Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This work presents a new neural network learning algorithm that removes some of the constraints required by the traditional backpropagation algorithm. Constraints such as explicit bidirectional connections and symmetric weights between the forward and feedback paths are not used with the proposed algorithm. Through experiments on multiple popular datasets, the authors demonstrate their algorithm is competitive or better than several other learning algorithms including Feedback Alignment and Direct Feedback Alignment despite having fewer constraints.

This work also provides a thorough overview of the signals propagated through the neural network for algorithms like backpropagation, feedback alignment, direct feedback alignment, and weight mirroring. From this review, it is easy to distinguish the differences between how these signals are combined to generate updates for forward and backward paths.
main_review: The algorithm proposed in this work appears to be novel, but the benefit of using this particular idea over others seems to be the avoidance of direct bidirectional connections. Beyond the weight transport problem, this paper suggests that bidirectional connections are also biologically unlikely. But there is no clear definition found in the text of what is strictly a bidirectional connection. From a full read-through, it may be defined as both the feedforward and feedback paths having a direct co-dependency with one another over the same set of variables (h, \delta). But this definition of directionality is rather weak because any chain a 3-step chain of dependency would escape this constraint. The proposed activation sharing algorithm has a 3-step dependency (see Figure 1b h -> \delta_{l+2} -> \delta_{l+1} ). It is unclear why a 3-step dependency is more justifiable than a direct two-point dependency.

What constitutes a feedforward path vs a feedback pathway in biological systems? Given any randomly selected patch of cortex, what would qualify a neuron as a feedforward as opposed to feedback? Is there any identifiability of these classes of pathways that translate into analogous artificial neural network counterparts? Answers to this are critical to currently justify this algorithm over alternatives.

While removing constraints to backpropagation and other algorithms is useful in its own right, an analysis empirical or theoretical of the utility of removing constraints would help justify this algorithm beyond simply being more 'biologically plausible'. 

Overall, the Forward Alignment concept proposed in this work is creative and shows another way backpropagation can be modified drastically and still support reasonable efficiency in learning. The work also does well in building upon previous efforts in this direction and adopting aspects like asymmetric paths into the proposed learning method.
limitations_and_societal_impact: Modifications to consider based on the main review:

-Adding a formal definition of what constitutes a feedback path.

-A table showing the direct mapping of how the components of the artificial model proposed map to their respective biological counterparts.

-Justification for why identical weight updates is a more reasonable possibility in biological models as compared to identical weights.

-An ablation to show the impact of weight decay on empirical results because it appears to be theoretically necessary (eq 24, eq 25)
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: The paper proposes a novel approximation to backpropagation that solves the need for bidirectional connections between the forward pass neurons, and the backwards pass circuitry. This is done via activation sharing, meaning that the weight update is computed by the backward pass circuitry and activations of some layer prior to the current one.
main_review: Originality: The activation sharing idea is new, and the overall algorithm (ASAP) combines it with the Kolen-Pollack algorithm to also avoid the weight transport problem. However, the paper might benefit from comparison (in terms of both biological plausibility and performance) of their algorithm with other biologically plausible learning rules that do not approximate backprop, but still achieve competitive performance. Some examples include layer-wise learning rules [1-4] and equilibrium propagation [5]. It might also be a good idea to discuss the predictive coding view on backprop approximations (e.g. [6]).

Quality: The theoretical results in the paper are sound, and the experiments good enough (although again, should be compared with alternative methods mentioned above). 
   
Clarity: Overall, the paper is well-written. However, I think a few claims should be corrected. 
In the abstract, “also achieving good performance even on deep convolutional neural networks, unlike other biologically plausible algorithms” does not hold as alternative methods (see citations above) have achieved comparable performance too. 
In line 26, “it is impossible to make their weights identical without explicitly passing the weights between the paths” contradicts the weight mirror and Kolen-Pollack algorithms discussed later, as they do exactly that. Also, I would change dots over variables to tilde, as dots usually denote a time derivative.
     
Significance: The paper proposes an interesting approximation to backprop. However, I have a major concern about the biological plausibility of the proposed algorithm. 
First, the bidirectional connections might actually be a good idea, for instance if the backward pass is done within the neuron via apical dendrites [7]. 
Second, activation sharing makes the final algorithm more biologically implausible that just Kolen-Pollack, in my opinion. In approximations to backprop, the error signal is neuron-specific: each neuron receives its own $\\delta$, and uses the pre-synaptic activity to do the weight update. In ASAP, each synapse, not neuron, receives a unique error signal that doesn’t use any information available in either pre- or post-synaptic neurons. The authors should discuss how this can be implemented. 

