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REVIEW 4 major objections 4 minor 52 references

Scaling of hardware-compatible perturbative training algorithms

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A perturbative training method can match backpropagation accuracy on million-parameter networks, because time-to-accuracy does not scale with size.

desk verdict Makes a useful distinction between gradient-estimation time and time-to-target-accuracy for perturbative training, but the claim of backprop-matching accuracy at million-parameter scale outruns the evidence. read the letter →

arxiv 2501.15403 v1 pith:D4PGJ6XI submitted 2025-01-26 cs.LG cs.NEmath.OC

Bakhrom G. Oripov , Andrew Dienstfrey , Adam N. McCaughan , Sonia M. Buckley This is my paper · ORCID
classification cs.LGcs.NEmath.OC MSC 68T0790C56
keywords multiplexedgradientdescentperturbativetrainingzeroth-orderoptimizationweightperturbationnodeneuromorphichardwareestimationscalingtime-to-accuracy
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

Multiplexed gradient descent (MGD) is a zeroth-order training method that treats a neural network as a black box: it applies small random perturbations to weights or nodes, reads the resulting change in loss, and correlates the two to estimate the gradient. The paper's central claim is that the time to estimate that gradient grows with network size, but the time to actually train the network to a target accuracy does not—in simulations, iterations to reach 80% accuracy vary by less than an order of magnitude while network size changes by more than three orders of magnitude. This matters because the presumed linear scaling of gradient estimation has been the main reason perturbative methods were dismissed as impractical for training large analog neuromorphic hardware. The paper further shows that the MGD gradient can replace the backpropagation gradient inside standard optimizers such as Adam, and that a network with over one million parameters trains to the same testing accuracy as backpropagation.

What carries the argument

The central object is the MGD estimator $G = (1/\tau_\theta)\Lambda^{-1}\sum_{t=1}^{\tau_\theta}\Delta C(t)\Theta(t)$, where $\Theta(t)$ is a vector of mean-zero random perturbations, $\Delta C(t)$ is the resulting change in loss, $\Lambda$ is the perturbation covariance, and $\tau_\theta$ is a time constant controlling how many perturbation steps are averaged before a weight update. By Taylor expansion, $\Delta C(t) \approx \nabla_\Theta C \cdot \Theta(t)$, so correlating loss changes with perturbations recovers the gradient; the paper proves $G$ is unbiased and computes its covariance, which vanishes as $\tau_\theta\to\infty$. Two concrete perturbation schemes are studied: weight perturbation, which perturbs every parameter and costs $K=N$ perturbations per gradient estimate, and node perturbation, which perturbs the input to each activation and costs $K \approx \sqrt{N}$ for dense layers, at the price of a one-step local backpropagation and a multiplication per synapse. The three MGD time constants let the same framework interpolate between strategies such as coordinate descent and SPSA, and let an implementation trade more gradient averaging for fewer weight updates.

What would settle it

Run the same FashionMNIST architecture sweep on a physical MGD chip and measure wall-clock time to 80% testing accuracy for networks of $10^4$ and $10^6$ parameters; if the larger network takes roughly $10^2$ times longer, the claimed time-to-accuracy scaling does not survive real hardware costs.

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Extended reading notes

Core claim

On its own terms, the paper establishes a separation between two quantities that earlier analyses conflated: the number of iterations needed to estimate the gradient of the loss to a given accuracy, and the number of iterations needed to drive testing accuracy to a fixed target. For weight perturbation the former scales as $N$ and for node perturbation as $\sqrt{N}$, where $N$ is the number of parameters; for the latter, across networks from roughly $10^4$ to $10^6$ parameters, the iteration count to 80% testing accuracy stays within one order of magnitude and in parts of the range decreases. The same flat pattern does not hold when task complexity is varied: training time rises strongly with the number of FashionMNIST classes. The paper also proves that the MGD estimator $G$ is an unbiased estimator of the gradient with covariance that shrinks as the integration time $\tau_\theta$ grows, and demonstrates numerically that using $G$ inside the Adam update rule reduces the number of weight updates to 80% accuracy by about 37%.

