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Constructing neural networks for function approximation is a classical and longstanding topic in approximation theory. In this paper, we aim at constructing deep neural networks (deep nets for short) with three hidden layers to approximate…
We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations,…
The main flaw of neural network ensembling is that it is exceptionally demanding computationally, especially, if the individual sub-models are large neural networks, which must be trained separately. Having in mind that modern DNNs can be…
It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with…
Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…
Why deep neural networks (DNNs) capable of overfitting often generalize well in practice is a mystery [#zhang2016understanding]. To find a potential mechanism, we focus on the study of implicit biases underlying the training process of…
Deep neural networks (DNNs) are widely used in pattern-recognition tasks for which a human comprehensible, quantitative description of the data-generating process, e.g., in the form of equations, cannot be achieved. While doing so, DNNs…
Deep neural networks can struggle to learn continually in the face of non-stationarity. This phenomenon is known as loss of plasticity. In this paper, we identify underlying principles that lead to plastic algorithms. In particular, we…
Deep Models are increasingly becoming prevalent in summarization problems (e.g. document, video and images) due to their ability to learn complex feature interactions and representations. However, they do not model characteristics such as…
This paper introduces Progressively Diffused Networks (PDNs) for unifying multi-scale context modeling with deep feature learning, by taking semantic image segmentation as an exemplar application. Prior neural networks, such as ResNet, tend…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
Deep neural networks (DNNs) have demonstrated impressive performance on a wide array of tasks, but they are usually considered opaque since internal structure and learned parameters are not interpretable. In this paper, we re-examine the…
Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…
Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…
Real time application of deep learning algorithms is often hindered by high computational complexity and frequent memory accesses. Network pruning is a promising technique to solve this problem. However, pruning usually results in irregular…
Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…
Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…
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…
Artificial neural networks (ANNs) have become a very powerful tool in the approximation of high-dimensional functions. Especially, deep ANNs, consisting of a large number of hidden layers, have been very successfully used in a series of…