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Register a new userBatch Normalization Preconditioning for Neural Network Training
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Susanna Lange
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Batch normalization (BN) is a popular and ubiquitous method in deep learning that has been shown to decrease training time and improve generalization performance of neural networks. Despite its success, BN is not theoretically well understood. It is not suitable for use with very small mini-batch sizes or online learning. In this paper, we propose a new method called Batch Normalization Preconditioning (BNP). Instead of applying normalization explicitly through a batch normalization layer as is done in BN, BNP applies normalization by conditioning the parameter gradients directly during training. This is designed to improve the Hessian matrix of the loss function and hence convergence during training. One benefit is that BNP is not constrained on the mini-batch size and works in the online learning setting. Furthermore, its connection to BN provides theoretical insights on how BN improves training and how BN is applied to special architectures such as convolutional neural networks.
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Batch normalization (BN) is a key facilitator and considered essential for state-of-the-art binary neural networks (BNN). However, the BN layer is costly to calculate and is typically implemented with non-binary parameters, leaving a hurdle for the efficient implementation of BNN training. It also introduces undesirable dependence between samples within each batch. Inspired by the latest advance on Batch Normalization Free (BN-Free) training, we extend their framework to training BNNs, and for the first time demonstrate that BNs can be completed removed from BNN training and inference regimes. By plugging in and customizing techniques including adaptive gradient clipping, scale weight standardization, and specialized bottleneck block, a BN-free BNN is capable of maintaining competitive accuracy compared to its BN-based counterpart. Extensive experiments validate the effectiveness of our proposal across diverse BNN backbones and datasets. For example, after removing BNs from the state-of-the-art ReActNets, it can still be trained with our proposed methodology to achieve 92.08%, 68.34%, and 68.0% accuracy on CIFAR-10, CIFAR-100, and ImageNet respectively, with marginal performance drop (0.23%~0.44% on CIFAR and 1.40% on ImageNet). Codes and pre-trained models are available at: https://github.com/VITA-Group/BNN_NoBN.
Quantized Neural Networks (QNNs) use low bit-width fixed-point numbers for representing weight parameters and activations, and are often used in real-world applications due to their saving of computation resources and reproducibility of results. Batch Normalization (BN) poses a challenge for QNNs for requiring floating points in reciprocal operations, and previous QNNs either require computing BN at high precision or revise BN to some variants in heuristic ways. In this work, we propose a novel method to quantize BN by converting an affine transformation of two floating points to a fixed-point operation with shared quantized scale, which is friendly for hardware acceleration and model deployment. We confirm that our method maintains same outputs through rigorous theoretical analysis and numerical analysis. Accuracy and efficiency of our quantization method are verified by experiments at layer level on CIFAR and ImageNet datasets. We also believe that our method is potentially useful in other problems involving quantization.
Batch Normalization (BN) uses mini-batch statistics to normalize the activations during training, introducing dependence between mini-batch elements. This dependency can hurt the performance if the mini-batch size is too small, or if the elements are correlated. Several alternatives, such as Batch Renormalization and Group Normalization (GN), have been proposed to address this issue. However, they either do not match the performance of BN for large batches, or still exhibit degradation in performance for smaller batches, or introduce artificial constraints on the model architecture. In this paper we propose the Filter Response Normalization (FRN) layer, a novel combination of a normalization and an activation function, that can be used as a replacement for other normalizations and activations. Our method operates on each activation channel of each batch element independently, eliminating the dependency on other batch elements. Our method outperforms BN and other alternatives in a variety of settings for all batch sizes. FRN layer performs $approx 0.7-1.0%$ better than BN on top-1 validation accuracy with large mini-batch sizes for Imagenet classification using InceptionV3 and ResnetV2-50 architectures. Further, it performs $>1%$ better than GN on the same problem in the small mini-batch size regime. For object detection problem on COCO dataset, FRN layer outperforms all other methods by at least $0.3-0.5%$ in all batch size regimes.
Batch normalization (BN) has become a crucial component across diverse deep neural networks. The network with BN is invariant to positively linear re-scaling of weights, which makes there exist infinite functionally equivalent networks with various scales of weights. However, optimizing these equivalent networks with the first-order method such as stochastic gradient descent will converge to different local optima owing to different gradients across training. To alleviate this, we propose a quotient manifold emph{PSI manifold}, in which all the equivalent weights of the network with BN are regarded as the same one element. Then, gradient descent and stochastic gradient descent on the PSI manifold are also constructed. The two algorithms guarantee that every group of equivalent weights (caused by positively re-scaling) converge to the equivalent optima. Besides that, we give the convergence rate of the proposed algorithms on PSI manifold and justify that they accelerate training compared with the algorithms on the Euclidean weight space. Empirical studies show that our algorithms can consistently achieve better performances over various experimental settings.
In this work, we propose a novel technique to boost training efficiency of a neural network. Our work is based on an excellent idea that whitening the inputs of neural networks can achieve a fast convergence speed. Given the well-known fact that independent components must be whitened, we introduce a novel Independent-Component (IC) layer before each weight layer, whose inputs would be made more independent. However, determining independent components is a computationally intensive task. To overcome this challenge, we propose to implement an IC layer by combining two popular techniques, Batch Normalization and Dropout, in a new manner that we can rigorously prove that Dropout can quadratically reduce the mutual information and linearly reduce the correlation between any pair of neurons with respect to the dropout layer parameter $p$. As demonstrated experimentally, the IC layer consistently outperforms the baseline approaches with more stable training process, faster convergence speed and better convergence limit on CIFAR10/100 and ILSVRC2012 datasets. The implementation of our IC layer makes us rethink the common practices in the design of neural networks. For example, we should not place Batch Normalization before ReLU since the non-negative responses of ReLU will make the weight layer updated in a suboptimal way, and we can achieve better performance by combining Batch Normalization and Dropout together as an IC layer.
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