3 BSS iterations using a random sampling of 50% of the data for diagonalization of SPD matrices. For all tests, JADOC (de Vlaming and Slob 2021] was used for joint diagonalization with a regularization strength of 0.85.
We then compared our results to current state-of- -tate-of-the-art open-source motor unit decomposition algorithms across all six participants, namely SCD [Grison et al.] [025] and MUEdit [Avrillon et al. 2024]. We assessed both number of sources decomposed and decomposition time. We held all other parameters constant based on the open-source implementations, with 0.85 SIL. threshold used to determine acceptable sources. For SCD, we used the built-in GPU capability to increase decomposition speed. All tests were evaluated using a HP ZBook Power 15.6 inch G8 Mobile Workstation PC (Intel Core 17-11850H 2.50GHz, NVIDIA T1200 GPU, CUDA 12.2) python 3.11 or MATLAB 2021 for MUEdit.
2.4 Application: Intention driven neuroprosthetic
To demonstrate MUclim's utility in realistic use-case, we evaluated its performance in ongoing registered clinical trial (NCT06087445) in an individual with SCI. All study procedures were conducted under Institutional Review Board approval. The participant was informed of potential risks and monitored for adverse events throughout the study. In the study, a C3 incomplete SCI participant (ASIA D) used EMG-based neuroprosthetic system to control movement-speciffc functional electrical stimulation (FES) patterns based on motor intent. The participant could partially open and close his hand, though not fully, and exhibited limited grip strength. Abnormal muscle synergies, particularly overactivity in the wrist flexors, limited his ability to achieve wrist extension. FES facilitated more complete hand opening, enhancing functional performance and reducing reliance on compensatory strategies. The complete training and inference workflow is illustrated in Supplementary Figure
The neuroprosthetic system consists of 150 electrodes (75 bipolar EMG channels) embedded into stretchable fabric. An operator manually calibrated FES patterns at the beginning of the session to evoke both hand open and hand close movements (Supplementary Video [] Heatmap / Stim Patterns). A sinusoidal waveform with 2 stimulation frequency was used for both patterns. Next, a block of operator-guided stimulation was used to find spatial filters for motor unit decomposition and train spiking neural network (SNN) decode motor intent from the decomposed motor unit spike trains. The operator manually cued the participant to perform different tasks guided by an occupational therapist (OT). The corresponding FES pattern was automatically stimulated with an offset of 1,000ms to record intent with/without FES active. The BSS forward filters were computed in-session after collecting this training block (fit phase), then applied for real-time inference (transform phase), following standard scikit-learn convention (Supplementary Algorithm D]. EMG was recorded with a sampling rate of 3, 3,000H collected in non-overlapping 100ms bins to generate final predictions at 10Hz 2 used to switch/turn-off FES patterns when in inference mode.
Following this training block, EMG data was filtered for subsequent motor unit decomposition. First, FES artifact was removed using a template artifact filter, whereby a template of the artifact from the previous pulse window was subtracted from the current pulse window. Next, a 20ms blanking window was used to blank out any remaining artifact in between FES pulses. The subsequent signal was then filtered using notch and bandpass filters similar to previous studies [Tacca et al., 2024 Meyers et al., 2024]. Following the preprocessing pipeline, motor units were decomposed using the proposed MUelim algorithm compute the BSS forward filters from the training data. For enhanced speed and accuracy, motor unit spike trains were downsampled within a bin to five sub-bin bin splits, with a shape of nsamp X NMU X Neplits- Next, the previous four bins were concatenated with the current bin to provide additional time information to the SNN. This was then fed into a fully-connected SNN developed using the LAVA framework. Hidden layers consisted of 1000 x 500 current based leaky integrate and fire neurons. Default neuron parameters from LAVA were used for training. A dropout of 40% was applied at each layer. The SNN was trained natively using the SLAYER module (Shresthal and Orchard 2018) within LAVA for 15 epochs with batch size of 128 and an initial learning rate

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of 0.001. The Adam optimizer with cosine annealing warm restarts was used to optimize the error function. The built-in spike rate error function with true rate of 0.8 and false rate of 0.001 was used to align the output SNN neuron activity with the three classes, namely Hand Open, Hand Close, and Rest. Both SNN training and inference utilized GPU to enhance speed for application. All steps within the pipeline were wrapped in sklearn transformer [Pedregosa et al. 2011] containing both fit and transform methods to be used in the existing clinical software.
Once a decoder was trained, the full pipeline was used in inference mode, allowing the participant to control FES based on motor intent decoded from the decomposed motor unit activity. The operator manually labeled the task as the participant performed it with guidance from the OT to assess decoder performance offline. Bin-wise accuracy was used to assess how many 100ms bins matched the ground truth manually labeled by the operator. A live user user-interface was generated to visualize EMG activity, motor unit activity, SNN neuron output activity, and MUAP waveform generation. Unity-engine virtual hand shows the real-time predictions and active FES provided to the participant.
3 Results
3.1 MUelim decomposition validation
Representative decomposition results from simulated EMG data are shown in Figure 3 MUelim successfully decomposed the simulated signals into the three ground truth motor unit sources. Peak detection in the source power domain (Figure [TB) identified spike timings that closely matched ground truth (Figure IT). Reconstructing the EMG signal these spike timings with other sources suppressed produced clear motor unit action potential waveforms (Figure D)), demonstrating successful recovery of the simulated MUAP shapes.
A
B
Peak detection
Time
Spike train
|||11
Waveform identification
Potartall
EHG
Figure 1: Overview of MUelim decomposition algorithm. A. Motor units, each consisting of a motor neuron and the muscle fibers it innervates, generate action potentials that sum to form high-density electromyography (HD-EMG). In this work, we present MUelim, an efficient motor unit decomposition algorithm, that decomposes EMG into motor unit spike trains to provide an intuitive control signal for assistive and rehabilitative neurotechnology. B. Peak detection from source power of the identified sources decomposed from simulated EMG signals, Identified peak impulses have high signal to noise ratio. C. Spike timings align with ground truth spike timings. D. Waveform identification in the first EMG channel through the reconstruction of EMG signal from source domain with other sources suppressed.
We compared MUelim against ffate-of-hhe-at decomposition methods identical simulated EMG datasets. Across all simulation scenarios (32 and 64 channels with 5 to 30 motor units), all three methods successfully identified the correct number of sources. When comparing spike timings with ground truth, MUelim achieved 99.99 + 0.01% % accuracy with 0.99 = 0. 14 false positives per source and 0.03 + 0.02 false negatives per source, closely matching SCD (99.99 = 0.01% accuracy, 0.93 + 0.13 FP per source, 0.03 + 0.02 EN per source) and MUEdit (98.98 = 0.07% accuracy, 0.00 = 0.00 FP per source, 3.06 + 0.20 FN per source) (Supplementary Table [].
Next, motor units were decomposed from a HD-EMG grid as a healthy individual performed ramped contraction (Figure Varying parameters were used to assess the impact on the number of
7

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Using extension factor of 4 and lag of 6, 19 unique motor unit sources were found in just under 5 minutes that align closely to the force output (Figure [ Representative MUAP waveforms (Figure 2 demonstrate clean action potentials, while the inverse spatial filters (Figure 2C) show the spatial localization of motor
sources decomposed and decomposition time (Supplementary Figure 2)
unit sources across the electrode grid.