Load-bearing premise

The load-bearing premise is that one MGD iteration costs the same wall-clock time regardless of network size, because perturbations, loss readouts, and weight updates are assumed to happen in parallel on hardware.

Editorial extensions

If this is right

  • Gradient-estimation time is the wrong benchmark for judging perturbative training; time-to-accuracy is the quantity that matters for whether the approach can solve a real problem.
  • A network with more than one million parameters can be trained with MGD to the same testing accuracy as backpropagation on the same architecture, at least on FashionMNIST.
  • Because $G$ is a drop-in replacement for the backpropagation gradient, standard optimizer machinery such as momentum and Adam can be combined with MGD; in the paper Adam cuts the number of updates to 80% accuracy by roughly 37%.
  • Increasing the gradient integration time $\tau_\theta$ can reduce the required number of weight updates by orders of magnitude, which matters for hardware with limited write endurance.
  • Node perturbation is not universally faster than weight perturbation: its advantage depends on the target accuracy, and convolutional layers can have more activations than weights, reversing the naive scaling comparison.

Reading between the lines

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

  • The flat iteration-count scaling becomes a flat wall-clock scaling only if one MGD iteration costs the same time for any network size; on hardware that perturbs parameters or reads losses sequentially, the time-to-accuracy curves in the paper would need to be rescaled by a size-dependent factor.
  • The near-independence of training time from network size is consistent with overparameterized networks being easier to optimize, but the paper does not isolate that mechanism; a direct test would hold the architecture and optimizer fixed and vary only width while tracking the full loss trajectory.
  • The results suggest a benchmark shift for analog neuromorphic hardware: comparisons should report time-to-target-accuracy on actual devices rather than per-iteration gradient fidelity, and task complexity should be controlled separately from network size.
  • Because MGD needs only forward propagation and a global cost-change broadcast, its success hints at a route to online learning in spiking and other non-differentiable hardware; the paper flags this as future work rather than claiming it.
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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

4 major / 4 minor

Summary. The paper studies multiplexed gradient descent (MGD), a perturbative zeroth-order training method intended for in-situ training of analog neuromorphic hardware. It extends the MGD framework from weight perturbation to node perturbation, proves that the MGD estimator is unbiased and computes its covariance in Appendix A, and reports FashionMNIST simulations on convolutional networks whose size ranges from roughly 2.5e4 to more than 1e6 parameters. The central claims are that the time to estimate the gradient grows with network size in the expected way, but the time to reach a target accuracy does not follow this scaling and in fact often decreases with network size, and that MGD can train a network with more than one million parameters to the same testing accuracy as backpropagation. The paper also demonstrates that MGD can drive the Adam optimizer and discusses hardware-specific tuning of the MGD time constants.

Significance. If the central scaling claim holds on real hardware, it would materially change the practicality of perturbative, model-free training for large analog neuromorphic systems, because the standard objection that gradient-estimation time grows linearly with parameter count would not translate into wall-clock training time. The paper has genuine strengths: the unbiasedness and covariance derivation in Appendix A is careful and appears correct; the distinction between gradient-estimation time and time-to-accuracy is an important and testable framing; the pseudocode is complete; and the code is publicly available. However, the empirical support for the strongest form of the claim is incomplete, as detailed in the major comments, so the paper needs revision before the headline conclusions are fully supported.

