Related papers: Topology-Aware Activation Functions in Neural Netw…

Activation functions play a significant role in neural network design by enabling non-linearity. The choice of activation function was previously shown to influence the properties of the resulting loss landscape. Understanding the…

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…

Our goal is to infer the topology of a network when (i) we can send probes between sources and receivers at the edge of the network and (ii) intermediate nodes can perform simple network coding operations, i.e., additions. Our key intuition…

Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of…

Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…

In recent years, many techniques have been developed to improve the performance and efficiency of data center networks. While these techniques provide high accuracy, they are often designed using heuristics that leverage domain-specific…

The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural…

Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks…

Accurately and efficiently characterizing the decision boundary of classifiers is important for problems related to model selection and meta-learning. Inspired by topological data analysis, the characterization of decision boundaries using…

Machine Learning with Deep Neural Networks (DNNs) has become a successful tool in solving tasks across various fields of application. However, the complexity of DNNs makes it difficult to understand how they solve their learned task. To…

The expressive power of artificial neural networks crucially depends on the nonlinearity of their activation functions. Though a wide variety of nonlinear activation functions have been proposed for use in artificial neural networks, a…

The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both…

Model compression is an essential technique for deploying deep neural networks (DNNs) on power and memory-constrained resources. However, existing model-compression methods often rely on human expertise and focus on parameters' local…

The loss surfaces of deep neural networks have been the subject of several studies, theoretical and experimental, over the last few years. One strand of work considers the complexity, in the sense of local optima, of high dimensional random…

The non-convex nature of trained neural networks has created significant obstacles in their incorporation into optimization models. In this context, Anderson et al. (2020) provided a framework to obtain the convex hull of the graph of a…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barab\'asi and Albert. We find that the topology of the network connections may spontaneously induce periodic neural…

Many segmentation tasks for biomedical images can be modeled as the minimization of an energy function and solved by a class of max-flow and min-cut optimization algorithms. However, the segmentation accuracy is sensitive to the contrasting…

Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…