Paper:
CRITICAL LEARNING PERIODS IN DEEP NETWORKS
Similar to humans and animals, deep artificial neural networks exhibit critical periods during which a temporary stimulus deficit can impair the development of a skill. The extent of the impairment depends on the onset and length of the deficit window, as in animal models, and on the size of the neural network. Deficits that do not affect low-level statistics, such as vertical flipping of the images, have no lasting effect on performance and can be overcome with further training. To better understand this phenomenon, we use the Fisher Information of the weights to measure the effective connectivity between layers of a network during training. Counterintuitively, information rises rapidly in the early phases of training, and then decreases, preventing redistribution of information resources in a phenomenon we refer to as a loss of "Information Plasticity". Our analysis suggests that the first few epochs are critical for the creation of strong connections that are optimal relative to the input data distribution. Once such strong connections are created, they do not appear to change during additional training. These findings suggest that the initial learning transient, under-scrutinized compared to asymptotic behavior, plays a key role in determining the outcome of the training process. Our findings, combined with recent theoretical results in the literature, also suggest that forgetting (decrease of information in the weights) is critical to achieving invariance and disentanglement in representation learning. Finally, critical periods are not restricted to biological systems, but can emerge naturally in learning systems, whether biological or artificial, due to fundamental constrains arising from learning dynamics and information processing.

Review:
The authors analyze the learning dynamics in deep neural networks and identify an intriguing phenomenon that reflects what in biological learning is known as critical period: a relatively short time window early in post-natal development where organisms become particularly sensitive to particular changes in experience. The importance of critical periods in biology is due to the fact that specific types of perturbations to the input statistic can cause deficits in performance which can be permanent in the sense that later training cannot rescue them.
The authors did a great job illustrating the parallelism between critical periods in biological neural systems and the analogous phenomenon in artificial deep neural networks. Essentially, they showed that blurring the input samples of the cifar10 dataset during the initial phase of training had an effect that is very reminiscent of the result of sensory deprivation during the critical periods of visual learning in mammals, resulting in a long-term impairments in visual object recognition that persists even if blurring is removed later in training. The authors go as far as characterizing the effects of the length of the "sensory deprivation" window and its onset during training, and comparing the results to classic neuroscience monocular deprivation experiments in kittens, pointing out very striking phenomenological similarities.
Next, the authors establish a connection between critical periods in deep neural networks and the amount of information that the weights of the trained model contain about the task by looking at the Fisher Information Matrix (FIM). With this method they obtain a host of interesting insights. One insight is that there are two phases in learning: an initial one where the trace of the FIM grows together with a rapid increase in classification accuracy, and a second one where accuracy keeps slightly increasing, but Fisher Information trace globally decreases. They then go into detail and look at how this quantity evolves within individual layers of the deep learning architecture, revealing that the deficit caused by the blurring perturbation during the early epochs training is accompanied by larger FIM trace in the last layers of the architecture at the expense of the intermediate layers.
Besides the fact that deep neural network exhibit critical periods, another important result of this work is the demonstration that pretraining, if done inappropriately can actually be deleterious to the performance of the network.
This paper is insightful, and interesting. The conceptual and experimental part of the paper is very clearly presented, and the methodology is very appropriate to tease apart some of the mechanisms underlying the basic phenomenological observations. Here are some detailed questions meant to elucidate some points that are still unclear.
- Presumably, early training on blurred images prevents the initial conv filters from learning to discriminate high-frequency components (first of all, is this true?). The crucial phenomenon pointed out by the authors is that, even after removing the blur, the lower convolutions aren't able to recover and learn the high-frequency components. In fact, the high FIM trace in the latest layers could be due to the fact that they're trying to compensate for the lack of appropriate low-level feature extractors by composing low-frequency filters so as "build" high-frequency ones. If this makes sense, one would assume that freezing the last layers and only maintaining plasticity in the lower ones could be a way of "reopening" the critical period. Is that indeed the case?
- The authors show that their main results are robust to changes in the learning rate annealing schedule. However, it is not clear how changing the optimizer might affect the presence of the critical period. What would happen for instance using Adam or another optimization procedure that relies on the normalization of the gradient?
- On a related note, the authors point out the importance of forgetting, in particular as the main mechanism behind the second learning phase. They also point out that the deficit in learning the task after sensory deprivation is accompanied by large FIM trace in the last layers. What would happen in the presence of a standard regularizer like weight decay? Assuming that large FIM trace in the last layers is correlated with large weighs, that might mitigate the negative effect of early sensory deprivation.
- In neuroscience the opening of the critical period window if thought to be mechanistically mediated by the maturation of inhibition. Is that view compatible with the results presented in this paper? This is sort of complementary to the FIM analysis, since is mostly about net average input to a neuron, i.e. about the information contained in the activations, rather than the weights.