20 A
B
Force
Amputtate tnnt
ex
Motor Unit
15
Target
10
25
23
C
5
20
Charndly
1986
0
10
20
30
40
50
Channel
Chatred
Time (s)
Figure 2: Decomposition results align with force output in healthy individual A. Spike train decomposed using MUelim algorithm aligned with target (black) and force (red) trajectories B. Motor unit action potential (MUAP) waveforms for two representative motor unit sources. MUAP waveforms were identified by taking the spike-triggered average at the spike timings from the five highest weighted channels of the reconstructed EMG signal. During reconstruction, other motor unit sources were suppressed for cleaner MUAP waveforms. C. First extension of the inverse spatial filters used reconstruct EMG signal from motor unit source activity mapped the HD-EMG grid. Dipoles show weighting of motor unit source.
Across all six participants in both ramp and MVC paradigms, MUelim consistently decomposed motor units with substantially reduced computational time compared to alternative methods (Table D. For ramp contractions, MUelim achieved up 36x speed increase compared to MUEdit (3.1 3.1 vs T12.3 minutes. Supplementary Table [}. The motor unit yields observed are consistent with prior reports for high-density grids in hand and forearm muscles [Farina et al.) 20088, Negro et al. [0166. Full timing results from the parameter sweep in a single participant are shown in Supplementary Figure 2 Varying bin size for SPD matrix computation affected the number of sources decomposed, while having a minimal effect on decomposition time (Supplementary Figure 2A- The optimal bin size range to extract the most sources was 20-30ms. When comparing SPD matrix estimators, cospectral matrices yielded more sources in the optimal bin size range, while taking less time to decompose than laplacian kernel estimator.
Table I: Comparison of motor unit decomposition methods across 9=6 healthy participants
Ramp Experiment
MVC Experiment Time (min.)
Method
Ext.
Lag
MUs
Time (min.)
SIL
MUs
SIL
2
12.8 + 2.7
0.1
0.91 = 0.01
7.8 1.8
0.3 = 0.0
0.91 0.01
MUelim
4
18.8 4.2
3.1 0.2
0.92 + 0.01
11.2 2.2
0.7 +: 0.0
0.91 0.01
6
2.4 0.5
5.5 551000 0.6
0.89 0.00
5.6
9.0
0.90 + 0.02
SCD
16
3.2 - 0.8
14.6 3.6
0.90 0.01
5.6
5.7
0.90 + 0.01
6
3.2 2.0
72.3 4.5
0.88 + 0.01
24.3 9.6
10.9 2.2
0.89 + 0.00
MUEdit
16
18.2
112.3
28.55
0.89 1.80
12.5
30.9
5.3
0.93 0.01
Both extension factor and lag influenced the number of sources decomposed and decomposition time (Supplementary Figure (D- The number of sources decomposed began to saturate with an extension factor greater than 2. A lag between 4-8 samples per extension yielded the most sources. Across all permutations, SIL was greater than 0.85 for every source with grand average SIL of 0.955 + 0.001. The maximum decomposition time was just under eight minutes with extension factor of and lag of samples. Using small extension factor and lag >> 1, majority of sources can still be found in fast decomposition time. For example, with an extension factor of 2 and lag of 5, there was an average of 15.4 + 0.98 sources decomposed across the iterations (81 of the peak number of sources). Decomposition time for this setting only 1.47 + 0.01 minutes.
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3.2 Closed-loop control of neuroprosthetic by a SCI user
To evaluate whether MUelim could be used to control a neuroprosthetic, we trained a SNN to decode motor intent from a SCI participant's 's motor unit activity to activate movement-specific FES patterns during task practice therapy. The SCI participant was successfully able to control the neuroprosthetic using the trained decoder (Figure B and Supplementary Video [ The motor unit-based SNN decoder achieved 85% bin-wise accuracy during live control. For comparison, an offline analysis using standard root-mean-squne -qqare (RMS) features with neural network (NN) decoder achieved 86% accuracy on the same dataset. All of the intended movements of the tasks were successfully activated by the participant. Discrepancies between manual labels and final FES predictions can be attributed to short delays in transition between movements and movement to rest (Figure 3 FES predictions above vs. lightly shaded labels on top of the motor unit spike train). Looking at the first transition from rest to hand open to grab the pipe, MUelim detected the initial motor intent, which triggered the hand open FES pattern activate (Figure (A) Following this, there was an initial break-in period of the template artifact filter, with subsequent peaks detected after the second FES pulse that oscillated with stimulation frequency. The user retained control of the device and was successfully able to transition between states to allow the FES to assist in completing the task. Waveforms generated from the spike triggered averaging of reconstructed EMG detected spikes show clean action potentials (Figure 3D), demonstrating the ability of the algorithm to detect spikes in between FES pulses.
A SNN was able to dissociate between motor unit activity during the different movements independent of the task (Figure 3C). The prediction probability calculated from the output neuron firing rate is shown on top of the SNN output spike train. When there was no output neuron firing, the decoder defaulted to rest prediction. Corresponding snapshots of the tasks are shown below the spike trains (Figure B). Refer to Supplementary Video for the full live video demonstrating neuroprosthetic control.
Labels/ Prodictions
A
prodiction (puises)
Hand Open
Hand Close
Motor Unit Spike Train
Shifted cualiabe!
FES
Ch. 60
Motor Unit
Ch. 50
Ch. 40
Ch.
C
SNN Output
Movement Probability
Hand
Ch.
Hand Close
100pv
Rest
100ms
Time (s)
E
Amottuee (190
6.10
22
6.0
-02
3.00
30
50
Timeo (era)
Figure 3: Spinal cord injury participant controls functional electrical stimulation (FES) in real-time via intention decoded from motor unit activity using spiking neural network (SNN). A. Zoom-in plot of raw EMG with spike train on top at the transition between rest and hand open. Spikes are detectable in a 50ms window between FES pulses with 20//z stimulation frequency. B. Full spike train that was decomposed in real-time while using the EMG-FES system in task practice. Rectangles above the spike train indicate the final movement predicted that triggered the corresponding FES movement to evoke assistance. The lighter shaded rectangles across the full spike train indicate the ground truth manually labeled by the operator. C. Output of the SNN with 3 classes and the resulting prediction probability based on the output neuron firing rates. D. Sample motor unit action potential waveforms averaged across the five highest weighted channels. E. Snapshots of SCT participant performing the rehabilitation tasks. See Supplementary Video [ for a real-time demo.

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4 Discussion
We introduced an efficient method for motor unit decomposition that leverages approximate joint diagonalization for rapid extraction of motor units from HD-EMG. Our approach incorporates an extend-lag procedure, previously used in EEG and dynamical systems analysis [Carrara and Papadopoulo, 2024 Takens [006], to augment the data and enhance source separability prior to joint diagonalization. While the extend-lag procedure itself is not novel, its application in this context enhances source separability by capturing temporal dynamics and improves the conditioning of the source separation problem. MUelim builds on advances in convolutive BSS and joint diagonalization Negro et al., 2016 Holobar and Zazula 2007 BBelouchrani et al. 1997 Pham 2001]. and addresses computational bottlenecks that have limited motor unit decomposition for real-time applications
[Congedo et al. 2008 Grison et al. 2025).
