Curvature Explains Loss of Plasticity

Loss of plasticity is a phenomenon in which neural networks lose their ability to learn from new experience. Despite being empirically observed in several problem settings, little is understood about the mechanisms that lead to loss of plasticity. In this paper, we offer a consistent explanation for plasticity loss, based on an assertion that neural networks lose directions of curvature during training and that plasticity loss can be attributed to this reduction in curvature. To support such a claim, we provide a systematic empirical investigation of plasticity loss across several continual supervised learning problems. Our findings illustrate that curvature loss coincides with and sometimes precedes plasticity loss, while also showing that previous explanations are insufficient to explain loss of plasticity in all settings. Lastly, we show that regularizers which mitigate loss of plasticity also preserve curvature, motivating a simple distributional regularizer that proves to be effective across the problem settings considered.

Reinforcement Teaching

We propose Reinforcement Teaching: a framework for meta-learning in which a teaching policy is learned, through reinforcement, to control a student's learning process. The student's learning process is modelled as a Markov reward process and the teacher, with its action-space, interacts with the induced Markov decision process. We show that, for many learning processes, the student's learnable parameters form a Markov state. To avoid having the teacher learn directly from parameters, we propose the Parameter Embedder that learns a representation of a student's state from its input/output behaviour. Next, we use learning progress to shape the teacher's reward towards maximizing the student's performance. To demonstrate the generality of Reinforcement Teaching, we conducted experiments in which a teacher learns to significantly improve supervised and reinforcement learners by using a combination of learning progress reward and a Parameter Embedded state. These results show that Reinforcement Teaching is not only an expressive framework capable of unifying different approaches, but also provides meta-learning with the plethora of tools from reinforcement learning.

ZORB: A Derivative-Free Backpropagation Algorithm for Neural Networks

Gradient descent and backpropagation have enabled neural networks to achieve remarkable results in many real-world applications. Despite ongoing success, training a neural network with gradient descent can be a slow and strenuous affair. We present a simple yet faster training algorithm called Zeroth-Order Relaxed Backpropagation (ZORB). Instead of calculating gradients, ZORB uses the pseudoinverse of targets to backpropagate information. ZORB is designed to reduce the time required to train deep neural networks without penalizing performance. To illustrate the speed up, we trained a feed-forward neural network with 11 layers on MNIST and observed that ZORB converged 300 times faster than Adam while achieving a comparable error rate, without any hyperparameter tuning. We also broaden the scope of ZORB to convolutional neural networks, and apply it to subsamples of the CIFAR-10 dataset. Experiments on standard classification and regression benchmarks demonstrate ZORB's advantage over traditional backpropagation with Gradient Descent.