major comments (4)
  1. [Section 3.2, Fig. 4] The claim that 'a network with more than 1 million parameters can be trained to the same testing accuracy as backpropagation' is not supported by the reported experiments. Fig. 4a shows a backpropagation baseline only for N=2.55e5, reaching 91.6%, whereas Fig. 4b measures time to 80% accuracy for larger networks and shows no backpropagation curve at all. Since 80% is substantially below the accuracy backpropagation attains, the observed flat scaling could be an artifact of an undemanding threshold; the authors should report the time to reach the accuracy that backpropagation actually reaches for each network size, or otherwise demonstrate that the flatness persists at BP-comparable accuracy.
  2. [Section 3.2, Conclusion] The paper converts iteration counts into wall-clock time through an implicit hardware model. The statement that '10^9 MGD time iterations would take 16 minutes on hardware with a modest speed of 1 MHz for perturbations, inference and updates' assumes that one iteration costs O(1) time independent of N, i.e., that perturbations, loss readouts, and weight updates are fully parallel. Fig. 4b/c report iterations, not time; if the per-iteration cost on the target hardware grows with network size, the headline scaling of 'time to train' with N would be different. The authors should state this hardware model explicitly and, ideally, plot the projected wall-clock time under that model.
  3. [Appendix A, Algorithm 1] There is a mismatch between the theoretical estimator and the pseudocode. Appendix A analyzes G defined in Eq. (11) for simultaneous perturbations of all K parameters, with one cost change Delta C per timestep. Algorithm 1, however, loops over layers and computes a separate output, cost, and cost change Delta C_l for each layer l using only that layer's perturbation theta_l. This is a layer-wise perturbative estimator, not the simultaneous estimator of Eqs. (10)-(12). The normalization Gamma in Table 2 uses the total K, but the per-layer cost change involves only K_l parameters. The authors should clarify which algorithm was actually simulated, and either correct the pseudocode to match the theory or provide the corresponding moments for the layer-wise estimator.
  4. [Fig. 4b/c] The central scaling result is reported without error bars or a statement of how many random initializations were used. Fig. 3 reports quartile bands over 10 initializations, but the caption for Fig. 4 does not; the claim that time to 80% accuracy 'varies by less than one order of magnitude' needs variance information to be interpretable, especially because the conclusion contradicts earlier scaling arguments.
minor comments (4)
  1. [Section 3.2] The text says 'node perturbation was reduced by approximately a factor of 2 over node perturbation'; this should read 'over weight perturbation.'
  2. [Fig. 3b caption] There is a typo in 'weight nad node perturbation,' and the caption should state whether the dashed lines are theoretical predictions or fits to the data.
  3. [Section 2.2] The perturbations are called Bernoulli but they are symmetric +-delta; the term 'symmetric Bernoulli' or 'Rademacher' would be more precise.
  4. [Eq. (5)] The layer index l is used but the perturbation Theta is written without a layer superscript; clarifying that Theta is added to the pre-activation of the layer would remove ambiguity.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central scaling and accuracy claims are measured against an external backpropagation benchmark; the Ref. [27] self-citation introduces the MGD framework but does not carry the load.

full rationale

The paper's headline claim—that time to reach a target accuracy does not scale linearly with network size and can match backpropagation above 10^6 parameters—rests on the simulations in Figs. 3 and 4, not on an equation that is equal to its input. The gradient estimator G is defined by Eq. (11) and proven unbiased in Appendix A from the stated perturbation model and the linearized cost expansion (Eq. 10); the proof is checked against the true gradient ∇WC computed by backpropagation (Fig. 3a), so it is not a fit renamed as a prediction. The flat training-time scaling in Fig. 4b is measured directly as iteration counts to 80% test accuracy, and is deliberately contrasted with the separately measured gradient-estimation scaling in Fig. 3b, so it does not reduce to the N-scaling by construction. The only significant self-citation is Ref. [27], which introduced the MGD framework; here it provides the framework's time-constant structure, but the new results (accuracy matching, scaling behavior, optimizer compatibility) are independently simulated in this paper and benchmarked against backpropagation. No uniqueness theorem or ansatz is imported from the authors' prior work to force the conclusions. Whether the 80% threshold adequately supports the phrase 'actually solve the problem of interest' is an external-validity concern, not a circularity one.

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

The central claims rest on four free hyperparameters and four background assumptions. No new physical entities are introduced. The most fragile item is the hardware-time independence assumption, which converts iteration counts into the claimed scaling result.

