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Exploring why stochastic gradient descent (SGD) based optimization methods train deep neural networks (DNNs) that generalize well has become… (see more) an active area of research. Towards this end, we empirically study the dynamics of SGD when training over-parametrized DNNs. Specifically we study the DNN loss surface along the trajectory of SGD by interpolating the loss surface between parameters from consecutive \textit{iterations} and tracking various metrics during training. We find that the loss interpolation between parameters before and after a training update is roughly convex with a minimum (\textit{valley floor}) in between for most of the training. Based on this and other metrics, we deduce that during most of the training, SGD explores regions in a valley by bouncing off valley walls at a height above the valley floor. This 'bouncing off walls at a height' mechanism helps SGD traverse larger distance for small batch sizes and large learning rates which we find play qualitatively different roles in the dynamics. While a large learning rate maintains a large height from the valley floor, a small batch size injects noise facilitating exploration. We find this mechanism is crucial for generalization because the valley floor has barriers and this exploration above the valley floor allows SGD to quickly travel far away from the initialization point (without being affected by barriers) and find flatter regions, corresponding to better generalization.
This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this the… (see more)ory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.
This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this the… (see more)ory, a new regularization method in deep learning is derived and shown to outperform previous methods in CIFAR-10, CIFAR-100, and SVHN. Moreover, the proposed theory provides a theoretical basis for a family of practically successful regularization methods in deep learning. We discuss several consequences of our results on one-shot learning, representation learning, deep learning, and curriculum learning. Unlike statistical learning theory, the proposed learning theory analyzes each problem instance individually via measure theory, rather than a set of problem instances via statistics. As a result, it provides different types of results and insights when compared to statistical learning theory.
Generative adversarial networks are a learning framework that rely on training a discriminator to estimate a measure of difference between a… (see more) target and generated distributions. GANs, as normally formulated, rely on the generated samples being completely differentiable w.r.t. the generative parameters, and thus do not work for discrete data. We introduce a method for training GANs with discrete data that uses the estimated difference measure from the discriminator to compute importance weights for generated samples, thus providing a policy gradient for training the generator. The importance weights have a strong connection to the decision boundary of the discriminator, and we call our method boundary-seeking GANs (BGANs). We demonstrate the effectiveness of the proposed algorithm with discrete image and character-based natural language generation. In addition, the boundary-seeking objective extends to continuous data, which can be used to improve stability of training, and we demonstrate this on Celeba, Large-scale Scene Understanding (LSUN) bedrooms, and Imagenet without conditioning.
2018-02-15
International Conference on Learning Representations (published)
One of the most successful techniques in generative models has been decomposing a complicated generation task into a series of simpler gener… (see more)ation tasks. For example, generating an image at a low resolution and then learning to refine that into a high resolution image often improves results substantially. Here we explore a novel strategy for decomposing generation for complicated objects in which we first generate latent variables which describe a subset of the observed variables, and then map from these latent variables to the observed space. We show that this allows us to achieve decoupled training of complicated generative models and present both theoretical and experimental results supporting the benefit of such an approach.
