Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 9: Top 15% of accepted NeurIPS papers, strong accept
review_content: summary: The authors introduce a novel framework called Latent Equilibrium that enables quasi-instantaneous inference regardless of network depth and learning without phased plasticity in networks with slow neuronal elements.  Notably, the framework offers a biologically plausible model of back-propagation. Authors show that the models generated according to the framework have reasonable prediction quality on standard benchmark datasets. The authors also show that the framework can generate good models of cortical networks. Finally, authors explore heterogeneous substrates and conclude that framework is robust.
main_review: The LE framework and models presented in this manuscript are very novel, in particular the idea of “prospective” coding, which has no precedence in the literature as far as I am aware of. There are no obvious flaws that I can see in the theory and experiments presented in this paper. The paper is written clearly enough and provides enough experimental evidence to back the main claims introduced by the authors. The framework presented in this paper introduces a convincing proposal of a biologically-plausible implementation of the back-propagation algorithm, which is a fundamental concept in Deep Learning.  Therefore, I consider that the significance and potential impact of this paper is high. 
limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 8: Top 50% of accepted NeurIPS papers, clear accept
review_content: summary: The authors propose a scheme to reverse the deleterious effects of neuronal filtering / lags on inference and learning in neuronal networks. By formulating an energy function using the pre-filtered inputs to a neuron instead of the filtered inputs or outputs, they derive neuronal dynamics and plasticity rules involving pre-filtered inputs that overcome delays in inference and timing mismatches in plasticity leading to better learning.
main_review: The authors propose a neat tweak to energy functions introduced in earlier works to derive neuronal dynamics and local plasticity rules that approximate backpropagation. Pre-filtered inputs are used in place of filtered inputs or outputs in the energy function bypassing the lag for purposes of inference and learning. This yields neuronal dynamics and plasticity rules that reflect evidence for 'prospective coding' in biological neurons and raise possibilities in biological plasticity. The authors are urged to connect / contrast this work to earlier work on prospective coding in spiking neurons by Brea et al 2016, and also expand on what predictions are made for biological synaptic plasticity experiments and whether these are indeed not already observed. This work deserves wide dissemination since this simple tweak could enable considerable benefits to the community searching for biological and neuromorphic analogues / alternative to backprop, as well as to the neuroscience community in further probing prospective coding.
limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: The authors propose a framework from which a neuron model with (slow) neural dynamics close to physical substrates can be derived  along with a plasticity rule for learning that is similar to backprop. The neuron model allows fast propagation of signals through the network in spite of the slow dynamics of the components, which avoids having to control the timing of learning to turn it on only after the signal has propagated. The authors perform empirical evaluations of networks based on this model on various tasks.
main_review: **Update**: Based on the authors' response, I have revised my score to an accept.

## Originality: 
The proposed model is original to my knowledge. Although the term and concept of "prospective coding" is loosely similar to the one in (Brea et al. 2016) -- might be a good idea to clarify this in the text.  The derivation of the neuron dynamics and learning rules from the energy function is novel. The related work is adequately discussed and the differences are clear.

Brea, Johanni, et al. "Prospective coding by spiking neurons." PLoS computational biology 12.6 (2016): e1005003.

## Quality: 
The derivations of the neuron model and learning rule are technically sound. The evaluation of the model is adequate -- the fact that that model works well even with the standard convnet architecture for CIFAR10 is impressive. It would have been interesting to see results with other popular architectures like resnets.

The analysis of the robustness of the model to substrate imperfections is a bit simplistic -- since the actual imperfections in analog neuromorphic hardware can add a lot more than just noise and mismatches between internal variables. But given that actual testing on hardware is impractical, it is somewhat useful to see the model's robustness to the cases considered. 

I'm not clear what the takeway message is from Section 5, especially given the significant gap in biological plausibility described below.

The authors mention biological plausibility as a key component of their model and yet don't discuss the role of spiking in information transmission. This particular model assumes that the information in membrane potential is directly transmitted to downstream neurons -- which is not biologically realistic. The only alternative way of transmission I can think of would be through the firing rate of the neuron and this would introduce a pretty large lag in the information transmission, avoiding which is one of the primary goals of this paper. So in my opinion, this major caveat to the biological plausibility of the model should be stated clearly and prominently. 

## Clarity: 
The paper is reasonably well written and the derivations and experiments are sufficiently clear.

Some notes:
* l.106: It's not clear what the contrast is to the previous work.
* l.97: The neuronwise sum over energies doesn't seem to include the loss term.

Minor:
* l.101: Eqn. 3 should be Eqn. 4?

## Significance: 
The model itself is very clever and elegant, and well suited for implementation on certain types of neuromorphic substrates. But the arguments about biological plausibility are very shaky as I mentioned before, and I don't see how any insights can be gained there through the model. To be fair, many of the other cited similar papers also ignore the issue of actual information propagation through spikes. But since this paper purports to solve the problem of fast propagation of information, this issue is a lot more relevant here than in other work.
limitations_and_societal_impact: The authors don't discuss the limitations of the model in any detail.
review_title: null

final_score: rating: 8: Top 50% of accepted NeurIPS papers, clear accept
review_content: summary: The paper introduces Latent Equilibrium, a new framework for inference and learning in networks of slow components. 

Authors use the leaky integrator dynamics that characterize biological neurons to jointly derive disentangled neuron and synapse dynamics. The neuronal dynamics evolve along a constant-energy manifold, called the Latent Equilibrium. 

They show that LE allows for performance gains after the beginning of training, when the disruptive effects of relaxation begin to dominate, as well as robustness of LE on a MNIST classification task. 
main_review: This is a great paper, well-written and well-motivated, introducing a new, biologically-inspired framework for inference and learning in networks of slow components. Authors claim that LE allows to represent the true errors in the networks before reaching a fixed point, and alleviates a second form of catastrophic forgetting. 

The first point is well-proven in the experiments, but I find that the second one is not. I believe authors should include a transfer-learning type experiment, where we see the mitigation of the forgetting effect. Also, in the different experiments, authors should compare to other biologically-inspired architectures that alleviate this effect (such as Dendritic Gated Networks (Krishnagopal et al., Cosyne 2021)).

limitations_and_societal_impact: yes
review_title: null

Meta-review: Reviewers were in agreement the proposed framework provided a novel and elegant model for learning in neurons with physical delays, with clear writing and presentation, and thorough experimental results.

Decision: Accept (Oral)