Increasing Liquid State Machine Performance with Edge-of-Chaos Dynamics Organized by Astrocyte-modulated Plasticity

Abstract: Vladimir Ivanov, Konstantinos Michmizos

Reviews and author responses:

This paper presents a novel type of liquid state machine - neuron-astrocyte liquid state machine (NALSM), which introduces feedback from the network activity to the synaptic plasticity. The proposed mechanism helps to position the liquid (reservoir) layer in the edge-of-chaos dynamics regime, a known key factor to achieve good computational performance.
The main contribution of this paper is transforming a biological observation (the role played by astrocytes for modulating the synaptic plasticity) into a novel idea of modulating the liquid activity. It uses feedbacks to obtain edge-of-chaos property in liquid state machine (LSM), and further showing meaningful improvement over the previously proposed LSM-based methods for real-world tasks.  Originality:
I am impressed by how the self-organization property is introduced by balancing the activity between the input and the reservoir layer in the LSM via the STDP rule. This seems to be a simple, clean and yet effective approach to reach the edge-of-chaos. As far as I know, [19] is the first to study edge-of-chaos property under the context of the LSM, where the edge-of-chaos is measured by the Lyapunov exponents. To measure the Lyapunov exponents, two spike trains are generated with only a few difference in the spike sequence and then feed into the liquid. However, in this work, the authors take a different approach to estimate this measure - a much more straightforward approach - by computing the ratio between the number of spikes emitted from the input and the liquid (see Equ. (8)). This indeeds provides a new perspective of understanding the dynamics in the liquid. 

To further validate that the resulted reservoir is indeed in edge-of-chaos, would it be possible for the authors to measure the Lyapunov exponents as well? I am very curious to see if we further confirm the edge-of-chaos property in this traditional perspective. 


Quality & Clarity:
The paper is well organized and written clearly. One thing I want to further confirm is the liquid initialization for NALSM.  It seems that the liquid weights are first initialized by the LSM+STDP’s steps while enabling the LIM astrocyte. And it seems to me that the LIM is still in effect even during the training phase (after initialization), right?  If so, I am curious to know if we disable the LIM modulation model during the training phase, will it cause performance degradation? I am trying to further understand when the edge-of-chaos state is reached. Is it reached during the initialization phase or training phase and how that is impacting the performance? 

Significance:
Extensive experiments are conducted to compare against a series of baselines: LSM, LSM + STDP, LSM + AP-STDP (previous SOTA), and NALSM, clearly showing that the NALSM outperforms the others because its liquid is positioned in the edge-of-chaos regime. Furthermore, the authors also plot the Balancing Factor (one way to measure liquid dynamics regimes) as a function of liquid synaptic weight, demonstrating that the performance indeed peaks at the edge of chaos. The above are the strengths of the experimental results.

The one weakness of the current experiments is the number and variety of the datasets used. One of my concerns is that first of all, MNIST is not challenging enough. And it is not really a dataset geared towards the neuromorphic computing application as it is a static image and no spatio-temporal pattern can be exploited. Originated from MNIST, people argue that the N-MNIST is a “dummy” dataset for SNNs since the spatio-temporal pattern is sort of “faked” (obtained by 3D cameras rotating around the static images). I would highly suggest the authors to run the same experiment setups over 1) more challenging datasets (e.g.Fashion MNIST, and EMNIST) and 2) having spatio-temporal patterns naturally embedded (speech recognition dataset: TI46 and N-tidigits). There are already existing works on those dataset (Link1 and Link2). I totally understand the limited time during the rebuttal phase and there is no need to run the experiments for all the datasets listed here but at least any comments or initial results would be greatly appreciated. And I will certainly consider raising the score if more evidence is provided to show the NALSM is still outperforming baselines and even on par with the SOTA of the non-LSM based SNNs results. 

Link1: https://arxiv.org/pdf/1805.07866.pdf
Link2: https://arxiv.org/pdf/1908.06378.pdf

EDITS:
Thanks for the responsive comments! I have gone through all the comments from both authors and reviewers. I agree with eTQM that some of the statements are overarching. And the authors probably want to soften their tone.

As far as my own concerns, they are well addressed. I also appreciate their responsiveness. I understand that the authors cannot easily measure the EOC using the traditional methods and they seem to have some difficulty extending to more challenging datasets due to the limitation. This is fine as it can be challenging for LSM to achieve the SOTA results of those datasets. But at least they demonstrate the boost again for FashionMnist, which is a plus on my end.

