Data-agnostic quasi-imperceptible perturbations on inputs are known to degrade recognition accuracy of deep convolutional networks severely. This phenomenon is considered to be a potential security issue. Moreover, some results on statistical generalization guarantees indicate that the phenomenon can be a key to improve the networks' generalization. However, the characteristics of the shared directions of such harmful perturbations remain unknown. Our primal finding is that convolutional networks are sensitive to the directions of Fourier basis functions. We derived the property by specializing a hypothesis of the cause of the sensitivity, known as the linearity of neural networks, to convolutional networks and empirically validated it. As a by-product of the analysis, we propose an algorithm to create shift-invariant universal adversarial perturbations available in black-box settings.
Due to the substantial computational cost, training state-of-the-art deep neural networks for large-scale datasets often requires distributed training using multiple computation workers. However, by nature, workers need to frequently communicate gradients, causing severe bottlenecks, especially on lower bandwidth connections. A few methods have been proposed to compress gradient for efficient communication, but they either suffer a low compression ratio or significantly harm the resulting model accuracy, particularly when applied to convolutional neural networks. To address these issues, we propose a method to reduce the communication overhead of distributed deep learning. Our key observation is that gradient updates can be delayed until an unambiguous (high amplitude, low variance) gradient has been calculated. We also present an efficient algorithm to compute the variance with negligible additional cost. We experimentally show that our method can achieve very high compression ratio while maintaining the result model accuracy. We also analyze the efficiency using computation and communication cost models and provide the evidence that this method enables distributed deep learning for many scenarios with commodity environments.
The notion of flat minima has played a key role in the generalization studies of deep learning models. However, existing definitions of the flatness are known to be sensitive to the rescaling of parameters. The issue suggests that the previous definitions of the flatness might not be a good measure of generalization, because generalization is invariant to such rescalings. In this paper, from the PAC-Bayesian perspective, we scrutinize the discussion concerning the flat minima and introduce the notion of normalized flat minima, which is free from the known scale dependence issues. Additionally, we highlight the scale dependence of existing matrix-norm based generalization error bounds similar to the existing flat minima definitions. Our modified notion of the flatness does not suffer from the insufficiency, either, suggesting it might provide better hierarchy in the hypothesis class.
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