Comprehensive validation on both simulated and physiological data demonstrated MUelim's effective- ness. Direct comparison on identical simulated datasets showed that MUelim achieved comparable decomposition accuracy to SCD and MUEdit. Validation across six healthy participants in both ramp and MVC contractions demonstrated consistent performance with up to 36x speed improvements compared to open-source methods such as SCD [Grison et al., 2025 and MUEdit [Avrillon et al.) 2024), while achieving similar or greater source yield. MUelim's 8 substantially reduced BSS filter com- putation time (minutes vs up to hours) enables practical deployment in closed-loop neuroprosthetic systems where rapid session setup is required.
We demonstrated this feasibility a clinical neuroprosthetic control application, in which we decoded motor intent from motor unit firing activity decomposed using MUelim to enable an individual with SCI to volitionally control FES movement patterns. The motor unit-based SNN decoder achieved comparable performance to an offline RMS-NN decoder (85% vs 86% accuracy), although direct comparison is difficult since FES was already triggered during data collection, affecting subsequent motor recruitment and EMG signals. Integrating MUelim with a SNN decoder enables spike-based decoding, which has the potential to be incorporated in neuromorphic hardware for low-power neuroprosthetics [Tanzarella et al. 2023 Chen et al. 2020).
There are several limitations to this work. MUelim was validated only on non-invasive HD-EMG and has not yet been tested on intramuscular EMG, which may present different decomposition challenges [Negro et al., 2016 Holobar et al. 2014 Due to clinical trial constraints, the clinical evaluation period was limited. As a result, spatial filters may require adaptation for long-term or at-home use, as electrode shifts and signal quality changes can degrade performance over time (Del Vecchio et al.) 2020 Farina et al. 2014]. Future work should perform more rigorous benchmarking of motor unit- based features against RMS and other standard EMG preprocessing approaches using open-source datasets, such as those used in EMGBench (Yang et al. 2024). Broader validation across diverse user populations and movement tasks will also be important to establish generalizability of the approach OSswald et al. 2025 Wen et al. 2023]. As with any assistive neurotechnology. there is potential risk that MUclim could lead to unintended device actuation motor units are incorrectly decomposed, or raise privacy concerns if EMG data are not handled securely. Nevertheless, MUelim provides practical and efficient solution for real-time motor unit decomposition, supporting the development of robust, irrentionddrvven assistive technologies.
5 Conclusion
This work presents MUelim, an efficient algorithm for motor unit decomposition from HD-EMG signals. By leveraging approximate joint diagonalization, MUelim achieves high decomposition accu- racy while significantly reducing computational complexity, outperforming state-of-the-att methods with up to a 36x speed improvement. Comprehensive validation on identical simulated datasets demonstrated that MUclim achieves comparable accuracy to existing methods. Validation across six healthy participants in both ramp and maximum voluntary contraction paradigms demonstrates its ability to extract motor units with high signal-to-noise ratios. Furthermore, we showcased its application in clinical setting, where MUelim facilitated real-time decoding of motor intent to control a neuroprosthetic device by a SCI participant, highlighting its potential for advancing assistive neurotechnology.
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Disclaimer
The system used in the study referenced has not been approved cleared as safe effective by FDA. This device is limited by U.S. federal law to investigational use.
Acknowledgments
The authors would like thank the broader Battelle development, quality, and management teams for their engineering work and general project support. Algorithm development, data analysis, and manuscript drafting were funded through Battelle Memorial Institute internal research and development funds.
The spinal cord injury trial was supported by the Assistant Secretary of Defense for Health Affairs endorsed by the Department of Defense, in the amount of $2,004,786, through the Spinal Cord Injury Opinions,
Research Program under Award No. W81XWH-22-1-I1 1211119291111 and interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the Department of Defense.
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Justification: The clinical trial involving human subjects was conducted with IRB approval and informed consent was obtained from all participants. Participants were compensated for their time in accordance with ethical guidelines. Full instructions and screenshots are not central to the contribution and available upon request.
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Reviews:
[{"review_id": "8465KqwHKE", "reviewer": "Reviewer_jo6o", "summary": "This paper presents MUelim, a novel algorithm designed for real-time motor unit decomposition from high-density electromyography (HD-EMG) signals. The core contribution is an efficient method that leverages approximate joint diagonalization combined with a novel extend-lag data augmentation procedure to extract motor unit activity quickly and accurately. The method is validated on both simulated and physiological HD-EMG data and is shown to outperform state-of-the-art techniques in terms of decomposition speed—up to 3,700% faster—while maintaining comparable accuracy. MUelim is also demonstrated in a clinical setting, enabling an individual with spinal cord injury to control a neuroprosthetic device in real-time via decoded motor intent, showcasing its potential in assistive neurotechnology.", "questions": "1. How do you choose the extension factor R?\nThe paper performs a parameter sweep across R (extension factor) and lag, reporting that R = 4 and lag = 6 provides the best balance between number of decomposed sources and computation time. However, the choice of R is empirical and may benefit from adaptive tuning strategies.\n\n2. The study compares MUelim against two open-source baselines: MUEdit and Swarm Contrastive Decomposition. Are there any more comparison methods available? Further comparisons with deep learning-based or RMS-feature-based EMG decoding methods would be necessary for broader benchmarking.\n\n3. I did not find an analysis of algorithm complexity in the article. The paper lacks a formal complexity analysis, which would be helpful in understanding scalability, especially for embedded or wearable systems.\n\n4. In Table 1, is the extension factor R seriously affecting the response time? Increasing R leads to longer or shorter decomposition time but also more decomposed sources?\n\n5. In equation (1), dimensions of each component do not correspond to each other.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1. Efficiency: MUelim offers significant speed improvements over current methods, making it suitable for real-time applications.\n2. Clinical relevance: Demonstrated utility in a real clinical trial, enabling intention-driven control of a neuroprosthetic device.\n3. High accuracy: Achieved nearly perfect spike timing detection in simulated data (99.93% accuracy).\n4. Robust evaluation pipeline: Includes parameter sweeps (extension factor, lag, estimator types), detailed algorithm validation, and real-world application.\n5. Integration with spiking neural networks: Enables low-power, event-driven decoding for future neuromorphic applications.\n\nWeaknesses:\n\n1. Limited dataset diversity: Only tested on non-invasive HD-EMG; not validated on intramuscular EMG or broader subject populations.\n2. Simplified tasks: Real-world clinical task is relatively simple, potentially limiting generalization to more complex motor intentions.\n3. Algorithmic novelty: While practical, the core techniques are adapted from prior work rather than invented anew.\n4. Lack of theoretical complexity analysis: No formal time/space complexity or asymptotic runtime characterization is provided.", "was_revised": true, "final_justification": "The author solved my concerns and therefore I raised my final score.", "rebuttal": "We thank the reviewer for their thoughtful feedback and for recognizing the efficiency improvements, clinical relevance, high accuracy, and robust evaluation pipeline of our work. While the reviewer notes limitations regarding dataset diversity and task complexity, we emphasize that this work demonstrates for the first time the feasibility of real-time assistive device control for an individual with spinal cord injury using motor unit spike trains. The computational efficiency gains (up to 3,700% speed improvement) enable applications that were previously impractical, representing a significant advance for the field.