I kind of like this idea of using STDP to position the liquid to the EOC. That is my major reason for voting acceptance.

Since my concerns are reasonably addressed, I will raise my score from 6 to 7. It seems to me that the authors do not explicitly discuss the limitation of the work. I have raised the questions regarding limitations of this work in the main review. 

The authors extend the liquid state machine by incorporating spike-timing dependent plasticity (STDP) and an astrocyte that modulates the STDP, and study its performance on MNIST and N-MNIST. The new model (NALSM) shows improved performance compared to previous liquid state machine variants, and the authors argue that this improved performance is due to the dynamics of the model being at the edge of chaos.  ### Originality

The novelty of the work resides in the development of a new liquid state machine. Previous work is appropriately cited and it is clear how this work differs from previous contributions.


### Quality

The paper is technically sound, but some of the claims are not sufficiently backed by empirical evidence:

-the authors claim that the improved performance of NALSM is due to the dynamics at the edge of chaos. Although the authors show that NASLM have dynamics at the edge of chaos, they do not rigourosly show that it is these dynamics that underly the performance improvement;

-the authors point out the computational advantages of liquid state machines as compared to standard deep neural networks, but no empirical comparison is provided;

-section 3.5 studies the performance of NALSM for different connectivity sparsities. Rather than just showing that the performance of NALSM is not very sensitive to a range of connectivity sparsities, I would invite the authors to study explicitly the advantages of having sparse connectivity (e.g. computational efficiency);


### Clarity

The manuscript is for the most part clearly written. However, it sometimes lacks enough information or contains imprecisions for an expert reader to follow all the steps to evaluate and reproduce the results. Some comments to improve clarity:

-equations 4-6 seem to have a notation problem. These seem to be missing indices for the pre- and post-synaptic neurons ("j" and "i", respectively);

-when the authors write "For each sample, parameters A+ from (4) and b_{astro} from (7) were both initialized to 0:15 and decayed at a rate of 0:99 for the duration of sample input", is it correct that only A+ decays over time and not b_{astro}? If so, this should be less ambiguously stated in this sentence;

-Figure 2A has "liquid synaptic weight" as x-axis variable. However, if I understood correctly, the model has a whole matrix of connection weights. For clarity, the definition of such "liquid synaptic weight" variable should be specified in the text;

-Figure 3 plots "Kernel Quality of Liquid" for different models. As it is not a standard measure, I would invite the authors to provide a short description of the measure in the main body of the part, rather than just having it in the Appendix;

-in the discussion, the authors write "LSMs are the most brain-like". This is highly debatable and I would suggest the authors to refrain from writing this.



### Significance

Although the study provides a new liquid state machine, this model provides a minor improvement in performance compared to previous liquid state machines (Figure 3A, Figure 4). This is a significant weakness per se, and poses some doubts on whether the edge-of-chaos dynamics are the real source of the improvement.

### After rebuttal

Thank you for the answers to my review. Given the other reviews and the authors' rebuttal, I increased my rating to better reflect the quality and significance of the work. However, I still think that the improvement in performance is not expressive enough for me to recommend acceptance. That said, I believe this is solid work and definitely worth acceptance in the future with additional work. The authors do not sufficiently discuss the limitations of the study, such as the relatively minor improvements in performance compared to previous models.

 We thank the Reviewer for their insightful suggestions. Please find our responses to the comments below.

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Q3.1.  One thing I want to further confirm is the liquid initialization for NALSM. It seems that the liquid weights are first initialized by the LSM+STDP’s steps while enabling the LIM astrocyte. And it seems to me that the LIM is still in effect even during the training phase (after initialization), right?...

A3.1.  The Reviewer is correct. As we describe on l.140-144, STDP is modulated by LIM astrocyte during liquid initialization phase and also during training phase where liquid spike counts are generated. 

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Q3.2.  ...If so, I am curious to know if we disable the LIM modulation model during the training phase, will it cause performance degradation? I am trying to further understand when the edge-of-chaos state is reached. Is it reached during the initialization phase or training phase and how that is impacting the performance?

