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REVIEW 4 major objections 5 minor 34 references

Reproduction of AdEx dynamics on neuromorphic hardware through data embedding and simulation-based inference

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A 32-number code reveals a silicon neuron's hidden parameters

desk verdict Plausible proof-of-concept, but the autoencoder's contribution is undercut by unvalidated posterior and unexamined encoder retraining during SNPE. read the letter →

arxiv 2412.02437 v1 pith:T7GV2LXO submitted 2024-12-03 cs.NE

Jakob Huhle , Jakob Kaiser , Eric Müller , Johannes Schemmel This is my paper · ORCID
classification cs.NE
keywords neuromorphiccomputingsimulation-basedinferenceAdExneuronmodelautoencodersequentialneuralposteriorestimationBrainScaleS-2dataembeddingapproximation
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

This paper asks whether the parameters of a neuron model can be recovered from a voltage trace without a human deciding which features of the trace matter. On the BrainScaleS-2 neuromorphic chip, the authors record membrane traces from an adaptive exponential integrate-and-fire (AdEx) neuron, compress each trace into 32 numbers with a convolutional autoencoder, and feed those numbers to sequential neural posterior estimation (SNPE), a simulation-based inference algorithm that approximates the posterior distribution over model parameters. Using a single target trace, the approximated posterior clusters around the four parameters that generated it, and traces drawn from the posterior reproduce the target observation about as well as repeated hardware trials do. The result suggests that automatic feature extraction plus simulation-based inference can replace handcrafted summary statistics when calibrating complex physical or biological systems.

What carries the argument

The central object is the autoencoder's 32-dimensional latent code: a learned, low-dimensional summary of each 1,024-point membrane trace that stands in for the raw observation inside SNPE. The encoder is first trained to reconstruct hardware traces, then retrained together with a masked autoregressive flow (MAF), the neural density estimator that represents the posterior $p(\theta \mid \text{latent})$. The AdEx equations (membrane potential $V_m$ and adaptation current $w$) implemented as analog circuits on BrainScaleS-2 supply the simulator, and SNPE's round-based refinement sharpens the posterior around the target trace.

What would settle it

Run the pipeline on many hardware target traces recorded from known parameters, draw many parameter sets from the posterior, and compute how often the true parameters lie in the 90% highest-posterior-density region. If that empirical coverage is far from 90%, the latent embedding loses information or the posterior is overconfident, and the claimed identification of the correct parameter region does not generalize.

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Extended reading notes

Core claim

On its own terms, the paper establishes that a convolutional autoencoder's 32-dimensional latent code can act as the observation fed to SNPE, and that the resulting posterior identifies the correct region of the 4-dimensional AdEx parameter space on BrainScaleS-2 despite analog trial-to-trial noise. The posterior is narrower for the reset potential $V_r$ and the adaptation conductance $g_{\tau w}$ than for the subthreshold adaptation $a$ and spike-triggered adaptation $b$, and it shows a negative correlation between $b$ and $g_{\tau w}$ that follows from the hardware circuit's design. Posterior predictive traces match the target until roughly the second spike, after which divergence is comparable to repeated recordings of the same parameters. The authors present the method as removing the need for handcrafted feature extraction and as a first step toward inferring biological neuron parameters for emulation on accelerated hardware.

Load-bearing premise

The 32 numbers produced by the autoencoder are assumed to preserve all information in the membrane trace needed to identify the four parameters, but the paper checks reconstruction accuracy, not whether those features are sufficient for inference.

Editorial extensions

If this is right

  • Calibrating an AdEx neuron on BrainScaleS-2 no longer requires handcrafted summary statistics: a single target membrane trace can be compressed automatically and passed to SNPE.
  • The inferred posterior gives uncertainty information, not just point estimates, and reveals parameter correlations such as the negative $b$--$g_{\tau w}$ relation caused by the circuit design.
  • Trial-to-trial analog noise widens the posterior, so posterior samples should be compared against repeated recordings of the same parameters rather than against a single noiseless trace.
  • Because the encoder is retrained during inference, the pipeline can adapt its representation to the kind of trace being studied, which matters when target traces (like adaptation traces) are rare in the training set.

