Related papers: Most Activation Functions Can Win the Lottery With…

Our theoretical understanding of neural networks is lagging behind their empirical success. One of the important unexplained phenomena is why and how, during the process of training with gradient descent, the theoretical capacity of neural…

Activation function is crucial to the recent successes of deep neural networks. In this paper, we first propose a new activation function, Multiple Parametric Exponential Linear Units (MPELU), aiming to generalize and unify the rectified…

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…

Neural networks activated by the rectified linear unit (ReLU) play a central role in the recent development of deep learning. The topic of approximating functions from H\"older spaces by these networks is crucial for understanding the…

Deploying energy-efficient deep learning algorithms on computational-limited devices, such as robots, is still a pressing issue for real-world applications. Spiking Neural Networks (SNNs), a novel brain-inspired algorithm, offer a promising…

Bayesian neural networks (BNNs) are a useful tool for uncertainty quantification, but require substantially more computational resources than conventional neural networks. For non-Bayesian networks, the Lottery Ticket Hypothesis (LTH)…

In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…

Recent work on the lottery ticket hypothesis has produced highly sparse Transformers for NMT while maintaining BLEU. However, it is unclear how such pruning techniques affect a model's learned representations. By probing Transformers with…

This study introduces an innovative approach aimed at the efficient pruning of neural networks, with a particular focus on their deployment on edge devices. Our method involves the integration of the Lottery Ticket Hypothesis (LTH) with the…

Successfully training deep neural networks often requires either batch normalization, appropriate weight initialization, both of which come with their own challenges. We propose an alternative, geometrically motivated method for training.…

We study the expressive power of deep ReLU neural networks for approximating functions in dilated shift-invariant spaces, which are widely used in signal processing, image processing, communications and so on. Approximation error bounds are…

Deep neural networks (DNNs) generate much richer function spaces than shallow networks. Since the function spaces induced by shallow networks have several approximation theoretic drawbacks, this explains, however, not necessarily the…

The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that need not generalize, while the latter considers classes that…

Lottery Ticket Hypothesis (LTH) raises keen attention to identifying sparse trainable subnetworks, or winning tickets, which can be trained in isolation to achieve similar or even better performance compared to the full models. Despite many…

The advancement of deep learning has led to the development of neural decoders for low latency communications. However, neural decoders can be very complex which can lead to increased computation and latency. We consider iterative pruning…

The lottery ticket hypothesis (LTH) is well-studied for convolutional neural networks but has been validated only empirically for graph neural networks (GNNs), for which theoretical findings are largely lacking. In this paper, we identify…

In a function approximation with a neural network, an input dataset is mapped to an output index by optimizing the parameters of each hidden-layer unit. For a unary function, we present constraints on the parameters and its second…

The standard Universal Approximation Theorem for operator neural networks (NNs) holds for arbitrary width and bounded depth. Here, we prove that operator NNs of bounded width and arbitrary depth are universal approximators for continuous…

We consider a deep ReLU / Leaky ReLU student network trained from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). The student network is \emph{over-realized}: at each layer $l$, the number…

The lottery ticket hypothesis suggests that sparse, sub-networks of a given neural network, if initialized properly, can be trained to reach comparable or even better performance to that of the original network. Prior works in lottery…