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REVIEW 3 major objections 3 minor 19 references

Deep-Unrolling Multidimensional Harmonic Retrieval Algorithms on Neuromorphic Hardware

T0 review · 3 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that complex-valued S-LISTA networks for multidimensional harmonic retrieval can be converted to spiking neural networks that run on SpiNNaker2 at nearly five times the power efficiency of an embedded GPU, with moderate…

desk verdict A real engineering demo of complex FS-to-SNN conversion on SpiNNaker2, undermined by an overclaimed activation model and an inconsistent power ratio. read the letter →

arxiv 2412.04008 v1 pith:KMRAPDSH submitted 2024-12-05 eess.SP cs.AIcs.ARcs.NE

Vlad C. Andrei , Alexandru P. Drăguţoiu , Gabriel Béna , Mahmoud Akl , Yin Li , Matthias Lohrmann , Ullrich J. Mönich , Holger Boche This is my paper · ORCID
classification eess.SPcs.AIcs.ARcs.NE
keywords multidimensionalharmonicretrievaldeepunrollingspikingneuralnetworksANN-to-SNNconversionFewSpikescodingcomplex-valuedSpiNNaker2sparserecovery
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to show that a deep-unrolling sparse-recovery algorithm for multidimensional harmonic retrieval (MHR) can be moved from GPUs onto neuromorphic hardware without losing its practical usefulness. It converts the complex-valued S-LISTA network into a spiking neural network (SNN) by extending Few Spikes coding to complex-valued activations, then maps the SNN onto the SpiNNaker2 board. Measured against an NVIDIA Jetson Xavier, the SpiNNaker2 implementation consumes about 768 mW less on average, an almost five-fold power-efficiency gain, while support-recovery error stays comparable to FISTA and close to S-LISTA for few sources. This matters because energy-hungry GPU inference is a bottleneck for radar and wireless sensing systems that need single-snapshot harmonic estimation.

What carries the argument

The machinery is a complex-valued extension of Few Spikes coding: two FS neurons, one driven by the real part and one by the imaginary part, whose membrane dynamics release a serialized binary code over K timesteps, and whose weighted sum (Eq. 14) approximates the desired activation. Each activation in S-LISTA—the identity encoder and the complex soft-threshold for each layer—is replaced by its FS approximation trained by gradient descent on the squared error (Eq. 15). The SpiNNaker2 mapping uses pipelined receive-send cycles and 4-bit quantized projections for the convolution weights.

What would settle it

Measure the approximation error of the FS pair on a coupled complex function such as $s \cdot \max(1 - \alpha/|s|, 0)$ on a bounded disk; if the error does not fall toward zero as the number of timesteps $K$ grows and the sampling of the domain refines, the claim that the neuron model approximates arbitrary complex-valued activations fails, and the conversion fidelity for S-LISTA's soft-threshold is not established.

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Extended reading notes

Core claim

The central claim is that the Few Spikes (FS) neuron model, extended to a pair of coupled real-and-imaginary neurons, can approximate complex-valued activations well enough on a bounded domain that an entire complex-valued convolutional network solving MHR can be converted to an SNN and run on SpiNNaker2. The converted network achieves support recovery similar to S-LISTA for one to a few sources and beats FISTA, while drawing roughly one fifth of the GPU's power. The authors attribute residual performance loss to 4-bit weight quantization and to the residual errors in the FS neuron approximations.

Load-bearing premise

The load-bearing premise is that the two-neuron FS pair can approximate any complex activation that appears in the converted network; the pair is a sum of a function of the real part and a function of the imaginary part, so any activation whose real and imaginary outputs each depend on both input components, such as the standard complex soft-threshold, cannot be represented exactly.