A3.2.  The question of when exactly the liquid reaches edge-of-chaos dynamics is an interesting point raised by the Reviewer and opens up a new discussion, if not a research direction. Briefly, liquid initialization sets dynamics in the vicinity of the edge-of-chaos. However, since each sample has a different amount of input activity which is known to impact network dynamics [1], it has the potential to deviate dynamics slightly further away from edge-of-chaos, if weights are kept fixed. Hence, we speculate that disabling LIM modulation can cause the liquid to not operate as close to the edge-of-chaos as would be needed to maximize performance. Although we do report that the astrocyte is on during training (see l.140-144), we could only gather weak evidence for its attribution to the increase in performance. To address the Reviewer’s concern, we will briefly discuss the potential advantages of LIM-modulation in our final manuscript. 

References:

[1] Priesemann V. Spike avalanches in vivo suggest a driven, slightly subcritical brain state (2014)

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Q3.3.  To further validate that the resulted reservoir is indeed in edge-of-chaos, would it be possible for the authors to measure the Lyapunov exponents as well? I am very curious to see if we further confirm the edge-of-chaos property in this traditional perspective.

A3.3.  We thank the Reviewer for the well-thought out comment. We agree that measuring the Lyapunov exponents would further validate the proposed method but this is not possible in our case: Since our proposed mechanism modulates STDP on the millisecond timescale, we found measurement of Lyapunov exponents to be non-trivial due to the need for fixed synaptic weights/parameters or, at least, enough time-scale separation between activity and plasticity mechanisms to temporarily fixate all parameters. Interestingly, the edge-of-chaos measured with Lyapunov exponents has been found to coincide with the network branching factor (that we used in this work) in biologically plausible networks with excitation/inhibition (E/I) balance [1,2]. To address the Reviewer’s concern, we measured the E/I balance in the initialized liquid of our proposed model (NALSM) by taking the difference of positive weights and negative weights normalized by total non-zero weights (weights considered included input-to-liquid and liquid-to-liquid weights) as per [2]. Indicative of E/I balance, we obtained a value of -0.00882 (on a scale of -1 to 1, with 0 being perfect E/I balance). We will include a section detailing the E/I balance calculations and include the above clarifications into our final manuscript. We hope that the Reviewer will find this amendment as both reasonable and adequate to confirm the edge-of-chaos.

References:

[1] Haldeman C. and Beggs J. Critical Branching Captures Activity in Living Neural Networks and Maximizes the Number of Metastable States (2005)

[2] Krauss P. et al. Weight statistics controls dynamics in recurrent neural networks (2019)

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Q3.4.  The one weakness of the current experiments is the number and variety of the datasets used. One of my concerns is that first of all, MNIST is not challenging enough. And it is not really a dataset geared towards the neuromorphic computing application as it is a static image and no spatio-temporal pattern can be exploited…

A3.4.  We thank the Reviewer for their interesting question. Following the same reasons that most works that we cite here have been applied to these particular datasets, we also chose MNIST and N-MNIST datasets because they i) are the benchmark datasets for most algorithms of this kind, which allows for fair and reproducible comparison among them (Table 1), and ii) cover the range of static and event-based datasets. However, while our experiments are limited to MNIST and N-MNIST datasets, our learning rule can indeed be applied to more complex tasks. While we agree that MNIST in particular may not be challenging enough for complex models such as deep spiking CNNs, complex tasks would introduce the need for changes in the network architecture and make any comparison among the models more ambiguous. We hope that the Reviewer will agree that for our proposed model (NALSM), MNIST is challenging enough to demonstrate accuracy improvements over similar methods. Testing the model in more complex tasks is a direction worth pursuing but remains beyond the scope of this paper, as it will probably require significantly more resources than the ones found in an academic lab. 

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Q3.5.  ...Originated from MNIST, people argue that the N-MNIST is a “dummy” dataset for SNNs since the spatio-temporal pattern is sort of “faked” (obtained by 3D cameras rotating around the static images).

A3.5.  We agree with the Reviewer that the right choice of benchmarking datasets is an open debate in the neuromorphic community. That said, N-MNIST has so far been widely adopted from comparable efforts, which allows for a fair comparison and reproducibility among models (see also our previous answer). In fact, our results suggest that N-MNIST is indeed a more challenging dataset than MNIST, as evidenced by lower LSM and LSM+AP-STDP accuracy performance in Fig3 A. Also, we hope that the Reviewer will find the N-MNIST adequate to demonstrate our proposed model’s (NALSM) robustness to variable input rate over time, which can be seen in nearly equivalent accuracy performance as that on MNIST Fig3 A.