free parameters (4)
  • learning rate eta = not reported
    Set separately per network size to keep training stable; values not reported in the paper, so the scaling results in Fig 4b are conditional on this tuning.
  • perturbation amplitude delta = not reported
    Amplitude of Bernoulli perturbations; must be small enough for the linear approximation in Eq 10, but the value is not stated.
  • gradient integration time tau_theta = 1 for main scaling results, 1000 for Adam experiment
    Sets the number of perturbations per weight update; the main scaling uses tau_theta = 1, and the paper shows the number of weight updates decreases with tau_theta.
  • target accuracy threshold = 80% testing accuracy
    The 'time to train' figure of merit is measured to this threshold; conclusions about scaling may depend on this choice of threshold.
assumptions (4)
  • domain assumption The loss change is approximated by a first-order Taylor expansion (Eq 10), requiring sufficiently small perturbations.
    Section 2.2, Eqs 9-10. This is the basis for the unbiased estimator; standard but load-bearing.
  • standard math Perturbations theta_i(t) are independent over i and t, mean zero, and symmetric (odd moments vanish).
    Appendix A.1 assumptions 1-3; used to prove unbiasedness and covariance.
  • ad hoc to paper A single MGD iteration has a hardware cost independent of network size because perturbations and cost readouts are parallel.
    Section 3.2: 'iterations could be implemented very quickly on a dedicated analog hardware' with the 1 MHz example; this turns iteration counts into wall-clock time and is not demonstrated.
  • domain assumption For node perturbation, weight gradients are recovered from node perturbations by Eq 6b, requiring one backward multiplication per synapse and stored inputs.
    Section 2.1, Eq 6b; the hardware requirements are discussed but not implemented.

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Cite this review

Pith. "Pith review of Scaling of hardware-compatible perturbative training algorithms." pith.science (2026). https://pith.science/paper/D4PGJ6XI

@misc{pith2026250115403,
  author       = {Pith},
  title        = {Pith review of: Scaling of hardware-compatible perturbative training algorithms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D4PGJ6XI}},
  note         = {Machine review of arXiv:2501.15403}
}
read the original abstract

In this work, we explore the capabilities of multiplexed gradient descent (MGD), a scalable and efficient perturbative zeroth-order training method for estimating the gradient of a loss function in hardware and training it via stochastic gradient descent. We extend the framework to include both weight and node perturbation, and discuss the advantages and disadvantages of each approach. We investigate the time to train networks using MGD as a function of network size and task complexity. Previous research has suggested that perturbative training methods do not scale well to large problems, since in these methods the time to estimate the gradient scales linearly with the number of network parameters. However, in this work we show that the time to reach a target accuracy--that is, actually solve the problem of interest--does not follow this undesirable linear scaling, and in fact often decreases with network size. Furthermore, we demonstrate that MGD can be used to calculate a drop-in replacement for the gradient in stochastic gradient descent, and therefore optimization accelerators such as momentum can be used alongside MGD, ensuring compatibility with existing machine learning practices. Our results indicate that MGD can efficiently train large networks on hardware, achieving accuracy comparable to backpropagation, thus presenting a practical solution for future neuromorphic computing systems.

Figures

Figures reproduced from arXiv: 2501.15403 by the authors.

Figure 1
Figure 1. (a) Illustration of weight perturbation, where each weight is perturbed individually. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Illustration of gradient descent down a cost landscape using MGD, for varying [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Analyzing the behavior of gradient estimation in MGD. (a) The accuracy of the [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Time needed to successfully train networks with MGD as a function of network [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]
Figure 5
Figure 5. Figure 5: Number of weight updates required to train FashionMNIST on a 2 [PITH_FULL_IMAGE:figures/full_fig_p021_5.png]
Figure 6
Figure 6. Figure 6: Number of weight updates required to train FashionMNIST to 80% accuracy on [PITH_FULL_IMAGE:figures/full_fig_p024_6.png]

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Reference graph

Works this paper leans on

52 extracted references · 39 canonical work pages

  1. [1]

    & Fitch, A

    Hagey, K. & Fitch, A. Sam Altman Seeks Trillions of Dollars to Reshape Business of Chips and AI Accessed on 2024-05-10. https : / / www . wsj . com / tech / ai / sam - altman-seeks-trillions-of-dollars-to-reshape-business-of-chips-and-ai- 89ab3db0

    work page 2024

  2. [2]

    The Forward-Forward Algorithm: Some Preliminary Investigations 2022

    Hinton, G. The Forward-Forward Algorithm: Some Preliminary Investigations 2022. arXiv: 2212.13345 [cs.LG]

    arXiv 2022

  3. [3]