\n\nBelow, we address each of the reviewer's points in detail:\n\n**1. Limited dataset diversity: Only tested on non-invasive HD-EMG; not validated on intramuscular EMG or broader subject populations.**\n\nThe manuscript provides both simulated and physiological evaluations, as detailed in the Results section and Table 1 of the main text. Simulated data experiments (main text, Section 3.1 and Supplementary Figure S2) demonstrate ground-truth validation, while physiological experiments (main text, Figure 2) show robust decomposition in a real-world scenario. We note this limitation regarding intramuscular EMG evaluation in the Discussion section, which does not diminish the contribution of our work. The method is not inherently limited to non-invasive HD-EMG and can be extended to other modalities, as discussed in the Discussion section. We prioritized demonstrating real-time, intention-driven control in a clinical setting, which was not previously practical due to the computational demands of existing methods.\n\n**2. Simplified tasks: Real-world clinical task is relatively simple, potentially limiting generalization to more complex motor intentions.**\n\nThe clinical demonstration was designed as a proof-of-concept to establish the feasibility of real-time, closed-loop neuroprosthetic control using decomposed motor unit activity. As shown in main text Section 3.2 and Figure 3, the participant successfully controlled multiple movement classes in real time. While more complex tasks are an important direction for future work, the current results represent a significant advance, as previous methods required up to hours for decomposition, precluding any realistic real-time application outside of the research lab. The ability to perform decomposition and decoder training within a single session is a key step toward practical, user-driven neurotechnology.\n\n**3. Algorithmic novelty: While practical, the core techniques are adapted from prior work rather than invented anew.**\n\nWe disagree with this characterization. MUelim combines established techniques (approximate joint diagonalization, extend-lag augmentation, iterative elimination) in a novel way that enables previously unattainable speed and practical use. The specific combination and implementation represents a significant algorithmic contribution that enables real-time applications not possible with existing methods. We note that NeurIPS guidelines emphasize that originality includes novel combinations of existing techniques that advance the field, which our work clearly demonstrates.\n\n**4. Lack of theoretical complexity analysis: No formal time/space complexity or asymptotic runtime characterization is provided.**\n\nWe thank the reviewer for this suggestion. MUelim's computational complexity is primarily determined by the joint diagonalization step, which is performed on the extended data matrix. Specifically, the data is extended using R lagged versions of each channel, so the number of extended channels is C × R, where C is the number of original channels and R is the extension factor.\n\nFor the joint diagonalization step, the per-iteration computational cost is O(K(C×R)² + (C×R)³), where K is the number of matrices being diagonalized and C×R is the number of extended channels. For large C×R, the (C×R)³ term dominates, so the complexity is approximately O((C×R)³) per iteration. This scaling arises because the most expensive operation is matrix multiplications of size (C×R) × (C×R).\n\nAs channels or extension factor increases, decomposition time increases accordingly. However, MUelim's advantage becomes more pronounced with more motor unit sources, as it efficiently extracts many sources simultaneously rather than incrementally. We will add this computational complexity analysis to the manuscript revision.\n\n**5. How do you choose the extension factor R?**\n\nThe choice of extension factor R is addressed empirically in the manuscript. As shown in Supplementary Figure S3 and main text Section 3.1, we performed a parameter sweep across R and τ (lag parameter), reporting that R=4 and τ=6 provided the best balance between number of decomposed sources and computation time. This represents a key algorithmic improvement over prior work by Negro et al. (2016), who recommends R = 1000/N (where N is the number of channels) with τ=1. By incorporating a larger lag parameter (τ=6), we achieve effective decomposition with a much smaller extension factor (R=4), which significantly reduces computational cost while maintaining performance. The method is robust across a range of R values, as demonstrated by our parameter sweeps. Adaptive or data-driven selection of R is an interesting direction for future work, but the current approach is effective and robust across the tested scenarios.\n\n**6. Are there any more comparison methods available?**\n\nWe benchmarked MUelim against state-of-the-art open-source methods (MUEdit and SCD) using their recommended parameters and implementations (see Table 1 and Methods, Section 2.3). There are other methods in the field, such as DEMUSE, but these are commercially available and not accessible for independent benchmarking. \n\nDeep learning approaches for motor unit decomposition have also been proposed, but these require ground truth spike trains for training, which are obtained using convolutive BSS methods like the Negro method (MUEdit). Thus, deep learning models are not independent of BSS-based approaches and are only as good as the BSS methods used to generate their training data. This dependency makes comparison redundant, as the deep learning models inherit the limitations of the underlying BSS method used for ground truth generation.\n\nThe Negro et al. convolutive BSS approach (as implemented in MUEdit) is widely considered the gold standard for motor unit decomposition. One additional open-source package, emgdecomp (Formento 2021), implements an algorithm that is \"heavily based on Negro et al\". We chose to use MUEdit for comparison as it is the newer tool and comes from the original research group. Thus, our benchmarking covers the most relevant and rigorous open-source baselines available to the community for motor unit decomposition.\n\n**7. In Table 1, is the extension factor R seriously affecting the response time? Increasing R leads to longer or shorter decomposition time but also more decomposed sources?**\n\nYes, the extension factor R significantly affects decomposition time. As shown in Table 1 and Supplementary Figure S3, increasing R generally increases the number of decomposed sources but also increases decomposition time due to the larger extended data matrix. This follows the O((C×R)³) computational complexity we described earlier. The parameter sweep results provide guidance for selecting R to balance speed and source yield, with R=4 providing an optimal trade-off for our applications.\n\n**8. In equation (1), dimensions of each component do not correspond to each other.**\n\nWe thank the reviewer for identifying this dimensional inconsistency. This is due to a notational oversight. We framed the BSS problem using standard literature convention but did not update the dimensions to match our implementation where samples are along axis 0. We will correct the equation in the manuscript revision to ensure proper dimensional alignment."}, {"review_id": "XMZTuZUz13", "reviewer": "Reviewer_zrVp", "summary": "This paper shows a method for accurate and efficient motor unit decomposition called MUelim. The authors demonstrate motor unit decomposition for simulated EMG data, an able-bodied individual, and an individual with spinal cord injury.", "questions": "* How do these motor unit decomposition methods perform with public datasets?\n* How useful is motor unit decomposition for downstream tasks such as classification of hand open, hand close, and rest compared to other preprocessing methods?\n* ASIA D usually means significant motor function is retained by the user. How much was the FES needed to restore function for this user for the pick and place tasks demonstrated?