BIOLOGICALLY-PLAUSIBLE LEARNING ALGORITHMS CAN SCALE TO LARGE DATASETS
The backpropagation (BP) algorithm is often thought to be biologically implausible in the brain. One of the main reasons is that BP requires symmetric weight matrices in the feedforward and feedback pathways. To address this "weight transport problem" (Grossberg, 1987), two biologically-plausible algorithms, proposed by Liao et al. (2016b) and Lillicrap et al. (2016), relax BP's weight symmetry requirements and demonstrate comparable learning capabilities to that of BP on small datasets. However, a recent study by Bartunov et al. (2018) finds that although feedback alignment (FA) and some variants of target-propagation (TP) perform well on MNIST and CIFAR, they perform significantly worse than BP on ImageNet. Here, we additionally evaluate the sign-symmetry (SS) algorithm (Liao et al., 2016b), which differs from both BP and FA in that the feedback and feedforward weights do not share magnitudes but share signs. We examined the performance of sign-symmetry and feedback alignment on ImageNet and MS COCO datasets using different network architectures (ResNet-18 and AlexNet for ImageNet; RetinaNet for MS COCO). Surprisingly, networks trained with signsymmetry can attain classification performance approaching that of BP-trained networks. These results complement the study by Bartunov et al. (2018) and establish a new benchmark for future biologically-plausible learning algorithms on more difficult datasets and more complex architectures.
This work adds to a growing literature on biologically plausible (BP) learning algorithms. Building off a study by Bartunov et al. that shows the deficiencies of some BP algorithms when scaled to difficult datasets, the authors evaluate a different algorithm, sign-symmetry, and conclude that there are indeed situations in which BP algorithms can scale. This seemingly runs counter to the conclusions of Bartunov et al.; while the authors state that their results are "complementary", they also state that the findings “directly conflict” with the results of Bartunov, concluding that BP algorithms remain viable options for both learning in artificial networks and the brain.
To reach these conclusions the authors report results on a number of experiments. First, they show successful training of a ResNet-18 architecture on ImageNet using sign-symmetry, with their model performing nearly as well as one trained with backpropagation. Next, they demonstrate decent performance on MS COCO object detection using RetinaNet. Finally, they end with a discussion that seeks to explain the differences in their approach and the approach of Batunov et al, and with a potential biological implementation of sign symmetry.
Overall the clarity of the writing is sufficient. The algorithm is properly explained, and there are sufficient citations to reference prior work. The results are generally clear (though there is an incomplete experiment, I agree with the authors that it is unlikely for the preliminary results to change). I believe that there is enough detail for this work to be reproducible. The work is also sufficiently novel in that experiments using sign-symmetry on difficult datasets have not been undertaken, to my knowledge.
Unfortunately, the clarity and rigor of the *scientific argument* is insufficient for a number of reasons. These will be enumerated below.
First, the explicit writing and underlying tone of the paper reveal a misrepresentation of the scientific argument in Bartunov et al. The scientific question in Bartunov et al. is not a matter of whether BP algorithms can be useful in purely artificial settings, but rather whether they can say anything about the way in which the brain learns. In this work, on the other hand, there seems to be two scientific questions: first, to assess whether BP algorithms can be useful in artificial settings, and second, to determine whether they can say anything about how the brain learns, as in Bartunov (indeed, the author’s conclusions highlight precisely these two points). Unfortunately, the experiments and underlying experimental logic push towards addressing the first question, and use this as evidence towards a conclusion to the second question. More concretely, experiments are run on biologically problematic architectures such as ResNet-18, often with backpropagation in the final layer (though admittedly this doesn’t seem to be an important detail with sign-symmetry, for reasons explained below). This is fine under the pretense of answering the first question, but to seriously engage with the results of Bartunov et al. and assess sign-symmetry’s merit as a BP algorithm for learning in the brain, the work requires the authors the algorithms to be tested under similar conditions before claiming that there is a “direct conflict”. To this end, though the authors claim that the conditions on which Bartunov et al tested are “somewhat restrictive”, this logic can equally be flipped on its head: the conditions under which this paper tests sign-symmetry are not restrictive enough to productively move in the direction of assessing sign-symmetry’s usefulness as a description of learning in the brain, and so the conclusion that the algorithm remains a viable option for describing learning in the brain is not sufficiently supported. On the other hand, I think the conclusions regarding the first question -- whether sign-symmetry can be useful in artificial settings -- are fine given the experiments.
Second, the work does not sufficiently weigh the “degree” of implausibility of sign-symmetry compared to the other algorithms, and implicitly speaks of feedback alignment, target propagation, and sign-symmetry as equally realistic members of a class of BP algorithms. Of course, one doesn’t want to go down the road of declaring that “algorithm A is more plausible than algorithm B!”, but the nuances should at least be seriously discussed if the algorithms are to be properly compared. In backpropagation the feedback connections must be similar in sign and magnitude. Sign-symmetry eliminates the requirement that the connections be similar in magnitude. However, this factor is arguably the least important of the two (the direction of the gradient is more important than the magnitudes), and we are still left with feedback weights that somehow have to tie their sign to their feedforward counterparts, which is not an issue in target propagation or feedback alignment. The authors try to explain away this difficulty with an appeal to molecular biology, which leads into my third point.
Third, the appeal to molecular mechanisms to explain how sign-symmetry can arise is not rigorous. There is a plethora of molecular mechanisms at play in our cells; indeed, there are enough mechanisms to hand-craft *any* sort of circuit one likes. Thus, it is somewhat vacuous to conclude that a particular circuit can be “easily implemented” in the brain simply by appealing to a hand-crafted circuit. For this argument to hold one needs to appeal to biological data to demonstrate that such a circuit either a) exists already, b) most probably exists because of reasons X, Y, Z. Unfortunately there is no biological backing, rendering this argument a possibly fun thinking exercise, but not a serious scientific proposal. But perhaps most problematic, the argument leaves the problem of sign-switching in the feedforward network to “future work”. This is perhaps *the most* important problem at play here, and until it is answered, these arguments don’t have sufficient impact.
Altogether the scientific argument of this work needs tightening. The tone, the title, and the overall writing should be modified to better tackle the nuances underlying the arguments of biologically plausible learning algorithms. The claims and conclusions need to be more explicit, and the work needs to better seated in the context of both the previous literature, and the important questions at play for assessing biologically plausible learning algorithms.