Reading between the lines

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

  • Beyond the paper: because the encoder is retrained jointly with the density estimator, the reconstruction-quality numbers reported for the pretrained autoencoder do not validate the actual features used for inference; the informative check would be a posterior-predictive or calibration test on the final pipeline.
  • Beyond the paper: a direct comparison of the posterior obtained from the 32-number code with one obtained from the full 1,024-point trace would settle whether the embedding discards information the density estimator needs.
  • Beyond the paper: if the method transfers to biological recordings, the observed posterior width would conflate hardware noise, biological noise, and parameter uncertainty, so an explicit noise model or multi-trial observation would be needed to separate them.
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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 / 5 minor

Summary. The paper proposes a method for automatic feature extraction in simulation-based inference on neuromorphic hardware. The authors train a convolutional autoencoder on 200,000 membrane potential traces recorded from an AdEx neuron emulated on BrainScaleS-2, then use the trained encoder to compress 1024-point traces to a 32-dimensional latent space. This latent representation is fed to a masked autoregressive flow within the SNPE algorithm to approximate the posterior distribution of four AdEx parameters (a, b, g_tau_w, and V_r). The results show that posterior samples concentrate near the target parameter values and that posterior-predictive traces match the target observation until the second spike. The paper concludes that the combination of an autoencoder with SNPE is a promising method for calibrating complex neuronal models without handcrafted summary statistics.

Significance. If validated, this work would extend simulation-based inference to neuromorphic hardware with automatic feature extraction, potentially enabling inference for more complex models where handcrafted statistics are unavailable. The paper provides a detailed experimental setup, network architecture, and hyperparameter choices, making the method reproducible in principle. The hardware-realistic dataset and the explicit acknowledgment of limitations are strengths. However, the current evidence is largely qualitative: posterior accuracy is not quantified, no comparison is made to existing handcrafted-feature baselines, and the encoder is retrained during SNPE in a way that obscures the role of the pretrained autoencoder. The method is plausible as a proof of concept, but the central claims are under-supported.

major comments (4)
  1. [Section II-D and III-B] The autoencoder evaluation is disconnected from the features actually used for inference. The paper states that during NDE training the pretrained encoder is 'further retrained in parallel,' so the latent features used for SNPE are not the same as those whose reconstruction quality is reported in Section III-B and Figure 3. The reconstruction loss measures fidelity of trace compression, not the informativeness of the latent for parameter estimation. To support the claim that the autoencoder extracts essential features, the paper must either use the frozen pretrained encoder for SNPE and validate that the posterior is adequate, or describe the joint training objective (including the loss function, relative weights, and any regularization) and demonstrate that the retrained encoder still performs as an autoencoder, for instance by reporting reconstruction error after retraining.
  2. [Section III-C and IV] The posterior is never quantitatively validated. Section III-C presents only qualitative evidence: posterior samples scattered near the true parameters and a few posterior-predictive traces that diverge after the second spike. No coverage, calibration, or posterior-predictive statistic is computed, and the Discussion in Section IV explicitly lists posterior-predictive checks as future work. For a single target observation in a 4-dimensional parameter space, this is insufficient to establish that the approximated posterior is close to the true posterior. The authors should add quantitative metrics, such as posterior coverage across repeated simulations or a quantitative discrepancy between the target trace and posterior-predictive traces (for example, using the same normalized mean-squared error employed for reconstruction).
  3. [Section IV] The target observation is an adaptation trace, a regime under-represented in the training set. The authors note that 'the reconstructions of traces with stronger adaptation are worse than those of other traces' because only a small subset of the chosen parameter space produces such traces. Since the target is precisely such a trace and the encoder is retrained during SNPE, the retraining may overfit to the single target observation, potentially biasing the posterior or making it overconfident. This concern is acknowledged in the Discussion but not addressed. The paper should quantify the diversity of the dataset (e.g., the proportion of adaptation-like traces) and validate the method on a target trace from a well-represented regime as a control.
  4. [Whole paper / Contribution] The claimed contribution is the elimination of handcrafted features, but no baseline comparison is provided. Reference [10] (Kaiser et al.) applies SNPE with handcrafted features to the same neuromorphic hardware; the paper should compare the posterior quality, computational cost, and robustness of the autoencoder-based approach against such a baseline on the same target observation. Without this comparison, it is unclear whether the autoencoder provides any benefit over existing methods, or whether the observed performance is simply a property of the SNPE algorithm and the hardware.
minor comments (5)
  1. [Abstract / Section I] The hardware name is spelled 'Brain ScaleS-2' in the abstract and introduction, but 'BrainScaleS-2' elsewhere; please unify the spelling.
  2. [Section II-D] There is a typo: 'performence' should be 'performance.'
  3. [Figure 2 caption] The caption says 'Mean test and validation loss' but the plot appears to show training and validation loss; the text separately mentions the test loss. Please correct the caption to match the plotted curves.
  4. [Section II-A] The target parameter values used to generate the observation are not reported. Please provide these values (in the text or a table) to make the reproduction experiments fully reproducible.
  5. [End matter] The paper does not state whether code and data are publicly available; please add a data and code availability statement if applicable.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the empirical SBI pipeline is self-contained; the paper's own stated gaps are validation limitations, not by-construction reductions.