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Q3.6.  ...I would highly suggest the authors to run the same experiment setups over 1) more challenging datasets (e.g.Fashion MNIST, and EMNIST) and 2) having spatio-temporal patterns naturally embedded (speech recognition dataset: TI46 and N-tidigits). There are already existing works on those dataset (Link1 and Link2). I totally understand the limited time during the rebuttal phase and there is no need to run the experiments for all the datasets listed here but at least any comments or initial results would be greatly appreciated. And I will certainly consider raising the score if more evidence is provided to show the NALSM is still outperforming baselines and even on par with the SOTA of the non-LSM based SNNs results.

A3.6.  We thank the Reviewer for suggesting an extension to our results. Due to time and computational constraints, we ran additional experiments and evaluated our proposed model on the Fashion-MNIST dataset (suggested by the Reviewer). The results are consistent with the ones we have already reported and we will include them in the final manuscript. Specifically, NALSM8000 achieved an accuracy of 85.61 $\pm$ 0.18%, averaged over 5 random liquids. This high performance aligns with the results we reported for MNIST and N-MNIST, and it was marginally higher than state-of-the-art spiking methods trained without backpropagation, with a top reported accuracy of 85.31 $\pm$  0.16% [1,2], and comparable to fully-connected multilayer spiking networks trained with backpropagation, with reported accuracies ranging from 84.97 to 87.26% [3,4]. We hope that the Reviewer will find our efforts and the extra results reported here as adequate evidence for this paper. As the Reviewer suggests, our next step is to test our model to more complex domains with rich spatiotemporal information, such as speech and EEG data.

References:

[1] Guo W. et al. Neural Coding in Spiking Neural Networks: A Comparative Study for Robust Neuromorphic Systems (2021)

[2] Hao Y. et al. A Biologically Plausible Supervised Learning Method for Spiking Neural Networks Using the Symmetric STDP Rule (2019)

[3] Zhang W. and Li P. Spike-Train Level Backpropagation for Training Deep Recurrent Spiking Neural Networks (2019)

[4] Ororbia A. and Mali A. Biologically Motivated Algorithms for Propagating Local Target Representations (2018)


 We thank the Reviewer for their suggestions and constructive feedback. We detail below the responses to their comments and any actions we will take to improve the final version of the manuscript.

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Q2.1.  Although the study provides a new liquid state machine, this model provides a minor improvement in performance compared to previous liquid state machines (Figure 3A, Figure 4). This is a significant weakness per se, and poses some doubts on whether the edge-of-chaos dynamics are the real source of the improvement. The authors do not sufficiently discuss the limitations of the study, such as the relatively minor improvements in performance compared to previous models.

A2.1.  We clarify that the performance improvement provided by our proposed model (NALSM) is comparable to the improvement reported in previous works on liquid state machines (LSM) (see Refs [17,57]). It is also 4 times larger than the performance increase of LSM+AP-STDP over the LSM baseline (Fig. 3 A). Please note that, sharing the Reviewer’s concern, we had discussed the source of NALSM’s accuracy improvement to be the synergy of edge-of-chaos dynamics and STDP (see l.271-273). For a more thorough discussion and quantitative proof that the edge-of-chaos dynamics are the real source of that improvement, please see our answer to the Reviewer’s next comment below. We will revise the text to better present the significance of the reported improvements.

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Q2.2.  The authors claim that the improved performance of NALSM is due to the dynamics at the edge of chaos. Although the authors show that NASLM have dynamics at the edge of chaos, they do not rigourosly show that it is these dynamics that underly the performance improvement.

A2.2.  We thank the Reviewer for pointing this out. We indeed provide a quantitative analysis for the source of our method’s accuracy improvement. Specifically, we show that the combination of edge-of-chaos dynamics and STDP are needed to reach the increased performance of NALSM (Fig. 3 A). We discuss this on l.61-62 and l.277-280 and refer to Fig. 3 A that compares the performances of other models that are missing either edge-of-chaos dynamics (LSM+AP-STDP) or STDP (LSM), showing lower performance. We hope that the Reviewer will agree that this analysis sufficiently identifies the source of the accuracy improvement for our proposed model.

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Q2.3.  Section 3.5 studies the performance of NALSM for different connectivity sparsity. Rather than just showing that the performance of NALSM is not very sensitive to a range of connectivity sparsity, I would invite the authors to study explicitly the advantages of having sparse connectivity (e.g. computational efficiency).

