Summary
Predictive coding (PC) is a speculative but attractive theory of how certain parts of the brain—especially the so-called 'canonical' cortical microcircuit—might implement Bayesian inference, and hence focus processing effort on the 'surprising' rather than the 'predictable' features of (e.g., sensory) stimuli. PC requires a generative model and an optimization algorithm (i.e., given observations, what is the posterior associated with the model's parameters?).
While there exists a rich literature related to how PC might be implemented in the brain, previous work has been biologically implausible in a few different senses. In particular, usually (i) a simple (usually Gaussian) generative model is assumed; and/or (ii) inference involves some kind of approximation; and/or (iii) the algorithm is not necessarily fully 'local'.
The authors propose a novel implementation of PC that they argue is biologically plausible. They call it "population prediction coding" (PPC). They also show that their algorithm can solve some practical machine learning tasks.
Weaknesses
My main concerns are that the core ideas of the paper are confusingly presented, that the 'biological plausibility' claim may be too strong, and that the model's performance is a bit underwhelming.
A more minor concern is that figure real-estate is used strangely (why do 80 copies of the same picture take up a huge amount of space in Fig. 4?). It's 'cool', but why is the cortical microcircuit figure (Figure 1) there? It doesn't seem like any of its details are referenced in the main text. Much more helpful would be a diagram of the proposed PPC algorithm, or better yet, two side-by-side diagrams comparing the proposed PPC algorithm to a more 'vanilla' PC algorithm.
A very minor quibble: "PPC" in neuroscience is already used to refer to "probabilistic population codes" (see Ma et al. 2006) as well as the "posterior parietal cortex", so using PPC here is a bit confusing.
Another relatively minor point. Does vanilla PC really *require* Gaussian densities and the Laplace approximation (Table 1)? My understanding is that the framework itself doesn't *require* this; rather, this is just a useful assumption people use to get something simple and workable. I could be wrong, though. Discussing this point in the paper would be very helpful.
**Confusing presentation.** The meat of the work is in Sections 2 through 4, and I found these sections confusingly written. In Sections 2 and 3, this is probably in part because the authors have to both (a) discuss standard PC in detail, and (b) introduce their modifications to the standard idea. The way things were written made it hard for me to tell what's 'new' and what's not, so it would be extremely helpful if the sections of the text were very obviously separated between 'this is old PC' and 'this is a new modification to PC we are proposing'. As mentioned above, a diagram of vanilla PC vs the proposed modification to it would greatly help.
In a few places, the motivation for doing things a certain way is also not quite clear. For example, PPC involves using particle-based gradient descent; why? Why this particular approach to empirical Bayes and not some other one? Are there good reasons to believe this to be a good basis for a 'local' solution to empirical Bayes? This does not appear to be discussed in the text. Put differently, is it better to think of this as a *possible* way the brain could implement empirical Bayes, or for some reason a *really good candidate* for that?
**Biological plausibility.** This term is fraught and my view here is one that others may not agree with. But I think the authors are overclaiming here when they discuss biological plausibility. While they acknowledge that it means different things to different people (line 145), I still think this is insufficient.
The authors really mean *local computations* when they talk about biological plausibility, as they make clear between lines 145 and line 152. But biologically plausible neural computations involve neurons, and hence I think it is reasonable to expect that there is some discussion of whether or not neurons can implement the computations required. Locality is a start, but it is not the end, and in general it can be quite a bit of work to convert the steps of an algorithm into something neurons can plausibly do. There are references suggesting that neurons *might* be able to learn the required log-density gradients (line 175), but this is more of an afterthought than a core part of the contribution of this work, and these thoughts are not well-developed. Without a more specific proposal for how neurons can learn log-density gradients, and some in-silico validation that the proposed strategy works, I really think the term "biological plausibility" should be removed in many places, or else used with extreme caveats included near each use.
Finally, part of the goal of developing 'biologically plausible' algorithms is to make predictions about biology. What are the specific predictions here? If there are some interesting ones, how do they compare to the predictions of other variants of PC? This should be explicitly discussed.
**Underwhelming performance.** First, I found the tasks used in Sec. 5 confusingly described. It would be helpful if the details of the reconstruction and generation tasks, as well as the training procedure, were better explained in the main text. Second, there are not that many comparisons shown in Table 2; are there other alternatives PPC could be compared to? Third, in Table 3, PPC's FID score is shown as a question mark; I am not sure if this is an error. I assume "undefined" would not be good.
Finally, there are some issues related to training time and speed. Can plots analyzing these features be included? How do other PC approaches compare on these axes? (Is there some time - performance tradeoff, for example?)
Questions
1. Can the authors briefly summarize the 'new' features of their algorithm relative to other PC ideas?
2. Why particle-based gradient descent as opposed to some other approach to empirical Bayes?
3. Concretely, how might neurons learn log-density gradients?
4. What is the FID score of PPC in Table 3?
5. Is PPC strictly better than other PC algorithms, or is there some kind of tradeoff?
Limitations
The authors discuss some limitations (line 296). I think they could have better discussed limitations related to whether neurons can perform the desired computations, and whether particle-based gradient descent is the only / most appropriate possibility here. I think possible tradeoffs related to (e.g., training) time could also be interesting to discuss.