Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes the layer outputs during training using the statistics of each mini-batch. BN accelerates training procedure by allowing to safely utilize large learning rates and alleviates the need for careful initialization of the parameters. In this work, we study BN from the viewpoint of Fisher kernels that arise from generative probability models. We show that assuming samples within a mini-batch are from the same probability density function, then BN is identical to the Fisher vector of a Gaussian distribution. That means batch normalizing transform can be explained in terms of kernels that naturally emerge from the probability density function that models the generative process of the underlying data distribution. Consequently, it promises higher discrimination power for the batch-normalized mini-batch. However, given the rectifying non-linearities employed in CNN architectures, distribution of the layer outputs show an asymmetric characteristic. Therefore, in order for BN to fully benefit from the aforementioned properties, we propose approximating underlying data distribution not with one, but a mixture of Gaussian densities. Deriving Fisher vector for a Gaussian Mixture Model (GMM), reveals that batch normalization can be improved by independently normalizing with respect to the statistics of disentangled sub-populations. We refer to our proposed soft piecewise version of batch normalization as Mixture Normalization (MN). Through extensive set of experiments on CIFAR-10 and CIFAR-100, using both a 5-layers deep CNN and modern Inception-V3 architecture, we show that mixture normalization reduces required number of gradient updates to reach the maximum test accuracy of the batch normalized model by ∼31%-47% across a variety of training scenarios. Replacing even a few BN modules with MN in the 48-layers deep Inception-V3 architecture is sufficient to not only obtain considerable training acceleration but also better final test accuracy. We show that similar observations are valid for 40 and 100-layers deep DenseNet architectures as well. We complement our study by evaluating the application of mixture normalization to the Generative Adversarial Networks (GANs), where "mode collapse" hinders the training process. We solely replace a few batch normalization layers in the generator with our proposed mixture normalization. Our experiments using Deep Convolutional GAN (DCGAN) on CIFAR-10 show that mixture normalized DCGAN not only provides an acceleration of ∼58% but also reaches lower (better) "Fréchet Inception Distance" (FID) of 33.35 compared to 37.56 of its batch normalized counterpart.
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HGAN: Hybrid generative adversarial network
In this paper, we present a simple approach to train Generative Adversarial Networks (GANs) in order to avoid a mode collapse issue. Implicit models such as GANs tend to generate better samples compared to explicit models that are trained on tractable data likelihood. However, GANs overlook the explicit data density characteristics which leads to undesirable quantitative evaluations and mode collapse. To bridge this gap, we propose a hybrid generative adversarial network (HGAN) for which we can enforce data density estimation via an autoregressive model and support both adversarial and likelihood framework in a joint training manner which diversify the estimated density in order to cover different modes. We propose to use an adversarial network to transfer knowledge from an autoregressive model (teacher) to the generator (student) of a GAN model. A novel deep architecture within the GAN formulation is developed to adversarially distill the autoregressive model information in addition to simple GAN training approach. We conduct extensive experiments on real-world datasets (i.e., MNIST, CIFAR-10, STL-10) to demonstrate the effectiveness of the proposed HGAN under qualitative and quantitative evaluations. The experimental results show the superiority and competitiveness of our method compared to the baselines.
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- Award ID(s):
- 1650474
- NSF-PAR ID:
- 10328358
- Date Published:
- Journal Name:
- Journal of Intelligent & Fuzzy Systems
- Volume:
- 40
- Issue:
- 5
- ISSN:
- 1064-1246
- Page Range / eLocation ID:
- 8927 to 8938
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Generative adversarial networks (GANs) have been impactful on many problems and applications but suffer from unstable training. The Wasserstein GAN (WGAN) leverages the Wasserstein distance to avoid the caveats in the minmax two-player training of GANs but has other defects such as mode collapse and lack of metric to detect the convergence. We introduce a novel inferential Wasserstein GAN (iWGAN) model, which is a principled framework to fuse autoencoders and WGANs. The iWGAN model jointly learns an encoder network and a generator network motivated by the iterative primal-dual optimization process. The encoder network maps the observed samples to the latent space and the generator network maps the samples from the latent space to the data space. We establish the generalization error bound of the iWGAN to theoretically justify its performance. We further provide a rigorous probabilistic interpretation of our model under the framework of maximum likelihood estimation. The iWGAN, with a clear stopping criteria, has many advantages over other autoencoder GANs. The empirical experiments show that the iWGAN greatly mitigates the symptom of mode collapse, speeds up the convergence, and is able to provide a measurement of quality check for each individual sample. We illustrate the ability of the iWGAN by obtaining competitive and stable performances for benchmark datasets.
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3233/JIFS-201202
