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The movement of large quantities of data during the training of a Deep Neural Network presents immense challenges for machine learning workloads. To minimize this overhead, especially on the movement and calculation of gradient information, we introduce streaming batch principal component analysis as an update algorithm. Streaming batch principal component analysis uses stochastic power iterations to generate a stochastic k-rank approximation of the network gradient. We demonstrate that the low rank updates produced by streaming batch principal component analysis can effectively train convolutional neural networks on a variety of common datasets, with performance comparable to standard mini batch gradient descent. These results can lead to both improvements in the design of application specific integrated circuits for deep learning and in the speed of synchronization of machine learning models trained with data parallelism.
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Training convolutional neural network models is memory intensive since back-propagation requires storing activations of all intermediate layers. This presents a practical concern when seeking to deploy very deep architectures in production, especially when models need to be frequently re-trained on updated datasets. In this paper, we propose a new implementation for back-propagation that significantly reduces memory usage, by enabling the use of approximations with negligible computational cost and minimal effect on training performance. The algorithm reuses common buffers to temporarily store full activations and compute the forward pass exactly. It also stores approximate per-layer copies of activations, at significant memory savings, that are used in the backward pass. Compared to simply approximating activations within standard back-propagation, our method limits accumulation of errors across layers. This allows the use of much lower-precision approximations without affecting training accuracy. Experiments on CIFAR-10, CIFAR-100, and ImageNet show that our method yields performance close to exact training, while storing activations compactly with as low as 4-bit precision.
Many state-of-the-art ML results have been obtained by scaling up the number of parameters in existing models. However, parameters and activations for such large models often do not fit in the memory of a single accelerator device; this means that it is necessary to distribute training of large models over multiple accelerators. In this work, we propose PipeDream-2BW, a system that supports memory-efficient pipeline parallelism. PipeDream-2BW uses a novel pipelining and weight gradient coalescing strategy, combined with the double buffering of weights, to ensure high throughput, low memory footprint, and weight update semantics similar to data parallelism. In addition, PipeDream-2BW automatically partitions the model over the available hardware resources, while respecting hardware constraints such as memory capacities of accelerators and interconnect topologies. PipeDream-2BW can accelerate the training of large GPT and BERT language models by up to 20$times$ with similar final model accuracy.
Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified by the kernel through row normalization. However, in many cases, it is desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Unfortunately, no systematic framework exists to impose such user-defined constraints. Here, we introduce a path entropy maximization based approach to derive the transition probabilities of Markov chains using a kernel and additional user-specified constraints. We illustrate the usefulness of these Markov chains with examples.
There were many algorithms to substitute the back-propagation (BP) in the deep neural network (DNN) training. However, they could not become popular because their training accuracy and the computational efficiency were worse than BP. One of them was direct feedback alignment (DFA), but it showed low training performance especially for the convolutional neural network (CNN). In this paper, we overcome the limitation of the DFA algorithm by combining with the conventional BP during the CNN training. To improve the training stability, we also suggest the feedback weight initialization method by analyzing the patterns of the fixed random matrices in the DFA. Finally, we propose the new training algorithm, binary direct feedback alignment (BDFA) to minimize the computational cost while maintaining the training accuracy compared with the DFA. In our experiments, we use the CIFAR-10 and CIFAR-100 dataset to simulate the CNN learning from the scratch and apply the BDFA to the online learning based object tracking application to examine the training in the small dataset environment. Our proposed algorithms show better performance than conventional BP in both two different training tasks especially when the dataset is small.
Adversarial training is a popular method to give neural nets robustness against adversarial perturbations. In practice adversarial training leads to low robust training loss. However, a rigorous explanation for why this happens under natural conditions is still missing. Recently a convergence theory for standard (non-adversarial) supervised training was developed by various groups for {em very overparametrized} nets. It is unclear how to extend these results to adversarial training because of the min-max objective. Recently, a first step towards this direction was made by Gao et al. using tools from online learning, but they require the width of the net to be emph{exponential} in input dimension $d$, and with an unnatural activation function. Our work proves convergence to low robust training loss for emph{polynomial} width instead of exponential, under natural assumptions and with the ReLU activation. Key element of our proof is showing that ReLU networks near initialization can approximate the step function, which may be of independent interest.
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