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We study training one-hidden-layer ReLU networks in the neural tangent kernel (NTK) regime, where the networks' biases are initialized to some constant rather than zero. We prove that under such initialization, the neural network will have sparse activation throughout the entire training process, which enables fast training procedures via some sophisticated computational methods. With such initialization, we show that the neural networks possess a different limiting kernel which we call bias-generalized NTK, and we study various properties of the neural networks with this new kernel. We first characterize the gradient descent dynamics. In particular, we show that the network in this case can achieve as fast convergence as the dense network, as opposed to the previous work suggesting that the sparse networks converge slower. In addition, our result improves the previous required width to ensure convergence. Secondly, we study the networks' generalization: we show a width-sparsity dependence, which yields a sparsity-dependent Rademacher complexity and generalization bound. To our knowledge, this is the first sparsity-dependent generalization result via Rademacher complexity. Lastly, we study the smallest eigenvalue of this new kernel. We identify a data-dependent region where we can derive a much sharper lower bound on the NTK's smallest eigenvalue than the worst-case bound previously known. This can lead to improvement in the generalization bound. 

Transfer learning from the model trained on large datasets to customized downstream tasks has been widely used as the pre-trained model can greatly boost the generalizability. However, the increasing sizes of pre-trained models also lead to a prohibitively large memory footprints for downstream transferring, making them unaffordable for personal devices. Previous work recognizes the bottleneck of the footprint to be the activation, and hence proposes various solutions such as injecting specific lite modules. In this work, we present a novel memory-efficient transfer framework called Back Razor, that can be plug-and-play applied to any pre-trained network without changing its architecture. The key idea of Back Razor is asymmetric sparsifying: pruning the activation stored for back-propagation, while keeping the forward activation dense. It is based on the observation that the stored activation, that dominates the memory footprint, is only needed for backpropagation. Such asymmetric pruning avoids affecting the precision of forward computation, thus making more aggressive pruning possible. Furthermore, we conduct the theoretical analysis for the convergence rate of Back Razor, showing that under mild conditions, our method retains the similar convergence rate as vanilla SGD. Extensive transfer learning experiments on both Convolutional Neural Networks and Vision Transformers with classification, dense prediction, and language modeling tasks show that Back Razor could yield up to 97% sparsity, saving 9.2x memory usage, without losing accuracy. The code is available at: https://github.com/VITA-Group/BackRazor_Neurips22. 

Convolutional neural networks (CNNs) have been increasingly deployed to edge devices. Hence, many efforts have been made towards efficient CNN inference on resource-constrained platforms. This paper attempts to explore an orthogonal direction: how to conduct more energy-efficient training of CNNs, so as to enable on-device training? We strive to reduce the energy cost during training, by dropping unnecessary computations, from three complementary levels: stochastic mini-batch dropping on the data level; selective layer update on the model level; and sign prediction for low-cost, low-precision back-propagation, on the algorithm level. Extensive simulations and ablation studies, with real energy measurements from an FPGA board, confirm the superiority of our proposed strategies and demonstrate remarkable energy savings for training. For example, when training ResNet-74 on CIFAR-10, we achieve aggressive energy savings of >90% and >60%, while incurring a top-1 accuracy loss of only about 2% and 1.2%, respectively. When training ResNet-110 on CIFAR-100, an over 84% training energy saving is achieved without degrading inference accuracy.