full rationale

No circularity is identified in the claimed derivation chain. The empirical pipeline is: generate a hardware dataset from uniformly drawn parameters, train a convolutional autoencoder with MSE reconstruction loss (Section II-C and Table I), encode observations into a 32-dimensional latent space, then run SNPE with an NDE to approximate p(theta | x*) from simulated parameter-trace pairs (Sections I-B and II-D). Each component is defined independently of the target result: the autoencoder is optimized for reconstruction fidelity, and the SNPE posterior is an approximation of the Bayesian posterior obtained from the mechanistic model, prior, and observation, not a quantity set equal to an autoencoder output or to any fitted parameter. The target observation is recorded before training, and the posterior samples are evaluated by re-simulating the hardware model, which is an external check rather than a tautology. Two limitations are explicitly stated by the paper and are properly classified as validation gaps, not circular reductions: (i) the encoder is 'further retrained in parallel' with the NDE during SNPE (Section II-D), so the reconstruction-quality evidence of Figure 3 concerns a different encoder than the one used in the final inference, weakening attribution but not making the posterior definitionally dependent on the trained features; and (ii) the Discussion states that 'the posterior distribution needs to undergo more rigorous testing' and that 'systematic posterior-predictive checks' remain future work, acknowledging that the posterior is not quantitatively validated. The Discussion also notes that the target trace was an adaptation trace under-represented in the training set, which reinforces the decision to retrain the encoder; this is a risk of overfitting to the single target observation, not an equation-level circularity. Self-citations to prior SNPE work [8], [10], [25] and to the BSS-2 hardware [12] are background or method references; no load-bearing uniqueness theorem is invoked, and no fitted parameter is renamed as a prediction. No step reduces to its own input by construction, so the circularity score is 0.

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

No physical entities are postulated. The free parameters are machine-learning hyperparameters chosen by hand, and the key assumptions are that the analog hardware faithfully implements the AdEx equations and that the learned 32-dimensional embedding is a sufficient statistic for the parameters of interest.

free parameters (4)
  • Autoencoder latent dimension = 32
    Hand-chosen trade-off between reconstruction accuracy and dimensionality reduction for SNPE (Section II-C, Discussion).
  • Number of SNPE rounds = 20
    Chosen without systematic search; authors state hyperparameter searches are needed (Section II-D, Discussion).
  • Samples per SNPE round = 1000
    Ad hoc setting; no sensitivity analysis provided (Section II-D).
  • MAF density estimator configuration = 5 transformations, 50 hidden units per block
    Taken from prior publications [8,10] without tuning for this problem (Section II-D).
assumptions (4)
  • domain assumption The BrainScaleS-2 analog circuits faithfully emulate the AdEx differential equations (1)-(2) with the stated parameter mappings.
    The inference pipeline treats the hardware as the generative model M; any mismatch between the circuit behavior and the AdEx model assumed by the authors would bias the posterior. Relies on [12], same group, not independently verified here.
  • domain assumption The 32-dimensional latent code is a sufficient statistic for the four inferred parameters.
    The success of SNPE depends on the learned summary retaining all relevant information. The paper provides no formal or empirical guarantee; reconstruction loss measures fidelity, not informativeness for inference (Section II-C).
  • domain assumption SNPE with a MAF density estimator converges to the true posterior for this problem with 20 rounds of 1000 samples.
    Standard SBI convergence assumption; not verified via posterior-predictive checks or calibration tests, which the authors acknowledge are needed (Discussion, citing Hermans et al. [27]).
  • ad hoc to paper The uniform prior over the full configuration range is appropriate for the inference.
    Chosen for convenience to cover the hardware range; the posterior is restricted to a small region, and the prior may affect the reported marginals (Section II-D).

