EDIT: Before you read my comment below, please see https://news.ycombinator.com/item?id=26702815 and https://openreview.net/forum?id=PdauS7wZBfC for a different view. -- If the results hold, they seem significant enough to me that I'd go as far as saying the authors of the paper would end up getting an important award at some point, not just for unifying the fields of biological and artificial intelligence , but also…
"Relaxing the Constraints on Predictive Coding Models" (https://arxiv.org/abs/2010.01047), from the same authors. Looks at ways to remove neurological implausibility from PCM and achieve comparable results. Sadly they only do MNIST in this one, and are not as ambitious in testing on multiple architectures and problems/datasets, but the results are still very interesting and it covers some of the important theoretical and biological concerns.
"Predictive Coding Can Do Exact Backpropagation on Convolutional and Recurrent Neural Networks" (https://arxiv.org/abs/2103.03725), from different authors. Uses an alternative formulation that means it always converges to the backprop result within a fixed number of iterations, rather than approximately converges "in practice" within 100-200 iterations. Not only is this a stronger guarantee, it means they achieve inference speeds within spitting distance of backprop, levelling the playing field. (Edit: also noted by eutropia)
It'd be interesting to see what a combination of these two could do, and at this point I feel like a logical next step would be to provide some setting in popular ML libraries such that backprop can be switched for PCM. Being able to verify this research just be adding a single extra line for the PCM version, and perhaps replicating state-of-the-art architectures, would be quite valuable.