    P., Santoro, A., Marris, L., Akerman, C

    Lillicrap, T. P., Santoro, A., Marris, L., Akerman, C. J. & Hinton, G. Backpropagation and the brain. Nature Reviews Neuroscience 21, 335–346. issn: 1471-0048 (Apr. 2020)

    work page 2020

  4. [4]

    Li, C. et al. Efficient and self-adaptive in-situ learning in multilayer memristor neural networks. Nature Communications 2018 9:1 9, 1–8. issn: 2041-1723. https://www. nature.com/articles/s41467-018-04484-2 (1 June 2018). 36

    work page 2018

  5. [5]

    Science 380, 398–404

    Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380, 398–404. issn: 10959203. https://www.science.org/doi/10. 1126/science.ade8450 (6643 Apr. 2023)

    work page 2023

  6. [6]

    Nandakumar, S. R. et al. Mixed-Precision Deep Learning Based on Computational Memory. Frontiers in Neuroscience 14, 519263. issn: 1662453X. www.frontiersin. org (May 2020)

    work page 2020

  7. [7]

    Van Doremaele, E. et al. Hardware implementation of backpropagation using progres- sive gradient descent for in situ training of multilayer neural networks.Science Advances

    work page

  8. [8]

    Nature Communications 2023 14:1 14, 1–18

    Hardware-aware training for large-scale and diverse deep learning inference workloads using in-memory computing-based accelerators. Nature Communications 2023 14:1 14, 1–18. issn: 2041-1723. https://www.nature.com/articles/s41467-023-40770-4 (1 Aug. 2023)

    work page 2023

Show all 52 references
  1. [9]

    & McCaughan, A

    Buckley, S. & McCaughan, A. A general approach to fast online training of modern datasets on real neuromorphic systems without backpropagation in ICONS 2022: Inter- national Conference on Neuromorphic Systems (2022)

    2022

  2. [10]

    https://www.science.org/doi/10.1126/sciadv.ado8999 (28 July 2024)

    issn: 23752548. https://www.science.org/doi/10.1126/sciadv.ado8999 (28 July 2024)

    2024 doi

  3. [11]

    Wright, L. G. et al. Deep physical neural networks trained with backpropagation.Nature 601, 549–555. issn: 1476-4687 (7894 2022)

    2022

  4. [12]

    Bichler, O. et al. Visual pattern extraction using energy-efficient ”2-PCM synapse” neuromorphic architecture. IEEE Transactions on Electron Devices 59, 2206–2214. issn: 00189383 (8 2012)

    2012

  5. [13]

    Friedmann, S. et al. Demonstrating Hybrid Learning in a Flexible Neuromorphic Hard- ware System. IEEE Transactions on Biomedical Circuits and Systems 11, 128–142. issn: 19324545 (1 Feb. 2017). 37

    2017

  6. [14]

    Frontiers in Neural Circuits 0, 53

    Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of NeoHebbian Three-Factor Learning Rules. Frontiers in Neural Circuits 0, 53. issn: 1662-5110 (July 2018)

    2018

  7. [15]

    & Kailath, T

    Dembo, A. & Kailath, T. Model-Free Distributed Learning. IEEE Transactions on Neural Networks 1, 58–70 (1990)

    1990

  8. [16]

    & Koga, M

    Matsumoto, T. & Koga, M. Novel learning method for analogue neural networks. ElL 26, 1136. issn: 0013-5194 (Sept. 1990)

    1990

  9. [17]

    A Fast Stochastic Error-Descent Algorithm for Supervised Learning and Optimization in Advances in Neural Information Processing Systems 5 (NIPS 1992) (1992), 244–251

    Cauwenberghs, G. A Fast Stochastic Error-Descent Algorithm for Supervised Learning and Optimization in Advances in Neural Information Processing Systems 5 (NIPS 1992) (1992), 244–251

    1992

  10. [18]

    & Jabri, M

    Flower, B. & Jabri, M. Summed weight neuron perturbation in NIPS’92: Proceedings of the 5th International Conference on Neural Information Processing Systems (1992), 212–219

    1992

  11. [19]

    Alspector, R

    J. Alspector, R. Meir, B. Yuhas, A. Jayakumar & D. Lippe. A parallel gradient descent method for learning in analog VLSI neural networks — Proceedings of the 5th Interna- tional Conference on Neural Information Processing Systems in NIPS’92: Proceedings of the 5th Internationa...