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Cite this review

Pith. "Pith review of Reproduction of AdEx dynamics on neuromorphic hardware through data embedding and simulation-based inference." pith.science (2026). https://pith.science/paper/T7GV2LXO

@misc{pith2026241202437,
  author       = {Pith},
  title        = {Pith review of: Reproduction of AdEx dynamics on neuromorphic hardware through data embedding and simulation-based inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T7GV2LXO}},
  note         = {Machine review of arXiv:2412.02437}
}
read the original abstract

The development of mechanistic models of physical systems is essential for understanding their behavior and formulating predictions that can be validated experimentally. Calibration of these models, especially for complex systems, requires automated optimization methods due to the impracticality of manual parameter tuning. In this study, we use an autoencoder to automatically extract relevant features from the membrane trace of a complex neuron model emulated on the BrainScaleS-2 neuromorphic system, and subsequently leverage sequential neural posterior estimation (SNPE), a simulation-based inference algorithm, to approximate the posterior distribution of neuron parameters. Our results demonstrate that the autoencoder is able to extract essential features from the observed membrane traces, with which the SNPE algorithm is able to find an approximation of the posterior distribution. This suggests that the combination of an autoencoder with the SNPE algorithm is a promising optimization method for complex systems.

Figures

Figures reproduced from arXiv: 2412.02437 by the authors.

Figure 1
Figure 1. Random samples drawn from the dataset. – For visualization, only the first 300 µs are displayed; the traces are recorded for 1 ms. Due to the finite sampling frequency of the ADC and the interpolation of the recorded traces, the potentials at spike time are not identical. When the reset potential Vr is high, the membrane voltage remains at high levels. 0 20 40 60 80 100 120 140 Epochs 10 2 Loss Training Set Validati… view at source ↗
Figure 2
Figure 2. Training of the autoencoder – Mean test and validation loss during training as well as one standard deviation of the validation loss. Both losses decrease continuously over the course of the training. that the model does not tend to overfit. We recorded the lowest validation loss after 140 epochs and will use this model for all future evaluations. At this point, the validation loss (0.001 63) is close to the test lo… view at source ↗
Figure 4
Figure 4. Samples drawn from the approximated posterior – One- and two-dimensional marginals of 500 samples drawn from the approximated posterior. The vertical and horizontal lines represent the parameterization of the target trace. Note, uniform priors from 0 to 1022 were chosen for all parameters, i.e. the posterior distribution is restricted to a much smaller region of the parameter space. Trial-to-trial Traces Posterior T… view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: Example traces for different experiment trials and parameteri￾zations drawn from the approximated posterior – Black traces represent the chosen target observation. On the left side, the experiment is repeated several times with the same parameterization. Due to tempora…

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Works this paper leans on

34 extracted references · 22 canonical work pages

  1. [10]

    Simulation-based inference for model parameterization on analog neuromorphic hardware,

    J. Kaiser et al., “Simulation-based inference for model parameterization on analog neuromorphic hardware,” Neuromorphic Comput. Eng. , vol. 3, no. 4, p. 044 006,

    work page

  2. [1]

    A comparative survey of automated parameter-search methods for compartmental neural models,

    M. C. Vanier et al., “A comparative survey of automated parameter-search methods for compartmental neural models,” J Comput Neurosci, vol. 7, no. 2, pp. 149–171,

    work page

  3. [2]

    Systematic generation of biophysically detailed models for diverse cortical neuron types,