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 2, "strengths_and_weaknesses": "Strengths\n* Significant speed improvement of 3700% over an alternative method\n* Evaluates motor unit decomposition with a user with spinal cord injury and uses this for real-time inference for FES\n* Shows similar SNR and number of motor units decomposed as the baseline methods\n\nWeaknesses\n* Does not compare with public datasets for motor unit decomposition\n* Limited machine learning evaluation. ML evaluation is with a single participant in what seems to be a single trial for three similar pick and place tasks task. \n* Even with an able-bodied individual, only a single individual is tested for motor unit decomposition \n* Does not compare with other machine learning preprocessing methods for ML task (e.g. classification on raw signals, RMS signals, or time-frequency transforms).", "was_revised": true, "final_justification": "I acknowledge the significance of a fast motor unit decomposition algorithm for specific tasks, such as real-time neurorehabilitation through FES. The authors responded to my review satisfactorily where although machine learning evaluations seemed limited to me  NeurIPS has a stated focus of neural information processing systems and neuroscience applications. Additional evaluations on other datasets were not evaluated in this work, however showing feasibility of this algorithm in real-time is still significant.", "rebuttal": "We thank the reviewer for their constructive feedback and for recognizing the significant speed improvements, clinical relevance, and robust validation of MUelim. We emphasize that this work introduces a neural signal processing algorithm that aligns directly with NeurIPS's focus on neural information processing systems and neuroscience applications. The contribution is the algorithmic innovation that enables efficient motor unit decomposition, with the ML application serving as a validation of practical feasibility rather than the primary contribution.\n\nThe fundamental challenge we address is computational. Existing motor unit decomposition methods require hours to find BSS filters, while MUelim reduces this to minutes (up to 3,700% speed improvement). This enables practical deployment in clinical and at-home settings where lengthy setup procedures are prohibitive.\n\nBelow, we address the main points raised:\n\n**1. Does not compare with public datasets for motor unit decomposition.**\n\nWe acknowledge the value of benchmarking on public datasets. However, public dataset benchmarking would conflate algorithmic performance with downstream decoder performance, making it difficult to isolate the decomposition algorithm's effectiveness. Our focus was on validating the decomposition algorithm itself through simulated data with ground truth (Section 3.1) and physiological validation (Figure 2). This approach directly evaluates the decomposition algorithm without confounding factors from decoder choice or task complexity. Future work will include validating MUelim in decoding applications on public datasets.\n\n**2. Limited machine learning evaluation; only a single participant and trial for ML task.**\n\nThe ML component serves as a proof-of-concept demonstration that practical motor unit-based applications are feasible, not as the primary contribution. The core algorithmic contribution is validated through comprehensive simulated experiments (Section 3.1) and benchmarking against state-of-the-art methods (Table 1). The single-participant clinical demonstration establishes deployment in a challenging real-world scenario in an individual with motor impairment.\n\n**3. Does not compare with other machine learning preprocessing methods for ML task (e.g., classification on raw signals, RMS signals, or time-frequency transforms).**\n\nWe appreciate this suggestion to add to the manuscript. In an offline analysis trained using the same dataset used in session, our default RMS-NN pipeline achieved 86% bin-wise accuracy on the test set compared to the live 85% accuracy for the MU-SNN pipeline. Note that because FES was already triggered by the MU-based decoder live during the session, direct online comparison is not possible as we are evaluating the closed-loop response after FES has already been applied, which affects motor recruitment and subsequent EMG signals. With further SNN optimization, we could likely close this small gap, though this was not the focus of the work. The algorithmic contribution is enabling motor unit decomposition in minutes rather than hours, making these features when in inference mode accessible for real-time applications. We will add this comparison to the results and include a brief discussion of the implications in the discussion section.\n\n**4. How do these motor unit decomposition methods perform with public datasets?**\n\nAs noted above, benchmarking on public datasets is an important direction for future work. The present study focused on demonstrating feasibility and clinical translation, but we are committed to evaluating MUelim on open-source datasets and in broader ML contexts in future studies.\n\n**5. How useful is motor unit decomposition for downstream tasks such as classification of hand open, hand close, and rest compared to other preprocessing methods?**\n\nWe demonstrate motor unit features in an assistive technology application using an SNN decoder. Motor unit information provides distinct advantages for neural control applications. First, motor units can serve as a useful neural control signal and a proxy for cortical activity. In an FES-based rehabilitative device, this coupling between motor intent and movement enhances neuroplasticity through Hebbian principles by synchronizing descending motor commands with FES-enabled movement. Second, previous studies have shown that motor unit features are physiological biomarkers for monitoring and predicting motor function, providing detailed characterization of neural control strategies that aggregate signals cannot capture. Alternative preprocessing methods such as EMG envelope features or muscle synergies can also be used in these applications by analyzing gross muscle activity and muscle coordination. However, motor units provide a more precise neural signal that may enable more nuanced neural control and provides an understanding of motor function with higher specificity than gross EMG-based features.\n\n**6. ASIA D usually means significant motor function is retained by the user. How much was the FES needed to restore function for this user for the pick and place tasks demonstrated?**\n\nThank you for this question. The participant was able to partially open and close his hand, though not fully, and exhibited limited grip strength. Abnormal muscle synergies, particularly overactivity in the wrist flexors, limited his ability to achieve wrist extension. FES facilitated more complete hand opening, enhancing functional performance and reducing reliance on compensatory strategies. We will add this information to Section 2.4."}, {"review_id": "koICg3gY9J", "reviewer": "Reviewer_1GJy", "summary": "- The authors introduce a new algorithm MUelim for decomposing high-density surface EMG into the motor units that generated the signals.\n- The algorithm shows great speed improvements (up to 3700%) versus the current state-of-the-art methods\n- They demonstrated the usefulness of the decomposition by having a participant with SCI control their hand through FES by decoding the intention (hand open, close, rest) from the extracted MUAPs using a spiking neural network.", "questions": "Methods:\n1. Paragraph on how the MUAP waveforms are extracted (lines 181-186) is not very clear. Please add more details into how this process works.\n2. You mention in the introduction that the addition of time-delayed extensions prior to joint diagonalizations helps with potentially extracting more sources than channels. However, in section 2.3 you only evaluate cases in which there are many more channels than sources. What happens when the number of sources is higher than the number of channels? Also, please compare the simulation results you got with existing methods (such as MUedit and SCD). \n3. In section 2.4, please add how much residual movement the participant had available. Were they able to open and close their hand by themselves?\n4. The manuscript would greatly benefit from some diagram of the training procedure and inference during the neuroprosthetic experiment, potentially as an addition to Figure 3.\n5. Was the EMG decomposition done before starting the inference experiment? If so, how did you decompose the EMG signal in real-time? Please clarify. If you are pre-computing the forward filters, please clarify.\n\nResults:\n1. Please add a figure to the main text with the results from the simulation experiment, as it can give key insights into whether the proposed method is working as expected. At the beginning of the results section you cite Figure 1, but that doesn’t really contain simulation results.\n2. Make sure that the units of Figure 2B (especially the right plot) are correct. \n3. Figure 2C is not mentioned in the main text: what is the message you are trying to convey with it?\n4. In Table 1, why do you show variability for MUelim but not for the other methods? Also, add a discussion on what the expected number of motor units should be, to better understand the results.\n5. How does the per-bin accuracy looks like if you use the full non-decomposed EMG rather than motor units? I would imagine that it would be much higher performance, but that would depend on how much residual movement the participant may have. Please add a few sentences to the limitations paragraph related to this method in this participant.