A2.3.  We thank the Reviewer for suggesting this intriguing direction. We clarify that we chose to tackle the robustness of our proposed model (NASLM) to highly sparse liquid-astrocyte connectivity, because current neuromorphic chips have resource/architectural constraints which limit the number of connections that can be easily deployed (see Ref. [3]). To address the Reviewer’s concern, we point out that previous works have demonstrated the benefits of sparse connectivity on computational efficiency [1,2].

References:

[1] Shafayet S. et al. Spatio-Temporal Pruning and Quantization for Low-latency Spiking Neural Networks (2021)

[2] Rathi N. et al. STDP-Based Pruning of Connections and Weight Quantization in Spiking Neural Networks for Energy-Efficient Recognition (2019)

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Q2.4.  The authors point out the computational advantages of liquid state machines as compared to standard deep neural networks, but no empirical comparison is provided.

A2.4.  We clarify that our main goal in proposing a novel liquid state machine (LSM) model was to compare its performance against the state-of-the-art LSMs. Although this is a valid concern, an empirical comparison between an LSM and a deep neural network would entail a significant number of design choices, ranging from the number of neurons to the deep network’s architecture, that could cast doubts on the validity of the results. That is why we chose to empirically compare only LSM models. That said, we also point out to the computational advantages of LSM (see l.24-30), namely their ability to use depth and recurrence without the downsides associated with backpropagation of gradients, such as vanishing gradients and costly backward passing of information [1,2]. Further, the compatibility of LSM with neuromorphic hardware enables orders of magnitude more energy efficient deployment than that of standard deep neural networks deployed on GPUs. This is discussed on l.25-27 but, per the Reviewer’s suggestion, we will reinforce the final manuscript with a better description of the computational advantages of LSMs in the introduction.

References:

[1] Ma WD.K. et al. The HSIC Bottleneck: Deep Learning without Back-Propagation (2019)

[2] Lee DH. et al. Difference Target Propagation (2015)

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Q2.5.  Equations 4-6 seem to have a notation problem. These seem to be missing indices for the pre- and post-synaptic neurons ("j" and "i", respectively).

A2.5.  We thank the Reviewer for scrutinizing our equations. We clarify that equations 4-6 refer to a single synapse and don’t need indices for pre/post-synaptic neurons since there is only one of each. 

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Q2.6.  When the authors write "For each sample, parameters $A_{+}$ from (4) and $b_{astro}$ from (7) were both initialized to 0:15 and decayed at a rate of 0:99 for the duration of sample input", is it correct that only $A_{+}$ decays over time and not $b_{astro}$? If so, this should be less ambiguously stated in this sentence.

A2.6.  We clarify that both $A_{+}$ and $b_{astro}$ decayed, since both must equal each other as we explain on l.105. Thank you again for the thorough comments.

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Q2.7.  Figure 2A has "liquid synaptic weight" as x-axis variable. However, if I understood correctly, the model has a whole matrix of connection weights. For clarity, the definition of such "liquid synaptic weight" variable should be specified in the text.

A2.7.  The Reviewer is correct, we do use a sparse matrix of connection weights (described on l.130-131). In the case of the LSM model (Fig. 2 A), all weights had the same absolute weight value which is the ‘liquid synaptic weight’. It is straightforward to clarify this in the final manuscript and we will do so.

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Q2.8.  Figure 3 plots "Kernel Quality of Liquid" for different models. As it is not a standard measure, I would invite the authors to provide a short description of the measure in the main body of the part, rather than just having it in the Appendix.

A2.8.  We agree with the Reviewer and will briefly describe kernel quality in the main part of the final paper instead of having it in the Appendix.

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Q2.9.  In the discussion, the authors write "LSMs are the most brain-like". This is highly debatable and I would suggest the authors to refrain from writing this.

A2.9.  We agree and see how this statement may be highly debatable in a broader context of all possible learning models. We will remove this statement from our final manuscript.


 We thank the Reviewer for their well thought out comments and suggestions. Below you may find our responses and the description of the associated changes on the manuscript.

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Q1.1.  This precise astrocyte function seems to be mostly inspired by what the model needs, rather than an attempt to replicate an aspect of neurophysiology... 

