Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: The paper applies a formalism from quantum theory to ANNs and SNNs that offers to deal with time discrete and asynchronous events. The theory is applied to temporal spiking neuronal networks (tSNNs) that are shown to be equivalent under certain conditions to ANNs. The coding is applied to CIFAR 10 & 100, and it is shown that the suggested operator-discretized tSNN have a better “throughput” than the Euler. discretization of tSNN, and that operator-discretized tSNN are comparable in “throughput” with ANN.
strengths_and_weaknesses: It is certainly always interesting to transfer successful methods from other fields. Yet, in the current example, it does not become clear, what one really gains over existing techniques in simulating ANNs, or tSNNs transformed to ANNs.
questions: (1)	The equivalence between tSNNs and ANNs is only shown with some restrictions that are not so clearly spelled out. In general, tSNNs are treated as ANNs in the literature mainly for time-to-first-spike (TTFS) coding, assuming an overall clock that resets the state of the system at discrete times, and from there on considers time as the analog variable of the ANN. This special case does not include the processing of multiple spiking signals, emitted from each single neuron, in real and continuous time, but never synchronized with an external clock or with other neurons of the network. Does you theorem contribute to this more general case? In what sense does it go beyond the well studied TTFS coding?

(2)	Event-based simulations of spiking neurons has a long tradition and is shown in many papers and simulation platforms to dramatically outperform naïve Euler-discretized simulations of spiking networks. In what sense does your approach go beyond these event-based simulations of SNNs?

(3)	If the aim is to contribute to the simulation of tSNNs, then the comparison in the simulations should be done with state-of-the art methods to simulate tSNNs. Can you show such results?

(4)	So far the paper simply shows that the performance is comparable to ANNs, supporting the theorem, but begging the question whether the technique can really be used for the analysis of SNN on behavioral time scales, as explained in the Introduction. It is said that at present, the networks are not fully asynchronous, and this is justified by the slow waves in the brain. But slow waves are seen on the level of field potentials, and are far away from globally imposing spike times in individual neurons, as it is assumed in the paper. Can you give a hint how the technique will overcome this?

limitations: yes
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: The authors used the linear algebra which is well established in the quantum theory to rewrite the transmission line model, which is as fine as the cable model. By adding some assumptions, they built the tSNN (operator) model which likes a rate model including the time delay information. The keys to simplify the cable-level model to the rate-level model are the use of the constant velocity assumption which can eliminate the distance x and the use of the inner-product-based detection which can eliminate the time t.
strengths_and_weaknesses: Strengths:
1) The work makes a connection between a cable-level model to rate-level model, though there are some unclear issues (see below).

Weaknesses:
1) From the perspective of neuroscience, from the start, the motivation of setting the global clock T_c closer to our behavioral time scale is wrong. At the circuit level (not the function level), the neural dynamics is continuous. The signal detection process (Eq.16) is far from reality. There is a gap between the aggregated signal (Eq.29) and the event firing time (Eq.30), which needs to clarified by the authors. This gap leads to another question that all neurons in the model share the same time clock (Eq.32), which is not true in reality. 
2) From the perspective of artificial intelligence, the author gave a model (Eq.30 or Eq.33) which is equivalent to a feedforward network in some cases. However, it seems that the connection matrix in the equivalent feedforward network have to remain the same between layers. Though the author claims that their tSNN can encode the time delay information, the model (Eq.33) has just two variables which is not interesting in AI. In fact, we can intuitively get the ultimate model (Eq.33) without the complex linear algebra.

questions: Overall, to me, this work does not bring any really new contribution to neuroscience and AI (see the above). Please clarify it. 
limitations: The authors should address the limitations of their model in detail, in particular, those assumptions used which are not biologically plausible.
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: The authors propose a mathematical framework based on methods in quantum physics and category theory to interpret analog and spiking neural networks. I did not understand the motivation behind the study nor its contribution to the field. I am entering a brief review with low confidence score because the techniques employed in this paper are well outside my area of expertise. 
strengths_and_weaknesses: I will not comment on the technical details of this paper -- I have asked that the area chairs consider replacing me with another reviewer with more domain knowledge in quantum physics.

Nevertheless, I will comment briefly on the appeal of this paper to a general machine learning audience. In short, the paper is not well-written to appeal to this audience and on these grounds alone it may be justified to reject this paper. The abstract and introduction do not explain the basic ideas that will be employed and instead drops hints and jargon to those with a strong physics background ("It is tempting for those with some physics background to apply techniques..." and "operator algebra has been applied to Hopfield networks [18]"... without defining operator algebra.) I expect the technical details of this paper would not be easily digested to the average NeurIPS reader (e.g. Bra–ket notation is used without any explanation).

