Related papers: Neural Persistence: A Complexity Measure for Deep …

We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…

Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…

Lightweight model design has become an important direction in the application of deep learning technology, pruning is an effective mean to achieve a large reduction in model parameters and FLOPs. The existing neural network pruning methods…

The performance of attractor neural networks has been shown to depend crucially on the heterogeneity of the underlying topology. We take this analysis a step further by examining the effect of degree-degree correlations -- or assortativity…

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive…

In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…

Using rough path techniques, we provide a priori estimates for the output of Deep Residual Neural Networks in terms of both the input data and the (trained) network weights. As trained network weights are typically very rough when seen as…

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…

Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or…

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…

Interpreting the learning dynamics of neural networks can provide useful insights into how networks learn and the development of better training and design approaches. We present an approach to interpret learning in neural networks by…

Purpose: We propose a novel method for continual learning based on the increasing depth of neural networks. This work explores whether extending neural network depth may be beneficial in a life-long learning setting. Methods: We propose a…

Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…

Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…

Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the…

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these…

To advance deep learning methodologies in the next decade, a theoretical framework for reasoning about modern neural networks is needed. While efforts are increasing toward demystifying why deep learning is so effective, a comprehensive…