Related papers: Understanding training and generalization in deep …

Characterizing the remarkable generalization properties of over-parameterized neural networks remains an open problem. In this paper, we promote a shift of focus towards initialization rather than neural architecture or (stochastic)…

Recent studies have shown that deep neural networks (DNNs) perform significantly better than shallow networks and Gaussian mixture models (GMMs) on large vocabulary speech recognition tasks. In this paper, we argue that the improved…

Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

Deep neural networks (DNNs) have demonstrated dominating performance in many fields; since AlexNet, networks used in practice are going wider and deeper. On the theoretical side, a long line of works has been focusing on training neural…

Understanding the advantages of deep neural networks trained by gradient descent (GD) compared to shallow models remains an open theoretical challenge. In this paper, we introduce a class of target functions (single and multi-index Gaussian…

Reduced numerical precision is a common technique to reduce computational cost in many Deep Neural Networks (DNNs). While it has been observed that DNNs are resilient to small errors and noise, no general result exists that is capable of…

Deep CNNs are known to exhibit the following peculiarity: on the one hand they generalize extremely well to a test set, while on the other hand they are extremely sensitive to so-called adversarial perturbations. The extreme sensitivity of…

Standard deep neural networks (DNNs) are commonly trained in an end-to-end fashion for specific tasks such as object recognition, face identification, or character recognition, among many examples. This specificity often leads to…

Low-bit deep neural networks (DNNs) become critical for embedded applications due to their low storage requirement and computing efficiency. However, they suffer much from the non-negligible accuracy drop. This paper proposes the stochastic…

Understanding the effect of depth in deep learning is a critical problem. In this work, we utilize the Fourier analysis to empirically provide a promising mechanism to understand why feedforward deeper learning is faster. To this end, we…

The lack of mathematical tractability of Deep Neural Networks (DNNs) has hindered progress towards having a unified convergence analysis of training algorithms, in the general setting. We propose a unified optimization framework for…

Deep Learning is considered to be a quite young in the area of machine learning research, found its effectiveness in dealing complex yet high dimensional dataset that includes but limited to images, text and speech etc. with multiple levels…

Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function…

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true…

Neural networks trained with gradient-based methods exhibit a strong simplicity bias: they learn simpler statistical features of their data before moving to more complex features. Previous analyses of this phenomenon have largely focused on…

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. Under such a training regime, our finding is that, the…

Deep neural networks (DNNs) are the workhorses of deep learning, which constitutes the state of the art in numerous application domains. However, DNN-based decision rules are notoriously prone to poor generalization, i.e., may prove…

Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…

How to train deep neural networks (DNNs) to generalize well is a central concern in deep learning, especially for severely overparameterized networks nowadays. In this paper, we propose an effective method to improve the model…