Perhaps most importantly for a NeurIPS audience, the practical demonstrations of this work feel weak and lacking. The authors only show a brief proof-of-principle on MNIST. If this result is surprising or significant it is lost on me and should be better explained.

Finally, I also want to note that several comments in the paper referring to biological networks strike me as concerning. For instance, "the biological brain operates with low-frequency brain waves closer to our behavioral time scale" -- is a dubious motivation for this study since (a) other neural oscillations are much faster than the theta frequency cited by the authors here, and (b) the biological function of all neural oscillations is still poorly understood and it is particularly controversial to suggest that these oscillations operate like a "clock"
questions: None.
limitations: I don't believe there are any negative societal impacts or ethical concerns. My concerns regarding limitations are summarized above.
review_title: null

final_score: rating: 3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
review_content: summary: The authors propose an alternative representation of artificial neural networks through the use of machinery usually used to analyze complex quantum systems.  Through formalisms from operator algebra, they are able to link analog neural networks (ANNs) and spiking neural networks (SNNs) through different choices of operators.   For example, operator representations typically applied to quantum wave packets are ported to artificial neural networks under the formalism outlined by the authors.  Their proposed framework also allows for more advanced detection strategies in comparison to simple threshold detection commonly used.  They also show the practical benefits of their representation.  

Past this, they they develop physical representations for the creation and annihilation operators for neural networks through considering transmission line models commonly used in quantum electrodynamics.  Their operator formalism then also allows them to consider the case of non-stationary neural signals, defining appropriate time dependent operators through re-use of operators they defined in the stationary case.
strengths_and_weaknesses: The main strength of the paper in my opinion is attempting to come up with a general framework to describe neural computation using notions from quantum computing.  As the authors note, this kind of theory goes both way — i.e. it can aid in certain aspects of quantum computing, but it may also provide another means to understand neural computation.  In addition to that, the authors also try to show the practical consequences/benefits of their framework by showing how it facilitates the conversion from temporally coded SNNs to ANNs.  As hardware implementations of neural computing advance in parallel to quantum computing over time, I believe that drawing these analogies and coming up with a cohesive framework can be of great benefit.


However, I find much of the paper difficult to read both conceptually and theoretically.  In my opinion the paper assumes working knowledge of many different fields/concepts that a great deal of readers would struggle to grasp, i.e. quantum electrodynamics, categorical theories, operator theories, and so on.  I would be okay with this if the references provided at least served as good introductions to these concepts and were presented in a way that I would be at least able to follow high level ideas presented in the paper.  Greatly expanding the appendix in this case would not just be a benefit to the common reader, but a necessity in this case.  I appreciate what the authors are trying to do, but the presentation in my opinion needs a great deal of work.

questions: Could the authors clarify -- when reading the introduction of the paper, the explanation of clock timings and comparing them to membrane time constants makes me think the point trying to be made there was to say that it is not the dynamics following much lower time scales that is important correct? but rather it is the dynamics that follow much larger time scales?  If this is the case, after that analogy what I am failing to see is how the proposed representation takes advantage of this fact; I think it would be extremely helpful to hammer away at the relation throughout the paper since it seems like such an important part of the introduction.  

I also think more clarification related to Fig. 2 is required.  I do not think I have the necessary requisite knowledge to fully understand the LC model for signals traveling between axons/dendrites -- but there is a great deal going on in the figure.  I am curious as well, although the LC model has the advantage as you say that it can better transmit information, does this mean it is not possible to create an equivalent RC model?
limitations: The greatest limitations of the paper in my opinion are the fact that it requires a great deal of requisite knowledge that many will not have.  Fleshing out the appendix here would help a lot — and I think the authors really have to guide the reader a great deal more.  For example, even jumping into the modified bra and ket notation for the newly introduced ‘cubits’ was a bit overwhelming and I think not necessarily well motivated.
review_title: null

Meta-review: metareview: Reviewers agree that manuscript presents a fresh attempt, but also that the manuscript is lacking in several aspects. The writing has a lot of room for improvement and not suitable for the NeurIPS community. It's neuroscientific claims are controversial, or relies on non-mainstream arguments without appropriate justifications. The theoretical and experimental results are limited.
confidence: Certain
Decision: Reject