[1] Deep supervised learning using local errors, Hesham Mostafa, Vishwajith Ramesh, and Gert Cauwenberghs

[2] Training neural networks with local error signals, Arild Nøkland and Lars Hiller Eidnes

[3] Kernelized information bottleneck leads to biologically plausible 3-factor Hebbian learning in deep networks, Roman Pogodin and Peter Latham

[4] Local plasticity rules can learn deep representations using self-supervised contrastive predictions, Bernd Illing, Jean Ventura, Guillaume Bellec, Wulfram Gerstner

[5] Scaling Equilibrium Propagation to Deep ConvNets by Drastically Reducing Its Gradient Estimator Bias, Axel Laborieux, Maxence Ernoult, Benjamin Scellier, Yoshua Bengio, Julie Grollier and Damien Querlioz

[6] Predictive Coding Approximates Backprop along Arbitrary Computation Graphs, Beren Millidge, Alexander Tschantz, Christopher L. Buckley

[7] Dendritic cortical microcircuits approximate the backpropagation algorithm, João Sacramento, Rui Ponte Costa, Yoshua Bengio, Walter Senn

**Update: increased the score from 6 to 7 (explanation in the thread below)**

limitations_and_societal_impact: The authors have adequately addressed the limitations and potential negative societal impact of their work.
review_title: null

final_score: rating: 4: Ok but not good enough - rejection
review_content: summary: This paper proposes a new learning rule in which the activations of earlier layers (potentially earlier than the presynaptic layer) are used in weight updates -- that is, activations are "shared" for use in weight updates of multiple subsequent layers.  This causes weights to partially align with the identity matrix through a feedback alignment-like mechanism, allowing useful updates to be performed without bidirectional connections between feedforward / feedback pathways (as is needed in algorithms like Kolen-Pollack / weight mirror)
main_review: I find the forward alignment idea, and its application (setting C = I) to the activation sharing algorithm interesting.  It is neat that this approach can work reasonably well on tasks like CIFAR.  However, I'm not convinced by the paper's motivation.  Sure, direct bidirectional connections between feedforward / feedback may not be common enough to exactly implement the Kolen-Pollack / weight mirror algorithms, but effective bidirectional connectivity via multisynaptic pathways should do the trick.  This paper's approach induces a lot of extra complexity -- how, mechanistically, are activations shared from earlier layers?  Is there any reason to think this is more biologically plausible than effective bidirectional connectivity?  Moreover, this complexity is introduced at a performance cost -- ASAP clearly lags behind backprop, while weight mirror / kollen-pollack have been shown to be very competitive with backprop (why are they not compared against directly?  Also, see https://arxiv.org/abs/2003.01513, which should probably also be cited / compared to).

Overall, I am not convinced that this paper makes practical ML advances or moves closer to biological plausibility, and hence I don't think it's ready for acceptance.
limitations_and_societal_impact: The authors do address limitations, and I don't think that addressing potential negative societal impact is necessary given the subject of this paper.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: Methods like backpropagation require the updates to be propagated along the same pathways and weights as the forward computation step (i.e. the "weight transport problem"). To solve this problem, the authors propose activation sharing, which uses random fixed weights both to forwardpropagate activations and to backpropagate error, without bidirectional connections. It is argued that this is more biologically plausible, and can be used to train deep networks (which previous methods could not do).

main_review: The ideas presented in this manuscript are very interesting, and it is nice to see that one can get reasonably good performance in deep neural networks even while propagating through random weights (i.e. the network learns how to learn). This paper is written well, in that it explains the significance and relevance of existing methods, as well as their limitations. The benchmarks were also selected well and were clear. In order to improve the clarity of the mathematical definitions of the ASAP algorithm, it would be preferable to redefine metrics like $\delta$ and $h$ occasionally, as it is easy to forget what they mean given the large number of different symbols being used.

limitations_and_societal_impact: The biggest real-world limitation is that the method does not perform as well as backprop. This is unfortunate, but also understandable. The authors do mention that ASAP has a lower memory footprint, but there are also other methods that can reduce memory footprints of neural networks trained using backprop.
Given that this method is worse than backprop, and it is also not easy to implement, I cannot see any practical use for it.