\n6. Mark the transition between rest and hand open in Figure 3A\n7. Figure 3D probably has wrong units.\n\nDiscussion:\n1. In lines 322-323 you claim “MUelim achieves similar or greater source yield with 323 substantially reduced computation time, supporting its use in closed-loop neuroprosthetic systems”. However, the computation times you show are in the order of minutes. If you are pre-computing the forward filters please clarify and tone down the claim.\n\nIf these comments and questions are addressed, I’ll increase my score.", "limitations": "Limitations are discussed in the manuscript and I have no ethical concerns with the submission.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n- The presented algorithm works fast and builds on existing literature\n- Having a fast and accurate algorithm for MUAP decomposition can be very valuable for a number of other projects\n- They show that the method works in simulated data, which is key to understand the behavior of the novel method.\n- They test it on a real scenario and show that it works and can be useful to extract control signals in a participant with SCI.\n- Paper is well written and leads the reader nicely through the methods and the results.\n\nWeaknesses:\n- During simulation, it would be good to have a comparison with other methods, making sure that the results are similar. Also, please add a figure to the main text related to simulation: making sure that the novel method can detect all sources and has results similar to existing methods is a key results of the paper. Finally, you discuss that one of the key parts of the method allowed to get more sources than the available channels, but you do not test this in simulation.\n- You mention in the paper that you were able to use the method online in the clinical setting. However, the time for decomposition you showed was in minutes. Did you pre-compute the decomposition and then use the forward matrix online? This needs an important clarification, as one of your motivation points talks about being able to use this online, and this may not be a big difference with existing methods.\n- The task you tested in the clinical setting is probably not the best way to motivate this method: from the video in the supplemental, I can see the participant had quite a bit of residual movement, which means that you could do the same task just by processing the full EMG. The method would be better motivated in cases in which you are interested in the MUAPs individually: maybe more neuroscience related questions, or tasks in which participants are instructed to control specific MUAPs.", "was_revised": true, "final_justification": "I believe the paper to be a valuable addition to NeurIPS. The authors addressed all my concerns, and their work will be valuable for researchers interested in motor unit decomposition.", "rebuttal": "We thank the reviewer for their thorough and constructive feedback, and for the many helpful suggestions to improve the manuscript. We are pleased that the reviewer found the work technically solid and well-motivated. \n\nBelow, we address each question and outline the corresponding changes we will make to the manuscript. Regarding the main weaknesses identified by the reviewer: (1) simulation comparison and figure updates are addressed in questions 2 and 6, (2) online vs offline decomposition clarification is covered in questions 5 and 13, and (3) clinical task motivation concerns are discussed in question 10.\n\n**1. Paragraph on how the MUAP waveforms are extracted (lines 181-186) is not very clear. Please add more details into how this process works.**\n\nMUAP waveforms are extracted using spike-triggered averaging (STA), which involves averaging the EMG signal around detected spike times to isolate the average waveform associated with each motor unit. Specifically, our implementation performs the following steps: (1) For each detected motor unit spike timing, we extract a time window of configurable duration (default 30ms) centered around the spike impulse. (2) To improve waveform quality, we reconstruct the EMG signal from source space using the computed BSS inverse filters while suppressing other motor unit sources, which reduces cross-contamination between motor units. (3) To handle temporal jitter in spike detection, we align waveforms to their global maxima across channels to ensure consistent temporal alignment before averaging. (4) The algorithm extracts waveforms from all available channels, and for visualization purposes, we display results from the 5 most active channels based on signal amplitude. (5) Individual MUAP traces can be computed using a sliding window approach spanning subsets of detected spikes to show temporal evolution throughout the recording. This reconstruction-based STA approach is advantageous because it leverages the spatial filtering capabilities of the BSS decomposition to provide cleaner, less contaminated MUAP waveforms compared to traditional direct EMG averaging. We will add these technical details to the Methods section to clarify the MUAP extraction process.\n\n**2. You mention in the introduction that the addition of time-delayed extensions prior to joint diagonalizations helps with potentially extracting more sources than channels. However, in section 2.3 you only evaluate cases in which there are many more channels than sources. What happens when the number of sources is higher than the number of channels? Also, please compare the simulation results you got with existing methods (such as MUedit and SCD).**\n\nThank you for this suggestion and catching an oversight on our part. The extend-lag procedure increases effective dimensionality from C channels to C×R extended channels, theoretically enabling extraction of up to C×R sources per BSS iteration. We will add simulation scenarios where the number of sources exceeds the original channel count to directly validate this key theoretical claim.\n\nRegarding simulation comparisons, we acknowledge this limitation and agree that direct comparison on identical synthetic data would strengthen our evaluation. We will include results comparing MUelim, SCD, and MUEdit on identical simulated datasets to provide ground truth validation of relative performance.\n\n**3. In section 2.4, please add how much residual movement the participant had available. Were they able to open and close their hand by themselves?**\n\nThe participant was able to partially open and close his hand, though not fully, and exhibited limited grip strength. Abnormal muscle synergies, particularly overactivity in the wrist flexors, limited his ability to achieve wrist extension. FES facilitated more complete hand opening, enhancing functional performance and reducing reliance on compensatory strategies. We will add this information to Section 2.4.\n\n**4. The manuscript would greatly benefit from some diagram of the training procedure and inference during the neuroprosthetic experiment, potentially as an addition to Figure 3.**\n\nWe agree with the reviewer that a diagram would improve clarity. We will add a diagram illustrating the training and inference workflow for the neuroprosthetic experiment.\n\n**5. Was the EMG decomposition done before starting the inference experiment? If so, how did you decompose the EMG signal in real-time? Please clarify. If you are pre-computing the forward filters, please clarify.**\n\nThe BSS forward filters are computed in-session (fit phase) after collecting a block of training data, then used for real-time inference (transform phase), following standard scikit-learn convention. The supplementary pseudocode shows these phases. We will clarify this procedure in the Methods section.\n\n**6. Please add a figure to the main text with the results from the simulation experiment, as it can give key insights into whether the proposed method is working as expected. At the beginning of the results section you cite Figure 1, but that doesn't really contain simulation results.**\n\nWe will incorporate simulation experiment results from the supplementary materials into a figure in the main text, as suggested by the reviewer.\n\n**7. Make sure that the units of Figure 2B (especially the right plot) are correct.**\n\nThank you for catching this. When combining figures with different axes, we mistakenly removed the units on the right plot. We will update the figure to ensure the units correspond appropriately to each axis.\n\n**8. Figure 2C is not mentioned in the main text: what is the message you are trying to convey with it?**\n\nFigure 2C shows the inverse BSS filters, which help to visually localize MU sources on the grid and assess their spatial properties. We will explicitly mention and explain Figure 2C in the main text.\n\n**9. In Table 1, why do you show variability for MUelim but not for the other methods? Also, add a discussion on what the expected number of motor units should be, to better understand the results.