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In practice, multi-task learning (through learning features shared among tasks) is an essential property of deep neural networks (NNs). While infinite-width limits of NNs can provide good intuition for their generalization behavior, the…

We prove a large deviation principle for deep neural networks with Gaussian weights and at most linearly growing activation functions, such as ReLU. This generalises earlier work, in which bounded and continuous activation functions were…

Neural networks are a powerful class of functions that can be trained with simple gradient descent to achieve state-of-the-art performance on a variety of applications. Despite their practical success, there is a paucity of results that…

Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian Error Linear…

We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical…

There currently exist two extreme viewpoints for neural network feature learning -- (i) Neural networks simply implement a kernel method (a la NTK) and hence no features are learned (ii) Neural networks can represent (and hence learn)…

Understanding when neural networks can be learned efficiently is a fundamental question in learning theory. Existing hardness results suggest that assumptions on both the input distribution and the network's weights are necessary for…

Recently, theoretical analyses of deep neural networks have broadly focused on two directions: 1) Providing insight into neural network training by SGD in the limit of infinite hidden-layer width and infinitesimally small learning rate…

Rectified linear activation units are important components for state-of-the-art deep convolutional networks. In this paper, we propose a novel S-shaped rectified linear activation unit (SReLU) to learn both convex and non-convex functions,…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

We study the improper learning of multi-layer neural networks. Suppose that the neural network to be learned has $k$ hidden layers and that the $\ell_1$-norm of the incoming weights of any neuron is bounded by $L$. We present a kernel-based…

Rectified linear unit (ReLU) activations can also be thought of as 'gates', which, either pass or stop their pre-activation input when they are 'on' (when the pre-activation input is positive) or 'off' (when the pre-activation input is…

Multiple Kernel Learning is a conventional way to learn the kernel function in kernel-based methods. MKL algorithms enhance the performance of kernel methods. However, these methods have a lower complexity compared to deep learning models…

We study depth separation in infinite-width neural networks, where complexity is controlled by the overall squared $\ell_2$-norm of the weights (sum of squares of all weights in the network). Whereas previous depth separation results…

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…

While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of…

Infinite width limit has shed light on generalization and optimization aspects of deep learning by establishing connections between neural networks and kernel methods. Despite their importance, the utility of these kernel methods was…

This paper presents an investigation of the approximation property of neural networks with unbounded activation functions, such as the rectified linear unit (ReLU), which is the new de-facto standard of deep learning. The ReLU network can…

We consider the problem of learning an unknown ReLU network with respect to Gaussian inputs and obtain the first nontrivial results for networks of depth more than two. We give an algorithm whose running time is a fixed polynomial in the…

We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural networks. First, we emphatically show that it is unsurprising…