A1.1.  The Reviewer is bringing up an interesting point. Indeed, our overarching goal is to develop neuromorphic machine learning methods that are guided by recent neurobiology knowledge, to tackle fundamental limitations in the current ML approaches. Mounting evidence reveals the cellular mechanisms underlying the long-suspected roles that astrocytes play in brain networks, from modulating learning [1] to controlling behavior [2]. That said, it has not escaped our attention that by translating biologically plausible cellular mechanisms to experimentally observed network functions, bio-inspired efforts like ours can become testbeds for multiscale hypotheses on the multi-faceted roles of astrocytes in brain health and disease. 

References:

[1] Gordon G. Astrocyte-mediated distributed plasticity at hypothalamic glutamate synapses (2009)

[2] Halassa M. and Haydon P. Integrated brain circuits: astrocytic networks modulate neuronal activity and behavior (2010)

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Q1.2.  ...Just an impression from reading it-- maybe that's not fair and the authors could elaborate. Several forms of homeostatic modulation have been studied in neural circuitry (e.g., ref 28 in the paper), and this seems to fit in that general class, whether or not astrocytes have a major role in the process in real biology. Thus, the study is fine work, I just find the motivation a bit thin and I think there is more solid foundation for the idea in the homeostatic plasticity literature, rather than the astrocyte literature. Not a major concern or limitation. Maybe my opinion isn't even widely shared. The paper cites a lot of literature, and thus I think the author(s) are probably familiar with these ideas already. 

A1.2.  This is a very interesting point on the motivation of our work raised by the Reviewer. There are both biological and engineering constraints that would hinder homeostatic plasticity to be regarded as the main mechanism for bringing networks, be it biological or artificial, near the edge of chaos. From a biological perspective, mounting experimental evidence supports the role that astrocytes play in modulating STDP. In fact, while computational neuroscience models have proposed fast (on the order of seconds) acting homeostatic plasticity as a likely candidate for STDP modulation, homeostatic plasticity observed in the brain is too slow (on the order of several hours) to adequately modulate STDP [1,2,3]. From an engineering perspective, by processing only local information, homeostatic plasticity requires more extensive dataset specific hand-tuning, as it has no way to measure global activity in the liquid. To support the motivation of our approach, we cite the experimental evidence (see l.52-56) suggesting that astrocytes 1) integrate neuronal activity into a calcium signal (on order of seconds and milliseconds), and 2) modulate synaptic plasticity. We will enhance this part of the discussion in the final manuscript to reflect the Reviewer’s comment on the possible (co-)existence of other non-glia mechanisms.

References:

[1] Zenke F. et al. Hebbian plasticity requires compensatory processes on multiple timescales (2017)

[2] Zenke F. et al. Synaptic plasticity in neural networks needs homeostasis with a fast rate detector (2013)

[3] Watt A. et al. Homeostatic plasticity and STDP: keeping a neuron's cool in a fluctuating world (2010)

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Q1.3.  But that brings me to this passage in the discussion: "Here, we introduced astrocytes as a second processing unit to neuromorphic computing. Our results help to dismantle a dogma that 'brain = neurons' and clear up the 100-years old 'neuron doctrine', that the neuron is the only processing unit in the brain [75–77]." Taking such credit for themselves is maybe a bit further than the authors might like to go: (1) putting the two search terms "neuromorphic" and "astrocyte" into Google Scholar returns hundreds of papers that also incorporate astrocyte functions into their work. So taking credit for introducting the idea here is not fair to the prior studies. (2) The dogma is maybe more of a straw man at this point. The exact details of what astrocytes do in circuitry is not settled, but plenty of neurophysiologists are gathering data to help determine their roles. It is not a fringe belief that glia are somehow involved circuit dynamics. (3) A modeling study is maybe not the gold standard evidence that will help dismantle a neurophysiological dogma. The author(s) may like to consider toning down that part of the discussion.

A1.3. We agree with the Reviewer and we will tone down the quoted part of the discussion to better reflect our contribution as part of a wide spectrum of efforts that aim to extend the dialogue between neuroscience and neurocomputing. We will better communicate that our work reinforces the direction of previous studies that are propelled by advancements in experimental Neuroscience and identify principles that endow non-neuronal cells with unique computational abilities, translating them into functional networks.