Editorial extensions

If this is right

  • If the conversion is sound, single-snapshot MHR estimation can be deployed on neuromorphic hardware with near-GPU accuracy and roughly one fifth the power draw.
  • The same pipeline extends S-LISTA-style deep-unrolling networks beyond image classification to complex-valued regression tasks in signal processing.
  • Because the converted SNN outperforms 100-iteration FISTA with only five layers, the conversion preserves the convergence benefit of deep unrolling while reducing execution cost.
  • For one to five sources, the converted SNN's support recovery remains comparable to S-LISTA and degrades gracefully as the number of sources grows.
  • The measured power-efficiency advantage makes neuromorphic deployment a credible option for bandwidth- and energy-constrained sensing systems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The authors do not draw this inference, but if the FS pair can only represent functions that are sums of a function of the real part and a function of the imaginary part, then coupled complex activations such as the standard complex soft-threshold cannot be represented exactly; a corrected rule would need cross-coupled membrane dynamics or an amplitude-phase decomposition.
  • The paper's own observation that quantization is the main bottleneck points to a testable extension: retraining with quantization-aware training, or using more than 4 bits for projections, should close much of the gap between the SNN and the original CNN.
  • The same conversion recipe could be applied to other complex-valued unrolled networks, such as learned ISTA variants for two- and three-dimensional MHR, once the memory constraints of larger neuromorphic boards are lifted.
  • The two-mode power distribution on SpiNNaker2, caused by dynamic voltage and frequency scaling, suggests that comparing only average power may overstate the benefit in continuously loaded scenarios and understate it in bursty inference workloads.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper proposes a conversion pipeline that maps the complex-valued, deep-unrolling S-LISTA algorithm for multidimensional harmonic retrieval into spiking neural networks (SNNs) using an extension of Few Spikes (FS) coding. A complex-valued two-neuron FS model is introduced, and a full ANN-to-SNN conversion is implemented on the SpiNNaker2 neuromorphic board. The authors report support-recovery performance on a 1-D harmonic retrieval task and power measurements comparing SpiNNaker2 with an NVIDIA Jetson Xavier, claiming an almost five-fold power efficiency gain at moderate performance loss.

Significance. If the claims were sound, the paper would contribute a useful step toward deploying complex-valued sparse-recovery algorithms on neuromorphic hardware, and the hardware demonstration on SpiNNaker2 is a genuine practical effort. The paper includes real measurements, a plausible pipeline for mapping trained convolutional layers to SNNs, and a clear comparison against FISTA. However, the central technical claims are undermined by a representational limitation in the proposed complex FS neuron and by inconsistencies in the power-efficiency numbers. The paper is therefore not currently publishable in its present form.

major comments (3)
  1. [Section III-A, Eqs. (10)-(14)] The claim in Contribution 1 that the two-neuron FS model can approximate arbitrary complex-valued activations on a bounded domain is not supported and appears to be false. In Eqs. (10)-(13), the real neuron's state evolves using only the real part of the input and the imaginary neuron's state using only the imaginary part; the output in Eq. (14) is thus of the form f_hat(s) = g(Re(s)) + j h(Im(s)). This class cannot represent the complex soft-threshold used in S-LISTA, S_alpha(s) = s * max(1 - alpha/|s|, 0), whose real part depends on Im(s) through |s|. The approximation results in Fig. 2 test only real-valued functions, so the conversion fidelity for the actual S-LISTA activation is not established. This is a load-bearing issue because the paper's entire conversion pipeline is justified by this approximation claim.
  2. [Section IV, Fig. 4 and power comparison] The reported power numbers are internally inconsistent. The text states that the Jetson mean is 1022.35 mW and that SpiNNaker2 consumes almost 768 mW less, which implies a SpiNNaker2 mean of approximately 254.35 mW. Yet the described PDF 'consist[s] of two spikes, one centered around 25 mW, the other one around 225 mW.' If the distribution were concentrated at these two modes, its mean could not exceed 225 mW unless there is additional unquantified mass above 225 mW. Moreover, the ratio 1022.35 / 254.35 is approximately 4.02, not 'almost 5×'; even comparing against 225 mW gives only about 4.54×. The 'almost 5×' claim in the abstract and conclusions is therefore not supported by the reported measurements.
  3. [Section IV, Eq. (17)] The support recovery error (SRE) definition is ill-posed as written. The expression inside the cardinality braces is a set of pairs (l, l') with l in supp(b_hat_d) and l' in supp(b_d), but the intended quantity appears to be the number of mismatched support indices normalized by the true support size, e.g., |supp(b_hat_d) Δ supp(b_d)| / |supp(b_d)|. As written, the metric would behave very differently and could inflate or distort the reported performance. This makes the quantitative support-recovery results in Fig. 3 difficult to interpret.
minor comments (3)
  1. [Section III-B and Fig. 2] There is a mismatch between the text and the figure caption: Section III-B says FS Id is obtained for f(s) = s, while Fig. 2 is captioned 'FS neuron approximating Eq. (5) (α = 1) and f(s) = s^2.' Please clarify which functions were actually approximated and whether they were evaluated on real or complex inputs.
  2. [Section IV, first paragraph] The phrase 'employing a bigger β' is ambiguous: β is earlier defined as the learning rate in line 'a learning rate of β = 0,009', and it is unclear how a larger learning rate mitigates approximation artifacts. The authors likely mean a larger number of timesteps K or a different hyperparameter; this should be stated explicitly.
  3. [General] The title and abstract emphasize 'multidimensional' harmonic retrieval, but the experimental evaluation is restricted to M = 1 dimension (N = 64, L = 128). The authors do note the memory limitation, but the mismatch between the claimed scope and the demonstrated scope should be acknowledged more clearly in the abstract or conclusions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: SNN performance and power efficiency are measured against external baselines; FS parameter fitting is standard approximation, not a renamed prediction.

