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Register a new userStochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks
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We propose NovoGrad, an adaptive stochastic gradient descent method with layer-wise gradient normalization and decoupled weight decay. In our experiments on neural networks for image classification, speech recognition, machine translation, and language modeling, it performs on par or better than well tuned SGD with momentum and Adam or AdamW. Additionally, NovoGrad (1) is robust to the choice of learning rate and weight initialization, (2) works well in a large batch setting, and (3) has two times smaller memory footprint than Adam.
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We present the remote stochastic gradient (RSG) method, which computes the gradients at configurable remote observation points, in order to improve the convergence rate and suppress gradient noise at the same time for different curvatures. RSG is further combined with adaptive methods to construct ARSG for acceleration. The method is efficient in computation and memory, and is straightforward to implement. We analyze the convergence properties by modeling the training process as a dynamic system, which provides a guideline to select the configurable observation factor without grid search. ARSG yields $O(1/sqrt{T})$ convergence rate in non-convex settings, that can be further improved to $O(log(T)/T)$ in strongly convex settings. Numerical experiments demonstrate that ARSG achieves both faster convergence and better generalization, compared with popular adaptive methods, such as ADAM, NADAM, AMSGRAD, and RANGER for the tested problems. In particular, for training ResNet-50 on ImageNet, ARSG outperforms ADAM in convergence speed and meanwhile it surpasses SGD in generalization.
Deep neural networks with batch normalization (BN-DNNs) are invariant to weight rescaling due to their normalization operations. However, using weight decay (WD) benefits these weight-scale-invariant networks, which is often attributed to an increase of the effective learning rate when the weight norms are decreased. In this paper, we demonstrate the insufficiency of the previous explanation and investigate the implicit biases of stochastic gradient descent (SGD) on BN-DNNs to provide a theoretical explanation for the efficacy of weight decay. We identity two implicit biases of SGD on BN-DNNs: 1) the weight norms in SGD training remain constant in the continuous-time domain and keep increasing in the discrete-time domain; 2) SGD optimizes weight vectors in fully-connected networks or convolution kernels in convolution neural networks by updating components lying in the input feature span, while leaving those components orthogonal to the input feature span unchanged. Thus, SGD without WD accumulates weight noise orthogonal to the input feature span, and cannot eliminate such noise. Our empirical studies corroborate the hypothesis that weight decay suppresses weight noise that is left untouched by SGD. Furthermore, we propose to use weight rescaling (WRS) instead of weight decay to achieve the same regularization effect, while avoiding performance degradation of WD on some momentum-based optimizers. Our empirical results on image recognition show that regardless of optimization methods and network architectures, training BN-DNNs using WRS achieves similar or better performance compared with using WD. We also show that training with WRS generalizes better compared to WD, on other computer vision tasks.
Training neural networks with large batch is of fundamental significance to deep learning. Large batch training remarkably reduces the amount of training time but has difficulties in maintaining accuracy. Recent works have put forward optimization methods such as LARS and LAMB to tackle this issue through adaptive layer-wise optimization using trust ratios. Though prevailing, such methods are observed to still suffer from unstable and extreme trust ratios which degrades performance. In this paper, we propose a new variant of LAMB, called LAMBC, which employs trust ratio clipping to stabilize its magnitude and prevent extreme values. We conducted experiments on image classification tasks such as ImageNet and CIFAR-10 and our empirical results demonstrate promising improvements across different batch sizes.
Highly distributed training of Deep Neural Networks (DNNs) on future compute platforms (offering 100 of TeraOps/s of computational capacity) is expected to be severely communication constrained. To overcome this limitation, new gradient compression techniques are needed that are computationally friendly, applicable to a wide variety of layers seen in Deep Neural Networks and adaptable to variations in network architectures as well as their hyper-parameters. In this paper we introduce a novel technique - the Adaptive Residual Gradient Compression (AdaComp) scheme. AdaComp is based on localized selection of gradient residues and automatically tunes the compression rate depending on local activity. We show excellent results on a wide spectrum of state of the art Deep Learning models in multiple domains (vision, speech, language), datasets (MNIST, CIFAR10, ImageNet, BN50, Shakespeare), optimizers (SGD with momentum, Adam) and network parameters (number of learners, minibatch-size etc.). Exploiting both sparsity and quantization, we demonstrate end-to-end compression rates of ~200X for fully-connected and recurrent layers, and ~40X for convolutional layers, without any noticeable degradation in model accuracies.
In this paper, we propose Stochastic Block-ADMM as an approach to train deep neural networks in batch and online settings. Our method works by splitting neural networks into an arbitrary number of blocks and utilizes auxiliary variables to connect these blocks while optimizing with stochastic gradient descent. This allows training deep networks with non-differentiable constraints where conventional backpropagation is not applicable. An application of this is supervised feature disentangling, where our proposed DeepFacto inserts a non-negative matrix factorization (NMF) layer into the network. Since backpropagation only needs to be performed within each block, our approach alleviates vanishing gradients and provides potentials for parallelization. We prove the convergence of our proposed method and justify its capabilities through experiments in supervised and weakly-supervised settings.
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