    N. W. Gouwens et al. , “Systematic generation of biophysically detailed models for diverse cortical neuron types,” Nature communications, vol. 9, no. 1, p. 710,

    work page

  4. [3]

    A novel multiple objective optimization framework for constraining conductance- based neuron models by experimental data,

    S. Druckmann et al. , “A novel multiple objective optimization framework for constraining conductance- based neuron models by experimental data,” Front Neurosci, vol. 1, no. 1, pp. 7–18, Nov. 2007. DOI: 10.3389/neuro.01.1.1.001.2007

    doi:10.3389/neuro.01.1.1.001.2007 2007

  5. [4]

    Deistler et al

    M. Deistler et al. , Differentiable simulation enables large-scale training of detailed biophysical models of neural dynamics, 2024. bioRxiv: 2024.08.21.608979

    work page 2024

  6. [5]

    The frontier of simulation-based inference,

    K. Cranmer et al. , “The frontier of simulation-based inference,” Proceedings of the National Academy of Sciences, vol. 117, no. 48, pp. 30 055–30 062, 2020. DOI: 10.1073/pnas.1912789117

    doi:10.1073/pnas.1912789117 2020

  7. [6]

    Flexible statistical inference for mechanistic models of neural dynamics,

    J.-M. Lueckmann et al., “Flexible statistical inference for mechanistic models of neural dynamics,” in Advances in Neural Information Processing Systems , vol. 30, 2017

    work page 2017

  8. [7]

    Automatic posterior transformation for likelihood-free inference,

    D. Greenberg et al., “Automatic posterior transformation for likelihood-free inference,” in Proceedings of the 36th International Conference on Machine Learning , vol. 97, PMLR, 2019, pp. 2404–2414

    work page 2019

Show all 34 references
  1. [8]

    Training deep neural density estimators to identify mechanistic models of neural dynamics,

    P. J. Gonçalves et al. , “Training deep neural density estimators to identify mechanistic models of neural dynamics,” eLife, vol. 9, Sep. 2020. DOI: 10 . 7554 / eLife.56261

    2020

  2. [9]

    Truncated proposals for scalable and hassle-free simulation-based inference,

    M. Deistler et al., “Truncated proposals for scalable and hassle-free simulation-based inference,” arXiv preprint,

  3. [11]

    The BrainScaleS-2 accelerated neuro- morphic system with hybrid plasticity,

    C. Pehle et al., “The BrainScaleS-2 accelerated neuro- morphic system with hybrid plasticity,” Front. Neurosci., vol. 16, 2022. DOI: 10.3389/fnins.2022.795876

    2022

  4. [12]

    An accurate and flexible analog emulation of AdEx neuron dynamics in silicon,

    S. Billaudelle et al., “An accurate and flexible analog emulation of AdEx neuron dynamics in silicon,” in 29th IEEE International Conference on Electronics, Circuits and Systems (ICECS) , 2022, pp. 1–4. DOI: 10.1109/ ICECS202256217.2022.9971058

    2022

  5. [13]

    Adaptive exponential integrate-and-fire model as an effective description of neuronal activity,

    R. Brette et al., “Adaptive exponential integrate-and-fire model as an effective description of neuronal activity,” J. Neurophysiol., vol. 94, pp. 3637–3642, 2005. DOI: 10.1152/jn.00686.2005

    2005

  6. [14]

    An analog dynamic memory array for neuromorphic hardware,

    M. Hock et al., “An analog dynamic memory array for neuromorphic hardware,” in Circuit Theory and Design (ECCTD), 2013 European Conference on , Sep. 2013, pp. 1–4. DOI: 10.1109/ECCTD.2013.6662229

    2013

  7. [15]

    Fast ε-free inference of simula- tion models with bayesian conditional density estimation,

    G. Papamakarios et al., “Fast ε-free inference of simula- tion models with bayesian conditional density estimation,” in Advances in Neural Information Processing Systems , vol. 29, Curran Associates Inc., 2016, pp. 1036–1044

    2016

  8. [16]

    Masked autoregressive flow for density estimation,

    G. Papamakarios et al., “Masked autoregressive flow for density estimation,” in Advances in Neural Information Processing Systems, vol. 30, 2017

    2017

  9. [17]

    Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows,

    G. Papamakarios et al., “Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows,” in Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics , ser. Proceedings of Machine Learning Research, vol. 89, PM...