full rationale

The paper's central claims—that S-LISTA can be converted to an SNN via complex-valued FS coding and that the converted SNN on SpiNNaker2 achieves roughly 5× better power efficiency at moderate performance loss—are supported by external measurements and comparisons against baselines such as FISTA and the original S-LISTA CNN on an NVIDIA Jetson. The FS neuron parameters (d,h,T) are fitted to the target activations by minimizing Eq. (15); this is ordinary function fitting, and the resulting approximations are then used inside a conversion pipeline whose output is evaluated on a support-recovery task with simulated data. No fitted parameter is renamed as a prediction: the support recovery error in Eq. (17) and the power measurements in Figure 4 are independent benchmarks. Self-citations, including the SpiNNaker2 hardware reference [4] and the representational-computing references [6]–[8], are background material and are not load-bearing for the measured efficiency claim. The skeptical concern that the two-neuron FS representation of Eqs. (10)–(14) may be unable to represent non-separable complex activations such as the complex soft-threshold is an expressiveness/correctness issue, not a circularity, and does not reduce any claimed result to its own inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claims rest on trained S-LISTA weights, fitted FS neuron parameters per activation, and untested representational assumptions about the two-neuron complex FS model. The power-efficiency result is measured, not derived, but the measurement is internally inconsistent.

free parameters (4)
  • FS neuron parameters per layer and activation (d_R, h_R, T_R, d_I, h_I, T_I) = K-dimensional real vectors per activation and layer
    Optimized in Eq. (15) to approximate the identity and soft-threshold functions; approximation quality is empirical and not guaranteed.
  • S-LISTA weights W1_t, W2_t and thresholds alpha_t = Learned from simulated MHR data via ADAM
    Trained on a labeled dataset with normalized SNR; the converted SNN inherits these trained weights.
  • Number of FS timesteps K = Chosen below 30 for good approximation
    Trade-off between approximation accuracy, latency and energy; selected empirically per Figure 2.
  • 4-bit weight quantization = 4 bits for real and imaginary parts
    Post-training quantization to fit SpiNNaker2 memory constraints; degrades task performance.
assumptions (5)
  • domain assumption The Few Spikes coding scheme of Stockl and Maass [13] is correct for real-valued approximation.
    The paper builds on the FS neuron model without re-deriving its properties.
  • domain assumption The S-LISTA architecture [14] solves MHR when trained.
    The paper uses S-LISTA as the base network and does not analyze its convergence or optimality.
  • ad hoc to paper The optimization in Eq. (15) with a triangular subgradient approximation converges to a good activation approximation.
    Used to fit FS parameters; no convergence guarantee is given, only empirical evidence for a few functions.
  • ad hoc to paper Complex-valued activations used in S-LISTA are within the representable class of the two-neuron FS model.
    Assumed in Section III-A when claiming arbitrary approximation; the model appears separable in Re and Im, so this is likely false for coupled activations.
  • domain assumption The power measurement methodology (idle subtraction, sleep times) isolates device power consumption.
    The paper relies on this to compare the Jetson and SpiNNaker2, but provides no calibration or cross-validation details.