 We thank the reviewers for their time and insightful feedback. We are encouraged that they found our work '"interesting from both the machine learning/neuromorphic computing side, and from the neuroscience side" (Reviewer eTQM), and that it "provides a new perspective of understanding the dynamics in the liquid" (Reviewer 4Eeo). We are pleased they found our work to be "technically sound" (Reviewer SaLC), "well organized and written clearly" (Reviewer 4Eeo), and that generally it "is clear how this work differs from previous contributions" (Reviewer SaLC). We are happy they also found our method "to be a simple, clean and yet effective approach to reach the edge-of-chaos" with "extensive experiments... conducted to compare against a series of baselines" (Reviewer 4Eeo). We answer specific questions below and will further describe how we will incorporate the feedback in the final manuscript.


The paper proposes a new version of LSM by adding a factor intended to mimic a proposed role for astrocytes: modulating STDP. The effect is homeostatic in nature and works to keep the network in a computationally efficient regime. It works. The result is a higher performance on MNIST and N-MNIST data sets.
  The main technology under consideration is the LSM, which is interesting from both the machine learning/neuromorphic computing side, and from the neuroscience side. So it could find an audience.

Astrocytes are a common cell type in the brain, and play important roles in neural circuitry, including neurovascular coupling and neurotransmitter uptake at synapses. It has also been suggested that astrocytes can play a role in synaptic plasticity. However, neurophysiological support for this idea is at best sparse (e.g., https://www.nature.com/articles/nn.4201, https://www.jneurosci.org/content/38/1/3.abstract, https://science.sciencemag.org/content/327/5970/1250.abstract). The specific implementation in this model is as a modulating factor for the STDP, the net action of which is to stabilize the network between ordered and chaotic. The input for the astrocyte component is "the difference in the number of spikes produced by liquid neurons and input neurons" and it works as a leaky integrator. 

The model was tested on MNIST and N-MNIST datasets, and several graphs detail the benchmarking, and compare to models in the literature.

The paper is clear, and has helpful diagrams and plots. I am generally supportive of the paper. It has been carefully prepared and could be an asset to the literature.

I have just a couple of minor points to ask the authors to consider:

(a) This precise astrocyte function seems to be mostly inspired by what the model needs, rather than an attempt to replicate an aspect of neurophysiology. Just an impression from reading it-- maybe that's not fair and the authors could elaborate. Several forms of homeostatic modulation have been studied in neural circuitry (e.g., ref 28 in the paper), and this seems to fit in that general class, whether or not astrocytes have a major role in the process in real biology. Thus, the study is fine work, I just find the motivation a bit thin and I think there is more solid foundation for the idea in the homeostatic plasticity literature, rather than the astrocyte literature. Not a major concern or limitation. Maybe my opinion isn't even widely shared. The paper cites a lot of literature, and thus I think the author(s) are probably familiar with these ideas already.

(b) But that brings me to this passage in the discussion: "Here, we introduced astrocytes as a second processing unit to neuromorphic computing. Our results help to dismantle a dogma that 'brain = neurons' and clear up the 100-years old 'neuron doctrine', that the neuron is the only processing unit in the brain [75–77]." Taking such credit for themselves is maybe a bit further than the authors might like to go: (1) putting the two search terms "neuromorphic" and "astrocyte" into Google Scholar returns hundreds of papers that also incorporate astrocyte functions into their work. So taking credit for introducting the idea here is not fair to the prior studies. (2) The dogma is maybe more of a straw man at this point. The exact details of what astrocytes do in circuitry is not settled, but plenty of neurophysiologists are gathering data to help determine their roles. It is not a fringe belief that glia are somehow involved circuit dynamics. (3) A modeling study is maybe not the gold standard evidence that will help dismantle a neurophysiological dogma. The author(s) may like to consider toning down that part of the discussion. No concerns.

Meta-review: The paper proposes a novel homeostatic mechanism to drive liquid state machines (LSMs) towards the Edge-of-Chaos in order to obtain a good dynamical regime of the network for training the readout. In this LSM variant, a homeostatic factor is computed (in a simple manner) that modulates local plasticity updates (STDP). The method is motivated from a previously proposed role of astrocytes in modulation of plasticity and homeostasis. 
All reviewers agree that the approach is interesting and novel. There have been a number of other approaches proposed previously, but none of them was convincing. This one seems to work very well on the performed experimental evaluations.
The manuscript is well-written and the results are sound.
There are a few weaknesses:
- the astrocyte function seems to be tailored to the model needs rather than informed by biology
- the model shows minor performance improvements compared to previous LSMs
- the model was only tested on MNIST and N-MNIST. A larger variety and more challenging datasets would strengthen the paper.

Decision: accept