Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper proposes a general theoretical framework for inference learning. To this end, the authors propose the Generalized Inference Learning (G-IL) algorithm. They are then able to show that G-IL closely approximates the implicit stochastic gradient descent (implicit SGD), which corresponds to the proximal update of the weight parameters and is distinct from the explicit SGD often used by backpropagation. In addition, the authors compare the performance of several algorithms based on backpropagation with those based on inference learning and establish that the latter converges more quickly on smaller mini-batches.
strengths_and_weaknesses: To the best of my knowledge, this paper offers a novel perspective on inference learning by establishing the connection between G-IL and implicit SGD. The authors do a good job of motivating the similarities between inference learning and biological learning processes. In addition, they provide both theoretical justifications and experimental results for their claims.

As for the weaknesses, I believe that the authors could explain or provide some ideas for some of the experimental results they observe in more detail (such as IL-SGD performing worse than BP-SGD, but IL-Adam and BP-Adam performing more similarly on CIFAR-10).
questions: While the authors claim that inference learning "has achieved equal performance to BP on supervised learning and auto-associative tasks", there is a clear discrepancy between the test accuracy of BP-SGD and IL-SGD with a mini-batch size of 64. While the authors mention this in their results, I was wondering where this non-negligible discrepancy comes from and what its implications for the comparison between inference learning and backpropagation would be.
limitations: The main limitation of the paper is that it mainly explores the case where a single data point is present in each mini-batch. The authors bring up this limitation in their work and provide a justification as to why it is not significant from a biological point of view. As such, I believe the authors adequately address the limitations of their work. However, I am not sure whether exploring the properties of larger mini-batch sizes in more detail could still yield some interesting results.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: This paper proposes an alternative to gradient back propagation in the form of inference learning. This algorithm has the advantage of being more compatible with a biophysical implementation, and the paper aims to develop a theoretical framework for this learning. The expected results are to obtain convergence results for this algorithm and to show the performance compared to classical BP algorithms. The abstract makes a very strong assumption about the result by stating that this algorithm can be superior to the BP algorithm.

strengths_and_weaknesses: A main strength of the paper is to show the state of the art in machine learning algorithms, and in particular to show the comparison between stochastic gradient descent type models and inference learning models. The model is well presented, and the notations are relatively clear. In particular, the main limitation of the back propagation algorithm is well highlighted by showing how to implement a local target estimation algorithm.

A first weakness of the paper is that it relies on details that are supplied in the (40 pages) appendix and that relying on this does not allow an independent evaluation of the results in the paper. Secondly, even if the results seem encouraging, they are still clearly insufficient to show the generality of the algorithm. Indeed, the only benchmark used is that of CIFAR and the results are obtained with results superior to BP only in the very restrictive case of a batch size equal to one. This simulation result does not therefore justify the conclusion made in the summary about the generality of the results.
questions: I have several questions about this work.
Firstly, from equation (1) the cost function used to calculate an optimal prediction is always an L2 norm. How can you justify this, and have you verified this result experimentally by looking at the distribution of errors in learning?
Secondly, in generalized inference learning, you introduce a decay term in equation (3). Could you justify more accurately the evidence for this finding in the simulation data?
Third, could you substantiate a comparison of your algorithm with hierarchical predictive coding algorithms that include both a sparseness regularization or a feedback term?

limitations: Overall, the paper suffers from a major limitation between the conclusions that are put forward in the abstract and the theoretical but also simulation results that are presented in the paper. It would surely have been more correct to make less far-reaching assumptions but fully validated by the theoretical and experimental results.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper gives a theoretical framework and justification for the biologically plausible "inference learning" neural-network training algorithm, a generalization of predictive coding. The paper shows that in the low-N regime, IL closely approximates implicit stochastic gradient descent: it steps in the gradient direction while also staying close to the current weights. Based on this theorem, the paper then improves IL to more closely approximate implicit SGD, which improves the stability and convergence of IL across learning rates and tasks.
strengths_and_weaknesses: Strengths:

* Strong bioplausibility motivation
* Beats backpropagation in the small-batch setting

Weaknesses:
* Beaten by backprop in the midsize-batch (N=64) setting
questions: Have the authors tested against implicit SGD with a backprop-based gradient estimator?
limitations: I can't quite see where this paper fits in.  Bioplausible training of artificial neural networks in the small-batch (eg: N=1) regime remains, to my knowledge, not a very common task.  If the idea is that the brain might do something like IL, can the authors point to any experiments specifically picking out IL as distinct from predictive coding in the brain?  If the idea is to train ANNs for tasks, why not just use BP and large batch-sizes?  Have the authors run any experiments in memory-constrained settings showing that IL does better there?

The authors have addressed these questions to my satisfaction in their response.
review_title: null

Meta-review: metareview: This paper presents an interesting connection between stochastic gradient descent by backpropagation and the "inference learning" algorithm for predictive coding. The key result is that inference learning approximates _implicit_ gradient descent, rather than explicit SGD as normally implemented. The implicit methods perform comparably to standard methods, and they may be of interest to computational neuroscientists interested in biologically plausible learning rules.

In addition to addressing the reviewers' concerns, I would encourage the authors to improve the exposition around Eqs. 1 and 2. The stated equalities require a few lines of calculus to derive, and you could spare the reader the trouble. 
confidence: Certain
Decision: Accept