**\n\nUncertainty was reported for MUelim because we ran the algorithm over multiple seeds for each parameter setting (main text, Sec. 2.3). For SCD, results were deterministic and for MUEdit, the manual nature of the tool precluded repeated runs. Regarding the expected number of motor units, the yield depends on the number of channels, muscle, and recording quality. In simulation and experimental studies (see Farina et al., 2008; Negro et al., 2016), typical yields for high-density grids in hand/forearm muscles are on the order of 10–30 unique motor units per contraction, with higher yields possible in ideal conditions. Our results are consistent with these expectations. We will add clarifying details to the text.\n\n**10. How does the per-bin accuracy looks like if you use the full non-decomposed EMG rather than motor units? I would imagine that it would be much higher performance, but that would depend on how much residual movement the participant may have. Please add a few sentences to the limitations paragraph related to this method in this participant.**\n\nWe appreciate this suggestion to add to the manuscript. In an offline analysis trained using the same dataset used in session, our default RMS-NN pipeline achieved 86% bin-wise accuracy on the test set compared to the live 85% accuracy for the MU-SNN pipeline. Note that because FES was already triggered by the MU-based decoder live during the session, direct online comparison is not possible as we are evaluating the closed-loop response after FES has already been applied, which affects motor recruitment and subsequent EMG signals. With further SNN optimization, we could likely close this small gap, though this was not the focus of the work. As suggested by the reviewer, we will add this limitation to the discussion section.\n\n**11. Mark the transition between rest and hand open in Figure 3A**\n\nWe will mark the transition between rest and hand open in Figure 3A as suggested by the reviewer.\n\n**12. Figure 3D probably has wrong units.**\n\nThank you for catching this error. The units should be mV, not µV. We will correct this in the revised manuscript.\n\n**13. \"MUelim achieves similar or greater source yield with substantially reduced computation time, supporting its use in closed-loop neuroprosthetic systems\". However, the computation times you show are in the order of minutes. If you are pre-computing the forward filters please clarify and tone down the claim.**\n\nThank you for this important clarification. Our method's fast BSS forward filter computation (minutes vs up to hours for existing methods) is what makes it well-suited for real-time applications. We will reference the supplementary pseudocode and update the text to make the fit/transform workflow clearer. We will revise this sentence to: \"MUelim achieves similar or greater source yield with substantially reduced BSS filter computation time (minutes vs up to hours), enabling practical deployment in closed-loop neuroprosthetic systems where rapid session setup is required.\"\n\nWe thank the reviewer again for their positive assessment and helpful feedback, which will significantly improve the clarity and quality of the manuscript."}, {"review_id": "xllLxOxWvU", "reviewer": "Reviewer_RhMr", "summary": "This manuscript introduces an approach MUEdit for decomposing motor unit action potentials from HD-sEMG. The proposed method uses a combination of joint diagonalization and expansion of the domain by time-lagging to identify motor unit sources and identify more sources than sEMG channels in a computationally efficient manner. They show successful recovery in synthetic data. They compare to a small set of alternative methods on a single subject, showing improvements in speed compared to alternative approaches. They show a demo using the extracted MUAPs to drive a spiking neural network in a spinal cord injury patient.", "questions": "* The synthetic data experiments are too easy, as the algorithm achieves perfect performance. Competing methods are not benchmarked on synthetic data, which is the only regime that has a ground truth, so its unclear exactly how these are compared. \n\n* The proposed algorithm is benchmarked in Figure 2 with extensive hyperparameter tuning as shown in Supplementary Figure 3 and then compared to alternative algorithms using open source hyperparameters. Its not clear if these hyperparameters were tuned on the evaluation set, and how the competing algorithms would perform with additional hyperparameter tuning. \n\n* The evaluation and comparison is only on a single subject. It is unclear what degree of tuning is needed to deploy this to additional subjects which would impact computation time. \n\n* The spiking NN demo does not add much to the manuscript. It is unclear if similar results could be achieved with any spike extraction approach. \n\nMinor\n\n* Why is uncertainty only reported in Table 1 for 1 method?\n\n* Can you be more specific about how alternative methods were computationally optimized. \n\n* What is the time scaling of approaches with channels and additional motor units\n\n* Where does the assumption of sparsity in the BSS fail\n\n* Can you give more details about the extracted MUAPs? Are their qualitative features that can be used to further convince the reader that these are 'real'", "limitations": "Yes", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\nThe algorithm appears to be novel and show some advantages in speed/computation time compared to other approaches. \nThere are several contemporary alternative approaches benchmarked. \n\nWeaknesses\n* Evaluations and baselines are unconvincing and limited\n* The advantages of the algorithm is not made especially clear, and its performance in different data regimes (e.g. sparse, dense, scaling with channel counts) is not shown. There is not a set of ablations that makes clear how different algorithmic properties and features factor into computational savings and data quality (e.g. removing time lag, approximations of joint diagonalization).", "was_revised": true, "final_justification": "Score increased 1 point based on rebuttal. The manuscript is still below the bar in my opinion, in large part because there is a single evaluation participant, which is simply inadequate by any standards, and because the synthetic data experiments don't truly probe the quality of the model.", "rebuttal": "We thank the reviewer for their constructive feedback and for recognizing the novelty and computational efficiency of our approach. Our primary goal was to introduce and validate the MUelim algorithm, with the physiological example serving as a pilot demonstration of its practical utility. The main advantage of MUelim is its substantial improvement in computation speed for motor unit decomposition, enabling real-time applications that are not feasible with existing methods.\n\nBelow, we address the main points raised:\n\n**1. Evaluations and baselines are unconvincing and limited. The advantages of the algorithm is not made especially clear, and its performance in different data regimes (e.g. sparse, dense, scaling with channel counts) is not shown. There is not a set of ablations that makes clear how different algorithmic properties and features factor into computational savings and data quality (e.g. removing time lag, approximations of joint diagonalization).**\n\nWe respectfully disagree and note that the manuscript provides both simulated and physiological evaluations with rigorous benchmarking: (1) comprehensive simulated data experiments (8 scenarios with 32-64 channels and 3-6 sources each), (2) physiological experiments on HD-EMG grid data, and (3) direct benchmarking against state-of-the-art methods using recommended parameters (Table 1 and Supp. Fig. S3).\n\nRegarding ablations, we conducted four key ablation studies (Supp. Fig. S3) evaluating computation time and sources extracted: (1) time lag and (2) extension factor ablation showing the extend-lag procedure effect. When extension factor=1, the extend-lag procedure is effectively removed (same number of channels with no extension or time lag). (3) Bin size and (4) SPD matrix estimator comparison evaluating parameters that affect what matrices are used as input for joint diagonalization. While we focus on one joint diagonalization method, this was deliberate as evaluating different approaches has been extensively studied in prior work.\n\n**2. The synthetic data experiments are too easy, as the algorithm achieves perfect performance. Competing methods are not benchmarked on synthetic data, which is the only regime that has a ground truth, so its unclear exactly how these are compared.**\n\nWe respectfully disagree that the synthetic data experiments are \"too easy.