    1992

  12. [20]

    Kirk, D. B. & Kerns, D. Analog VLSI Implementation of Multi-dimensional Gradient Descent in Advances in Neural Information Processing Systems 5 (NIPS 1992) (1992), 789–796

    1992

  13. [21]

    & Kanata, Y

    Maeda, Y., Hirano, H. & Kanata, Y. A learning rule of neural networks via simultaneous perturbation and its hardware implementation.Neural Networks 8, 251–259. issn: 0893- 6080 (Jan. 1995)

    1995

  14. [22]

    An analog VLSI recurrent neural network learning a continuous-time trajectory

    Cauwenberghs, G. An analog VLSI recurrent neural network learning a continuous-time trajectory. IEEE Transactions on Neural Networks 7, 346–361 (1996). 38

    1996

  15. [23]

    & Fiesler, E

    Moerland, P. & Fiesler, E. Hardware-friendly learning algorithms for neural networks: an overview in (Institute of Electrical and Electronics Engineers (IEEE), 1996), 117– 124

    1996

  16. [24]

    J., Gyurcsik, R

    Montalvo, A. J., Gyurcsik, R. S. & Paulos, J. J. Toward a general-purpose analog VLSI neural network with on-chip learning. IEEE Transactions on Neural Networks 8, 413– 423 (1997)

    1997

  17. [25]

    & Matsumoto, T

    Miyao, H., Noguchi, K., Koga, M. & Matsumoto, T. Multifrequency oscillation learning method for analog neural network: Its implementation in a learning LSI. Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 80 (1997)

    1997

  18. [26]

    Neural Networks in Analog Hardware - Design and Implementation Issues

    Draghici, S. Neural Networks in Analog Hardware - Design and Implementation Issues. International Journal of Neural Systems 10, 19–42 (Apr. 2000)

    2000

  19. [27]

    Analog VLSI Autonomous Systems for Learning and Optimization PhD thesis (Caltech, 1994)

    Cauwenberghs, G. Analog VLSI Autonomous Systems for Learning and Optimization PhD thesis (Caltech, 1994)

    1994

  20. [28]

    McCaughan, A. N. et al. Multiplexed gradient descent: Fast online training of modern datasets on hardware neural networks without backpropagation. APL Machine Learn- ing 1, 026118. issn: 2770-9019. eprint: https://pubs.aip.org/aip/aml/article- pdf / doi / 10 . 1063 / 5 . 01576...

    doi

  21. [29]

    & Ahmad, N

    Dalm, S., van Gerven, M. & Ahmad, N. Effective Learning with Node Perturbation in Deep Neural Networks Oct. 2023. https://arxiv.org/abs/2310.00965v3

    2023 arXiv

  22. [30]

    & Hinton, G

    Ren, M., Kornblith, S., Liao, R. & Hinton, G. Scaling Forward Gradient With Local Losses 2023. arXiv: 2210.03310 [cs.LG]

    2023 arXiv

  23. [31]

    Zhao, Y. et al. Tensor-Compressed Back-Propagation-Free Training for (Physics-Informed) Neural Networks Aug. 2023. https://arxiv.org/abs/2308.09858v2

    2023 arXiv

  24. [32]

    Bandyopadhyay, S. et al. Single chip photonic deep neural network with accelerated training Aug. 2022. arXiv: 2208.01623. http://arxiv.org/abs/2208.01623. 39

    2022 arXiv

  25. [33]

    Spall, J. C. Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation. IEEE Transactions on Automatic Control 37, 332–341 (3 1992)

    1992

  26. [34]

    P., Cownden, D., Tweed, D

    Lillicrap, T. P., Cownden, D., Tweed, D. B. & Akerman, C. J. Random synaptic feed- back weights support error backpropagation for deep learning. Nature Communications

  27. [35]

    https://doi.org/10.1038/ncomms13276 (Nov. 2016)

    2016 doi

  28. [36]

