In this supplementary material, we provide more details regarding implementation details in Appendix B, more analysis of ERDA in Appendix C, full experimental results in Appendix D, and studies on parameters in Appendix E.

This appendix is organized as follows: Section A: the detailed dataset statistics and a summary of model properties w.r.t. We present the details on each dataset in Table 4. Under the online continual setting, the tasks are observed following a fixed order and the data from each task is observed as a (one-pass) stream of samples. The batch size is 10 for all the datasets. We do not randomize the order of tasks or optimize the task orders.

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Parallel implementations of stochastic gradient descent (SGD) have received significant research attention, thanks to its excellent scalability properties. A fundamental barrier when parallelizing SGD is the high bandwidth cost of communicating gradient updates between nodes; consequently, several lossy compresion heuristics have been proposed, by which nodes only communicate quantized gradients. Although effective in practice, these heuristics do not always guarantee convergence, and it is not clear whether they can be improved. In this paper, we propose Quantized SGD (QSGD), a family of compression schemes for gradient updates which provides convergence guarantees. QSGD allows the user to smoothly trade off \emph{communication bandwidth} and \emph{convergence time}: nodes can adjust the number of bits sent per iteration, at the cost of possibly higher variance. We show that this trade-off is inherent, in the sense that improving it past some threshold would violate information-theoretic lower bounds. QSGD guarantees convergence for convex and non-convex objectives, under asynchrony, and can be extended to stochastic variance-reduced techniques. When applied to training deep neural networks for image classification and automated speech recognition, QSGD leads to significant reductions in end-to-end training time. For example, on 16GPUs, we can train the ResNet152 network to full accuracy on ImageNet 1.8x faster than the full-precision variant.

Knowledge distillation (KD) aims to train a lightweight classifier suitable to provide accurate inference with constrained resources in multi-label learning. Instead of directly consuming feature-label pairs, the classifier is trained by a teacher, i.e., a high-capacity model whose training may be resource-hungry. The accuracy of the classifier trained this way is usually suboptimal because it is difficult to learn the true data distribution from the teacher. An alternative method is to adversarially train the classifier against a discriminator in a two-player game akin to generative adversarial networks (GAN), which can ensure the classifier to learn the true data distribution at the equilibrium of this game. However, it may take excessively long time for such a two-player game to reach equilibrium due to high-variance gradient updates.

Training large neural networks requires substantial hardware and energy resources.

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