    2019

  10. [18]

    A comprehensive survey on design and application of autoencoder in deep learning,

    P. Li et al. , “A comprehensive survey on design and application of autoencoder in deep learning,” Applied Soft Computing , vol. 138, p. 110 176, 2023. DOI: 10. 1016/j.asoc.2023.110176

    2023

  11. [19]

    An efficient compression of ECG signals using deep convolutional autoencoders,

    O. Yildirim et al., “An efficient compression of ECG signals using deep convolutional autoencoders,” Cogni- tive Systems Research , vol. 52, pp. 198–211, 2018. DOI: 10.1016/j.cogsys.2018.07.004

    2018 doi

  12. [20]

    Firing patterns in the adaptive expo- nential integrate-and-fire model,

    R. Naud et al. , “Firing patterns in the adaptive expo- nential integrate-and-fire model,” Biological Cybernetics, vol. 99, no. 4, pp. 335–347, Nov. 2008. DOI: 10.1007/ s00422-008-0264-7

    2008

  13. [21]

    A scalable approach to modeling on accelerated neuromorphic hardware,

    E. Müller et al., “A scalable approach to modeling on accelerated neuromorphic hardware,” Front. Neurosci., vol. 16, 2022. DOI: 10.3389/fnins.2022.884128

    2022

  14. [22]

    PyNN: A common interface for neuronal network simulators,

    A. P. Davison et al. , “PyNN: A common interface for neuronal network simulators,” Front. Neuroinform., vol. 2, no. 11, 2009. DOI: 10.3389/neuro.11.011.2008

    2009 doi

  15. [23]

    Adam: A method for stochastic optimization,

    D. P. Kingma et al., “Adam: A method for stochastic optimization,” International Conference on Learning Representations, 2014

    2014

  16. [24]

    Pytorch: An imperative style, high- performance deep learning library,

    A. Paszke et al., “Pytorch: An imperative style, high- performance deep learning library,” in Advances in Neural Information Processing Systems 32, H. Wallach et al., Eds., Curran Associates, Inc., 2019, pp. 8024–8035

    2019

  17. [25]

    Benchmarking simulation- based inference,

    J.-M. Lueckmann et al. , “Benchmarking simulation- based inference,” in Proceedings of the 24th Interna- tional Conference on Artificial Intelligence and Statistics (AISTATS), vol. 130, PMLR, 2021, pp. 343–351

    2021

  18. [26]

    Sbi: A toolkit for simulation- based inference,

    A. Tejero-Cantero et al., “Sbi: A toolkit for simulation- based inference,” Journal of Open Source Software , vol. 5, no. 52, p. 2505, 2020. DOI: 10.21105/joss.02505

    2020 doi

  19. [27]

    A crisis in simulation-based infer- ence? beware, your posterior approximations can be unfaithful,

    J. Hermans et al., “A crisis in simulation-based infer- ence? beware, your posterior approximations can be unfaithful,” Transactions on Machine Learning Research, 2022

    2022

  20. [28]

    Active subspace methods in theory and practice: Applications to kriging surfaces,

    P. G. Constantine et al., “Active subspace methods in theory and practice: Applications to kriging surfaces,” SIAM J. Sci. Comput. , vol. 36, no. 4, A1500–A1524,

  21. [29]

    Limits to high-speed simulations of spiking neural networks using general-purpose comput- ers,

    F. Zenke et al. , “Limits to high-speed simulations of spiking neural networks using general-purpose comput- ers,” Front. Neuroinform., vol. 8, no. 76, 2014. DOI: 10.3389/fninf.2014.00076

    2014

  22. [1999]

    DOI: 10.1023/a:1008972005316

    doi

  23. [2014]

    DOI: 10.1137/130916138

    doi

  24. [2018]

    DOI: https://doi.org/10.1038/s41467-017-02718-3

    doi

  25. [2022]

    DOI: 10.48550/arxiv.2210.04815

    doi arXiv

  26. [2023]

    DOI: 10.1088/2634-4386/ad046d

    doi

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