\" The simulation scenarios were designed to include multiple sources, noise, and amplitude modulation, providing physiologically realistic scenarios. The high accuracy achieved reflects our approach's effectiveness on realistic EMG data, not oversimplified scenarios.\n\nHowever, we acknowledge the reviewer's valid point about direct comparison on synthetic data. We agree that benchmarking all methods on identical synthetic data would strengthen our work. We will include results comparing MUelim, SCD, and MUEdit on the same simulated datasets in the revision.\n\n**3. The proposed algorithm is benchmarked in Fig. 2 with extensive hyperparameter tuning as shown in Supp. Fig. 3 and then compared to alternative algorithms using open source hyperparameters. Its not clear if these hyperparameters were tuned on the evaluation set, and how the competing algorithms would perform with additional hyperparameter tuning.**\n\nAs shown in Supp. Fig. S3 and described in the main text (Sec. 3.1), the parameter sweeps for MUelim were not intended as hyperparameter tuning for performance optimization, but rather to demonstrate robustness and parameter effects on speed and source count. For competing methods, we used default parameters recommended in prior works and open-source implementations, which are already optimized (see Table 1 and Methods, Sec. 2.3). No tuning was performed on the evaluation set for any method, as stated in the manuscript.\n\n**4. The evaluation and comparison is only on a single subject. It is unclear what degree of tuning is needed to deploy this to additional subjects which would impact computation time.**\n\nMUelim was evaluated on both simulated and physiological datasets, and parameter sweeps demonstrate that the same algorithmic parameters worked well across all tested datasets. For the spinal cord injury participant demonstration, we used default parameter settings without prior tuning, demonstrating real-world applicability where parameter optimization is not feasible. We will clarify this in manuscript revision. However, we acknowledge that for deployment to new subjects, BSS filters would need recomputing, as these are subject-specific due to individual differences in anatomy, electrode placement, and muscle fiber organization.\n\n**5. The spiking NN demo does not add much to the manuscript. It is unclear if similar results could be achieved with any spike extraction approach.**\n\nThe reviewer is correct that similar results can be achieved with other spike extraction approaches. However, the key contribution is demonstrating practical feasibility in real-world settings. MUelim's fast decomposition enables use in clinical or at-home applications where lengthy setup procedures are not practical. We prioritized demonstrating this with a spinal cord injury participant as part of a clinical trial with strict time constraints. Other methods requiring hours for decomposition would not be feasible in such sessions. This represents the first demonstration of this workflow in a clinical population, as described in Supp. Video S1.\n\n**6. Why is uncertainty only reported in Table 1 for 1 method?**\n\nUncertainty was reported for MUelim because we ran the algorithm over multiple seeds for each parameter setting (main text, Sec. 2.3). For SCD, results were deterministic and for MUEdit, the manual nature of the tool precluded repeated runs. This is stated in the caption of Table 1 and in the main text (Sec. 3.1).\n\n**7. Can you be more specific about how alternative methods were computationally optimized.**\n\nFor SCD, we used built-in GPU acceleration as recommended by the authors (main text, Sec. 2.3). For MUEdit, we followed the standard workflow with default parameters as described in documentation and open-source implementation. No custom optimizations were performed for any method, as stated in Methods (main text, Sec. 2.3).\n\n**8. What is the time scaling of approaches with channels and additional motor units**\n\nMUelim's computational complexity is primarily determined by the joint diagonalization step, which is performed on the extended data matrix. Specifically, the data is extended using R lagged versions of each channel, so the number of extended channels is C × R, where C is the number of original channels and R is the extension factor.\n\nFor the joint diagonalization step, the per-iteration computational cost is O(K(C×R)² + (C×R)³), where K is the number of matrices being diagonalized and C×R is the number of extended channels. For large C×R, the (C×R)³ term dominates, so the complexity is approximately O((C×R)³) per iteration. This scaling arises because the most expensive operation is matrix multiplications of size (C×R) × (C×R).\n\nAs channels or extension factor increases, decomposition time increases accordingly. However, MUelim's advantage becomes more pronounced with more motor unit sources, as it efficiently extracts many sources simultaneously rather than incrementally. We will add this computational complexity analysis to the manuscript revision.\n\n**9. Where does the assumption of sparsity in the BSS fail**\n\nMotor unit spike trains are inherently sparse, consisting of discrete action potentials separated by periods of inactivity, with firing rates typically in the 2-30 Hz range. The sparsity assumption may fail in rare cases of highly overlapping or synchronous firing among many motor units, or during pathological conditions with dense coordinated activity. However, under typical physiological conditions, motor unit population activity remains sparse, and BSS methods like MUelim are well suited.\n\n**10. Can you give more details about the extracted MUAPs? Are their qualitative features that can be used to further convince the reader that these are 'real'**\n\nThe extracted MUAPs are real and physiologically plausible. MUAPs are electrical signatures generated by summation of action potentials from muscle fibers within a single motor unit. In our study, MUAPs were extracted using spike-triggered averaging of reconstructed EMG signal, which is a standard approach that effectively cancels noise and isolates the true underlying action potential waveform (main text, Sec. 3.1 and Fig. 2B).\n\nThe qualitative features of extracted MUAPs in our results are consistent with established physiological characteristics:\n\n• Morphology: MUAPs typically exhibit a triphasic or biphasic shape. This morphology reflects the depolarization and repolarization phases of muscle fiber action potentials.\n\n• Amplitude: Observed amplitudes are within the expected range for surface EMG, and vary according to the number and proximity of muscle fibers within the motor unit.\n\n• Duration: MUAP durations are consistent with known physiological values, typically ranging from 5 to 30 ms, reflecting realistic muscle fiber conduction velocities and spatial dispersion.\n\n• Firing rate: Extracted spike trains show realistic firing rates, typically in the range of 2-30 Hz that increase with force (main text, Fig. 2A).\n\n• Simulated data validation: We validated MUelim on simulated EMG data with known ground truth, confirming that the extracted MUAPs and spike timings closely match the true underlying sources (main text, Sec. 3.1 and Supp. Fig. S2)."}]

Author rebuttal:

Meta-review: I want to thank all the reviewers and authors for their work and for the discussion.

**Strengths:**

- All reviewers agreed that the empirical speedup compared to the current gold standard while maintaining comparable accuracy is impressive. I would add that crucial advances in the field of motor unit decomposition are fairly rare (as evidenced by the related work discussion in this paper) such that the step forward provided by this work weighs particularly heavy.
- While the topic of the approach (motor unit decomposition) is relatively niche, it is crucial in the clinical application context of neuro-prosthetic control.
- Multiple reviewers also mentioned the quality of the simulation studies (jo60 and 1GJy)

**Weaknesses:**

- Multiple reviewers were concerned by the low number of baselines. However, this was explained by the authors with specifics of the domain, limiting the number of matching baselines.
- Multiple reviewers mentioned that public data sets should also have been used to evaluate the model. The authors explained that this has the crucial drawback of lacking a ground truth (we do not know what the true spike trains would be).
- The user study was only performed with a single subject. However, with commendable effort, the authors recruited five additional subjects for the discussion period and presented additional results, consistent with the results reported in the paper.

Overall, the argument against public data set appears not quite convincing and such additional results would certainly have raised the empirical quality of the paper. However, the additional empiric results with healthy subjects provide (arguably) an even more convincing extension. As such, I still believe that acceptance is in order.
Decision: Accept (poster)