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We study the emergence of sparse representations in neural networks. We show that in unsupervised models with regularization, the emergence of sparsity is the result of the input data samples being distributed along highly non-linear or…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
We propose layer saturation - a simple, online-computable method for analyzing the information processing in neural networks. First, we show that a layer's output can be restricted to the eigenspace of its variance matrix without…
Self-organization and pattern formation in network-organized systems emerges from the collective activation and interaction of many interconnected units. A striking feature of these non-equilibrium structures is that they are often…
We propose a metric, Layer Saturation, defined as the proportion of the number of eigenvalues needed to explain 99% of the variance of the latent representations, for analyzing the learned representations of neural network layers.…
How the cells break symmetry and organize their edge activity to move directionally is a fun- damental question in cell biology. Physical models of cell motility commonly rely on gradients of regulatory factors and/or feedback from the…
We introduce a new neural architecture and an unsupervised algorithm for learning invariant representations from temporal sequence of images. The system uses two groups of complex cells whose outputs are combined multiplicatively: one that…
Living neural networks emerge through a process of growth and self-organization that begins with a single cell and results in a brain, an organized and functional computational device. Artificial neural networks, however, rely on…
Despite classical statistical theory predicting severe overfitting, modern massively overparameterized neural networks still generalize well. This unexpected property is attributed to the network's so-called implicit bias, which describes…
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…
We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the…
Localized receptive fields -- neurons that are selective for certain contiguous spatiotemporal features of their input -- populate early sensory regions of the mammalian brain. Unsupervised learning algorithms that optimize explicit…
Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among…
The open nonlinear electrodynamic system - nonlinear transverse non-homogeneous dielectric layer, is an example of inorganic system having the properties of self-organization, peculiar to biological systems. The necessary precondition of…
This tutorial is intended as an accessible but rigorous first reference for someone interested in learning how to model and analyze cellular network performance using stochastic geometry. In particular, we focus on computing the…
Dynamic multilayer networks frequently represent the structure of multiple co-evolving relations; however, statistical models are not well-developed for this prevalent network type. Here, we propose a new latent space model for dynamic…
Biological nervous systems consist of networks of diverse, sophisticated information processors in the form of neurons of different classes. In most artificial neural networks (ANNs), neural computation is abstracted to an activation…
We study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix. The probability distribution function of the components of the representative eigenvectors are proposed to describe…
A leading hypothesis for the surprising generalization of neural networks is that the dynamics of gradient descent bias the model towards simple solutions, by searching through the solution space in an incremental order of complexity. We…
Network science is increasingly being developed to get new insights about behavior and properties of complex systems represented in terms of nodes and interactions. One useful approach is investigating localization properties of…