Predictive coding has been unified with backpropagation

> Other than that I wish more unification was done on ML algorithms and dynamical systems, just in general. There's too much crossover to ignore.

Check out this work, "Deep relaxation: partial differential equations for optimizing deep neural networks" by Pratik Chaudhari, Adam Oberman, Stanley Osher, Stefano Soatto & Guillaume Carlier.

https://link.springer.com/article/10.1007/s40687-018-0148-y

The article says this:

> The backpropagation algorithm requires information to flow forward and backward along the network. But biological neurons are one-directional. An action potential goes from the cell body down the axon to the axon terminals to another cell's dendrites. An axon potential never travels backward from a cell's terminals to its body.

The point of the research here is that backpropagation turns out not to be necessary to fit a neural network, and that it can be approximated with predictive coding, which does not require end-to-end backwards information flow.

The back-prop learning algorithm requires information non-local to the synapse to be propagated from output of the network backwards to affect neurons deep in the network.

There is simply no evidence for this global feedback loop, or global error correction, or delta rule training in neurophysiological data collected in the last 80 years of intensive research. [1]

As for "why", biological learning it is primarily shaped by evolution driven by energy expenditures constraints and survival of the most efficient adaptation engines. One can speculate that iterative optimization akin to the one run by GPUs in ANNs is way too energy inefficient to be sustainable in a living organism.

Good discussion on biological constraints of learning (from CompSci perspective) can be found in Leslie Valiant book [2]. Prof. Valiant is the author of PAC [3] one of the few theoretically sound models of modern ML, so he's worth listening to.

[1] https://news.ycombinator.com/item?id=26700536

[2] https://www.amazon.com/Circuits-Mind-Leslie-G-Valiant/dp/019...

[3] https://en.wikipedia.org/wiki/Probably_approximately_correct...

> Predictive coding is the idea that BNNs generate a mental model of their environment and then transmit only the information that deviates from this model. Predictive coding considers error and surprise to be the same thing.

This reminds me of a Slate Star Codex article on Friston[1].

[1] https://slatestarcodex.com/2018/03/04/god-help-us-lets-try-t...

Copied from this URL, the final review comments that 1) summarized the other reviews, 2) describes the rational for rejection:

``` This paper extends recent work (Whittington & Bogacz, 2017, Neural computation, 29(5), 1229-1262) by showing that predictive coding (Rao & Ballard, 1999, Nature neuroscience 2(1), 79-87) as an implementation of backpropagation can be extended to arbitrary network structures. Specifically, the original paper by Whittington & Bogacz (2017) demonstrated that for MLPs, predictive coding converges to backpropagation using local learning rules. These results were important/interesting as predictive coding has been shown to match a number of experimental results in neuroscience and locality is an important feature of biologically plausible learning algorithms.

The reviews were mixed. Three out of four reviews were above threshold for acceptance, but two of those were just above. Meanwhile, the fourth review gave a score of clear reject. There was general agreement that the paper was interesting and technically valid. But, the central criticisms of the paper were:

Lack of biological plausibility The reviewers pointed to a few biologically implausible components to this work. For example, the algorithm uses local learning rules in the same sense that backpropagation does, i.e., if we assume that there exist feedback pathways with symmetric weights to feedforward pathways then the algorithm is local. Similarly, it is assumed that there paired error neurons, which is biologically questionable.

Speed of convergence The reviewers noted that this model requires many more iterations to converge on the correct errors, and questioned the utility of a model that involves this much additional computational overhead.

The authors included some new text regarding biological plausibility and speed of convergence. They also included some new results to address some of the other concerns. However, there is still a core concern about the importance of this work relative to the original Whittington & Bogacz (2017) paper. It is nice to see those original results extended to arbitrary graphs, but is that enough of a major contribution for acceptance at ICLR? Given that there are still major issues related to (1) in the model, it is not clear that this extension to arbitrary graphs is a major contribution for neuroscience. And, given the issues related to (2) above, it is not clear that this contribution is important for ML. Altogether, given these considerations, and the high bar for acceptance at ICLR, a "reject" decision was recommended. However, the AC notes that this was a borderline case. ```

The core reason is that the proposed model lacks biological plausibility. Or, if ignoring this weakness, the model is then computationally more intensive.

I HAVE NOT read the paper, but the review seems mostly based "feeling"; i.e., the reviewers feel that this work is not above the bar. Note that I am not criticizing the reviewers here, in my past review career of maybe in the range of 100+ papers, which I did until 6 years ago, most of them are junks. For the ones that are truly good work, which checks all the boxes: new result, hard problem, solid validation, it was easy to accept.

For yet a few other papers, which all seem to fall into the feeling category, everything looks right, but it was always on a borderline. And the review results can vary substantially based on the reviewers' own backgrounds.