Related papers: A Correspondence Between Random Neural Networks an…

We present Neural Random Forest Imitation - a novel approach for transforming random forests into neural networks. Existing methods propose a direct mapping and produce very inefficient architectures. In this work, we introduce an imitation…

We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint…

This short paper reports some initial experimental demonstrations of the theoretical framework: the massive amount of data in the large-scale cognitive radio network can be naturally modeled as (large) random matrices. In particular, using…

Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming…

Neural networks have been successfully employed in various domains such as classification, regression and clustering, etc. Generally, the back propagation (BP) based iterative approaches are used to train the neural networks, however, it…

Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…

We study the behavior of untrained neural networks whose weights and biases are randomly distributed using mean field theory. We show the existence of depth scales that naturally limit the maximum depth of signal propagation through these…

We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…

Time is at a premium for recurrent network dynamics, and particularly so when they are stochastic and correlated: the quality of inference from such dynamics fundamentally depends on how fast the neural circuit generates new samples from…

Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…

In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…

As experiments advance to record from tens of thousands of neurons, statistical physics provides a framework for understanding how collective activity emerges from networks of fine-scale correlations. While modeling these populations is…

In this paper, we develop a wavelet-based theoretical framework for analyzing the universal approximation capabilities of neural networks over a wide range of activation functions. Leveraging wavelet frame theory on the spaces of…

We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…

Model stitching (Lenc & Vedaldi 2015) is a compelling methodology to compare different neural network representations, because it allows us to measure to what degree they may be interchanged. We expand on a previous work from Bansal,…

We characterize the connectivity structure of feed-forward, deep neural networks (DNNs) using network motif theory. To address whether a particular motif distribution is characteristic of the training task, or function of the DNN, we…

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)…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network currently being complete. In this study, we analyzed…

Existing Bayesian treatments of neural networks are typically characterized by weak prior and approximate posterior distributions according to which all the weights are drawn independently. Here, we consider a richer prior distribution in…