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.
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.