On the theoretical side, although the ideas here are interesting, I take issue with the term "biologically plausible" and the appeal to biological networks. Given that cognitive neuroscience has not yet proceeded to a point where we understand how patterns and learning occur in brains, it is extremely premature to try and train networks that match biological neurons on the surface, and claim that we can expect better performance because they are biology inspired. To say that these networks behave more similarly to biological neurons is true only on the surface, and the claim that these networks should therefore be better or superior (in any metric, not just predictive performance) is completely unfounded (and in fact, we can see that the more "inspiration" we draw from biological neurons, the worse our artificial networks tend to be). In this particular case, humans can perform image classification nearly perfectly, and better than the best CNNs trained with backprop. And these CNNs trained with backprop do better than any networks trained using other methods (including ASAP). To clarify, I do not blame (or penalize) the authors for appealing to biological networks, since I think this is a bigger issue in the theoretical ML community as a whole, but I do implore them to soften the language and recognize the severe limitations that prevent us from claiming homology between artificial neural networks and biological neural networks (at least in this decade). I encourage the authors to explicitly clarify that: 1) biological neurons are not yet understood, so drawing inspiration from the little we know does not improve our chances at building better artificial networks; 2) the artificial networks trained using ASAP (and similar methods) do not improve our understanding of biological neurons at all; and 3) the artificial networks trained using ASAP (and similar methods) do not necessarily resemble biological networks (other than the weight transport problem, which is of arguable importance) more than other techniques like backprop. Again, I do not hold the authors accountable for this, and this does not affect the review I gave.
review_title: null

Meta-review: In this paper the authors present a solution to the problem of bidirectional connections that exist in some solutions to the weight transport problem. More specifically, Akrout et al. (2019) (https://arxiv.org/abs/1904.05391) proposed two algorithmic solutions to the weight transport problem that involved training a separate "error pathway" of neurons, wherein each neuron in the forward processing pathway had a paired error neuron that it was bidirectionally connected to. This is potentially problematic from a biological perspective, as there is no evidence for such a paired error pathway in the neocortex, and moreover, there is no guarantee of bidirectional connections in real neural networks. The present paper solves the bidirectional connection problem (but not the paired error pathway problem) by allowing feedforward neurons to project to multiple error neurons as long as they are equal to or higher in the hierarchy. The authors show that weight alignment and learning can still proceed fairly well under these conditions.

This paper received mixed reviews on the borderline. One of the reviewers was fairly positive, two were borderline accepts, and one felt it was a clear reject. The authors' responses were thorough and clear enough that one of the borderline reviewers updated their score from a 6 to a 7, leading to a final average score of 6 (i.e. a borderline accept). As such, this is a borderline case as an AC. This is especially so because biological plausibility is a tricky concept and sometimes hard to pin down. Generally, it is hard to justify rejecting a paper on biological plausibility alone. And, this paper appears to be technically sound. But, biological plausibility is also not a concept without any meaning, and there are some basic aspects of neurophysiology that we can generally employ when asking about biological plausibility. Moreover, when a paper is framed as having its central contribution be that it is more biologically plausible than previous algorithms the question of biological plausibility necessarily becomes the focus. 

Nonetheless, after all these considerations, and after a lot of discussion, an accept decision was reached. Ultimately, the paper is a sound contribution to the field and deserves to be published.

However, given the reviews, the authors may want to consider the following issues for when they prepare the camera ready version though:

1) The paper is focused 100% on solving a problem that exists for the algorithms proposed in the paper of Akrout et al. (2019). Only this paper assumes bidirectional connections between the backward and forward pathway neurons. Other papers on weight alignment (such as: https://www.nature.com/articles/s41593-021-00857-x, https://openreview.net/forum?id=rJxWxxSYvB, http://proceedings.mlr.press/v119/kunin20a.html and https://arxiv.org/abs/2005.04168) don't use a separate error pathway with paired neurons and bidirectional connections. Thus, at face value, this paper's contribution is really just to address a gap in biological plausibility introduced by a specific paper (Akrout et al. 2019). That's fine, but it makes the potential impact much more limited. Can the authors articulate how their approach may be used more broadly than to just solve the bidirectional connection issue in Akrout et al.?

2) The proposed solution is not clearly all that more biologically plausible than that proposed by Akrout et al., based on well-known facts of neurophysiology. Specifically, it appears that this model still mandates that an error pathway with paired neurons for the feedforward pathway exists (i.e. each feedforward neuron has an error neuron partner), and this was arguably the most problematic aspect of the Akrout et al. proposal, since there is zero empirical evidence for such paired pathways in the brain. Moreover, there are other biological plausibility issues that this paper introduces, as pointed out by the critical reviewers, such as the errors now being synapses specific and the need for additional feedforward pathways with the existing (and as noted) biologically implausible paired error pathway neurons. It would be good for the authors to address these concerns more in the final version.

In summary, this paper is technically sound, and potentially interesting, so it is an accept. But, per some of the reviews, at face value it is focused on solving a problem in a specific model, and there are still issues with biological plausibility, so the authors should consider these issues when preparing the camera ready version.

Decision: Accept (Poster)