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Cite this review

Pith. "Pith review of Deep-Unrolling Multidimensional Harmonic Retrieval Algorithms on Neuromorphic Hardware." pith.science (2026). https://pith.science/paper/KMRAPDSH

@misc{pith2026241204008,
  author       = {Pith},
  title        = {Pith review of: Deep-Unrolling Multidimensional Harmonic Retrieval Algorithms on Neuromorphic Hardware},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KMRAPDSH}},
  note         = {Machine review of arXiv:2412.04008}
}
read the original abstract

This paper explores the potential of conversion-based neuromorphic algorithms for highly accurate and energy-efficient single-snapshot multidimensional harmonic retrieval (MHR). By casting the MHR problem as a sparse recovery problem, we devise the currently proposed, deep-unrolling-based Structured Learned Iterative Shrinkage and Thresholding (S-LISTA) algorithm to solve it efficiently using complex-valued convolutional neural networks with complex-valued activations, which are trained using a supervised regression objective. Afterward, a novel method for converting the complex-valued convolutional layers and activations into spiking neural networks (SNNs) is developed. At the heart of this method lies the recently proposed Few Spikes (FS) conversion, which is extended by modifying the neuron model's parameters and internal dynamics to account for the inherent coupling between real and imaginary parts in complex-valued computations. Finally, the converted SNNs are mapped onto the SpiNNaker2 neuromorphic board, and a comparison in terms of estimation accuracy and power efficiency between the original CNNs deployed on an NVIDIA Jetson Xavier and the SNNs is being conducted. The measurement results show that the converted SNNs achieve almost five-fold power efficiency at moderate performance loss compared to the original CNNs.

Figures

Figures reproduced from arXiv: 2412.04008 by the authors.

Figure 1
Figure 1. Schematic representation of S-LISTA architecture. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FS neuron approximating Eq. (5) (α = 1) and f(s) = s 2 for different K. Blue denotes the true function, and orange is the approximation. 1 2 3 4 5 Number of Sources 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Support Recovery Error FISTA 100 Iterations Converted SNN LISTA 5 Layers [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. SRE averaged over SNRs from 10dB to 30dB. was reached [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Power consumption statistical distribution. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

19 extracted references · 14 canonical work pages

  1. [1]

    Integrated Sensing and Communications: Toward Dual-Functional Wire- less Networks for 6G and Beyond,

    F. Liu, Y . Cui, C. Masouros, J. Xu, T. X. Han, Y . C. Eldar, and S. Buzzi, “Integrated Sensing and Communications: Toward Dual-Functional Wire- less Networks for 6G and Beyond,” IEEE journal on selected areas in communications, vol. 40, no. 6, pp. 1728–1767, 2022

    work page 2022

  2. [2]

    Compressive Two-Dimensional Harmonic Retrieval via Atomic Norm Minimization,

    Y . Chi and Y . Chen, “Compressive Two-Dimensional Harmonic Retrieval via Atomic Norm Minimization,” IEEE Transactions on Signal Process- ing, vol. 63, no. 4, pp. 1030–1042, Feb. 2015

    work page 2015

  3. [3]

    Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing,

    V . Monga, Y . Li, and Y . C. Eldar, “Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing,” IEEE Signal Processing Magazine, vol. 38, no. 2, pp. 18–44, 2021

    2021

  4. [4]

    SpiNNaker2: A Large-Scale Neuromor- phic System for Event-Based and Asynchronous Machine Learning,

    H. A. Gonzalez, J. Huang, F. Kelber, K. K. Nazeer, T. Langer, C. Liu, M. Lohrmann, A. Rostami, M. Sch ¨one, B. V ogginger, T. C. Wunderlich, Y . Yan, M. Akl, and C. Mayr, “SpiNNaker2: A Large-Scale Neuromor- phic System for Event-Based and Asynchronous Machine Learning,” Jan. 2024, arXiv:2401.04491 [cs]

    arXiv 2024

  5. [5]

    Training Spiking Neural Networks Using Lessons From Deep Learning,

    J. K. Eshraghian, M. Ward, E. O. Neftci, X. Wang, G. Lenz, G. Dwivedi, M. Bennamoun, D. S. Jeong, and W. D. Lu, “Training Spiking Neural Networks Using Lessons From Deep Learning,” Proceedings of the IEEE, vol. 111, no. 9, pp. 1016–1054, Sep. 2023, conference Name: Proceedings of the IEEE

    work page 2023

  6. [6]

    Limitations of Deep Learning for Inverse Problems on Digital Hardware,

    H. Boche, A. Fono, and G. Kutyniok, “Limitations of Deep Learning for Inverse Problems on Digital Hardware,” IEEE Transactions on Information Theory , vol. 69, no. 12, pp. 7887–7908, Dec. 2023

    work page 2023

  7. [7]

    Remote State Estimation and Blum-Shub-Smale Machines-A Computability Analysis with Applications to Virtual-Twinning,

