Related papers: Learning Functions in Large Networks requires Modu…

The exploration of the structural topology and the organizing principles of genome-based large-scale metabolic networks is essential for studying possible relations between structure and functionality of metabolic networks. Topological…

Animals flexibly recombine a finite set of core motor motifs to meet diverse task demands, but existing behavior segmentation methods oversimplify this process by imposing discrete syllables under restrictive generative assumptions. To…

Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret…

Recently proposed neural network activation functions such as rectified linear, maxout, and local winner-take-all have allowed for faster and more effective training of deep neural architectures on large and complex datasets. The common…

The ubiquity of modules in biological networks may result from an evolutionary benefit of a modular organization. For instance, modularity may increase the rate of adaptive evolution, because modules can be easily combined into new…

Meso-scale structures (communities) are used to understand the macro-scale properties of complex networks, such as their functionality and formation mechanisms. Micro-scale structures are known to exist in most complex networks (e.g., large…

We study the effect of width on the dynamics of feature-learning neural networks across a variety of architectures and datasets. Early in training, wide neural networks trained on online data have not only identical loss curves but also…

Background: Networks in different domains are characterized by similar global characteristics while differing in local structures. To further extend this concept, we investigated network regularities on a fine scale in order to examine the…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al.…

We introduce a new algorithm for modularity-based community detection in large networks. The algorithm, which we refer to as a smart local moving algorithm, takes advantage of a well-known local moving heuristic that is also used by other…

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…

Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet simplifies away a major part of their complexities? In this…

Given the large size and complexity of most biochemical regulation and signaling networks, there is a non-trivial relationship between the micro-level logic of component interactions and the observed macro-dynamics. Here we address this…

Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…

Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…

In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…

Recently, a spate of papers have provided positive theoretical results for training over-parameterized neural networks (where the network size is larger than what is needed to achieve low error). The key insight is that with sufficient…

Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…