Learning with Plasticity Rules: Generalization and Robustness

Brains learn robustly, and generalize effortlessly between different learning tasks; in contrast, robustness and generalization across tasks are well known weaknesses of artificial neural nets (ANNs). How can we use our accelerating understanding of the brain to improve these and other aspects of ANNs? Here we hypothesize that (a) Brains employ synaptic plasticity rules that serve as proxies for GD; (b) These rules themselves can be learned by GD on the rule parameters; and (c) This process may be a missing ingredient for the development of ANNs that generalize well and are robust to adversarial perturbations. We provide both empirical and theoretical evidence for this hypothesis. In our experiments, plasticity rules for the synaptic weights of recurrent neural nets (RNNs) are learned through GD and are found to perform reasonably well (with no backpropagation). We find that plasticity rules learned by this process generalize from one type of data/classifier to others (e.g., rules learned on synthetic data work well on MNIST/Fashion MNIST) and converge with fewer updates. Moreover, the classifiers learned using plasticity rules exhibit surprising levels of tolerance to adversarial perturbations. In the special case of the last layer of a classification network, we show analytically that GD on the plasticity rule recovers (and improves upon) the perceptron algorithm and the multiplicative weights method. Finally, we argue that applying GD to learning rules is biologically plausible, in the sense that it can be learned over evolutionary time: we describe a genetic setting where natural selection of a numerical parameter over a sequence of generations provably simulates a simple variant of GD.