    H. Boche, Y . B ¨ock, C. Deppe, and F. H. P. Fitzek, “Remote State Estimation and Blum-Shub-Smale Machines-A Computability Analysis with Applications to Virtual-Twinning,” IEEE Transactions on Automatic Control, pp. 1–16, 2024

    work page 2024

  8. [8]

    Denial-of-Service Attacks on Communication Systems: Detectability and Jammer Knowledge,

    H. Boche, R. F. Schaefer, and H. V . Poor, “Denial-of-Service Attacks on Communication Systems: Detectability and Jammer Knowledge,” IEEE Transactions on Signal Processing , vol. 68, pp. 3754–3768, 2020

    work page 2020

Show all 19 references
  1. [9]

    Con- version of Continuous-Valued Deep Networks to Efficient Event-Driven Networks for Image Classification,

    B. Rueckauer, I.-A. Lungu, Y . Hu, M. Pfeiffer, and S.-C. Liu, “Con- version of Continuous-Valued Deep Networks to Efficient Event-Driven Networks for Image Classification,” Frontiers in Neuroscience , vol. 11, p. 682, Dec. 2017

    2017

  2. [10]

    Going Deeper in Spiking Neural Networks: VGG and Residual Architectures,

    A. Sengupta, Y . Ye, R. Wang, C. Liu, and K. Roy, “Going Deeper in Spiking Neural Networks: VGG and Residual Architectures,” Frontiers in Neuroscience, vol. 13, p. 95, Mar. 2019

    2019

  3. [11]

    Spiking Neural Network for Fourier Transform and Object Detection for Automotive Radar,

    J. L ´opez-Randulfe, T. Duswald, Z. Bing, and A. Knoll, “Spiking Neural Network for Fourier Transform and Object Detection for Automotive Radar,” Frontiers in Neurorobotics, vol. 15, Jun. 2021

    2021

  4. [12]

    Time-coded Spiking Fourier Transform in Neuromorphic Hardware,

    J. L ´opez-Randulfe, N. Reeb, N. Karimi, C. Liu, H. A. Gonzalez, R. Dietrich, B. V ogginger, C. Mayr, and A. Knoll, “Time-coded Spiking Fourier Transform in Neuromorphic Hardware,” IEEE Transactions on Computers, vol. 71, no. 11, pp. 2792–2802, Nov. 2022

    2022

  5. [13]

    Optimized Spiking Neurons Can Classify Images With High Accuracy Through Temporal Coding With Two Spikes,

    C. St ¨ockl and W. Maass, “Optimized Spiking Neurons Can Classify Images With High Accuracy Through Temporal Coding With Two Spikes,” Nature Machine Intelligence , vol. 3, no. 3, pp. 230–238, Mar. 2021

    2021

  6. [14]

    Structured lista for multidi- mensional harmonic retrieval,

    R. Fu, Y . Liu, T. Huang, and Y . C. Eldar, “Structured lista for multidi- mensional harmonic retrieval,” IEEE Transactions on Signal Processing , vol. 69, pp. 3459–3472, 2021

    2021

  7. [15]

    Tensor algebra and multidimensional harmonic retrieval in signal processing for mimo radar,

    D. Nion and N. D. Sidiropoulos, “Tensor algebra and multidimensional harmonic retrieval in signal processing for mimo radar,” IEEE Transac- tions on Signal Processing , vol. 58, no. 11, pp. 5693–5705, 2010

    2010

  8. [16]

    A fast iterative shrinkage-thresholding algo- rithm for linear inverse problems,

    A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algo- rithm for linear inverse problems,” SIAM Journal on Imaging Sciences , vol. 2, no. 1, pp. 183–202, 2009

    2009

  9. [17]

    Xception: Deep Learning with Depthwise Separable Convo- lutions,

    F. Chollet, “Xception: Deep Learning with Depthwise Separable Convo- lutions,” Apr. 2017, arXiv:1610.02357 [cs]

    2017 arXiv

  10. [18]

    Adam: A Method for Stochastic Optimization,

    D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” Jan. 2017, arXiv:1412.6980 [cs]

    2017 arXiv

  11. [19]

    NVIDIA Jetson Xavier NX Documentation

    “NVIDIA Jetson Xavier NX Documentation.” [Online]. Avail- able: https://docs.nvidia.com/jetson/archives/r35.4.1/DeveloperGuide/ text/SO/JetsonXavierNxSeries.html

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