    & Memmesheimer, R

    Z¨ uge, P., Klos, C. & Memmesheimer, R. M. Weight versus Node Perturbation Learn- ing in Temporally Extended Tasks: Weight Perturbation Often Performs Similarly or Better. Physical Review X 13. issn: 21603308 (2 Apr. 2023)

    2023

  29. [37]

    Kingma, D. P. & Ba, J. Adam: A Method for Stochastic Optimization 2014. arXiv: 1412.6980 [cs.LG]

    2014 arXiv

  30. [38]

    & Hinton, G

    Ren, M., Kornblith, S., Liao, R. & Hinton, G. Scaling Forward Gradient With Local Losses 2022

    2022

  31. [39]

    Yan, M. et al. Emerging opportunities and challenges for the future of reservoir com- puting. Nature Communications 2024 15:1 15, 1–18. issn: 2041-1723. https://www. nature.com/articles/s41467-024-45187-1 (1 Mar. 2024)

    2024

  32. [40]

    B., Zhu, Q

    Huang, G. B., Zhu, Q. Y. & Siew, C. K. Extreme learning machine: Theory and appli- cations. Neurocomputing 70, 489–501. issn: 0925-2312 (1-3 Dec. 2006)

    2006

  33. [41]

    How we created neuromorphic engineering

    Mead, C. How we created neuromorphic engineering. Nature Electronics 2020 3:7 3, 434–435. issn: 2520-1131. https://www.nature.com/articles/s41928-020-0448-2 (7 July 2020)

    2020

  34. [42]

    P., Kim, H., Budhathoki, R

    Adhikari, S. P., Kim, H., Budhathoki, R. K., Yang, C. & Chua, L. O. A circuit-based learning architecture for multilayer neural networks with memristor bridge synapses. IEEE Transactions on Circuits and Systems I: Regular Papers 62, 215–223 (Jan. 2015). 40

    2015

  35. [43]

    & Yao, W

    Wang, C., Xiong, L., Sun, J. & Yao, W. Memristor-based neural networks with weight simultaneous perturbation training. Nonlinear Dynamics 95, 2893–2906. issn: 1573- 269X (2019)

    2019

  36. [44]

    Seung, H. S. Learning in Spiking Neural Networks by Reinforcement of Stochastic Synaptic Transmission. Neuron 40, 1063–1073. issn: 0896-6273 (Dec. 2003)

    2003

  37. [45]

    Fiete, I. R. & Seung, H. S. Gradient Learning in Spiking Neural Networks by Dynamic Perturbation of Conductances. Phys. Rev. Lett. 97, 048104. https://link.aps.org/ doi/10.1103/PhysRevLett.97.048104 (4 July 2006)

    2006 doi

  38. [46]

    & Seung, H

    Werfel, J., Xie, X. & Seung, H. S. Learning Curves for Stochastic Gradient Descent in Linear Feedforward Networks. Neural Computation 17, 2699–2718. issn: 0899-7667 (Dec. 2005)

    2005

  39. [47]

    Mukhoty, B. et al. Direct Training of SNN using Local Zeroth Order Method. Advances in Neural Information Processing Systems 36, 18994–19014. https://github.com/ BhaskarMukhoty/LocalZO. (Dec. 2023)

    2023

  40. [48]

    & Lin, Z

    Xiao, M., Meng, Q., Zhang, Z., He, D. & Lin, Z. Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks. https://arxiv.org/abs/2407.12516v1 (July 2024)

    2024 arXiv

  41. [49]

    Hiratani, N., Mehta, Y., Lillicrap, T. P. & Latham, P. E. On the Stability and Scalability of Node Perturbation Learning. Advances in Neural Information Processing Systems 35, 31929–31941 (Dec. 2022)

    2022

  42. [50]

    Malladi, S. et al. Fine-Tuning Language Models with Just Forward Passes. https : //arxiv.org/abs/2305.17333v3 (May 2023)

    2023 arXiv

  43. [51]

    DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training Oct. 2023. https://arxiv.org/abs/2310.02025v4. 41

    2023 arXiv

  44. [52]

    & Zhang, S

    Han, Z., Gao, C., Liu, J., Zhang, J. & Zhang, S. Q. Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey Mar. 2024. https : / / arxiv . org / abs / 2403.14608v5. 42

    2024 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.