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We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized.…
We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution…
Social networks continuously change as new ties are created and existing ones fade. It is widely noted that our social embedding exerts a strong influence on what information we receive and how we form beliefs and make decisions. However,…
As individuals communicate, their exchanges form a dynamic network. We demonstrate, using time series analysis of communication in three online settings, that network structure alone can be highly revealing of the diversity and novelty of…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
We introduce a model for the emergence of innovations, in which cognitive processes are described as random walks on the network of links among ideas or concepts, and an innovation corresponds to the first visit of a node. The transition…
Characterizing the spatio-temporal evolution of networks is a central topic in many disciplines. While network expansion has been studied thoroughly, less is known about how empirical networks behave when shrinking. For transportation…
We study how long-lived, rational agents learn in a social network. In every period, after observing the past actions of his neighbors, each agent receives a private signal, and chooses an action whose payoff depends only on the state.…
The spread of socially-learnt behaviours occurs in many animal species, and understanding how behaviours spread can provide novel insights into the causes and consequences of sociality. Within wild populations, behaviour spread is often…
We suggest an underlying mechanism that governs the growth of a network of concepts, a complex network that reflects the connections between different scientific concepts based on their co-occurrences in publications. To this end, we…
For decades, complex networks, such as social networks, biological networks, chemical networks, technological networks, have been used to study the evolution and dynamics of different kinds of complex systems. These complex systems can be…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
Acceptance of an innovation can occur through mutliple exposures to individuals who have already accepted it. Presented here is a model to trace the evolution of an innovation in a social network with a preference $\lambda$, amidst…
Often in language and other areas of cognition, whether two components of an object are identical or not determines if it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…
Mostly acyclic directed networks, treated mathematically as directed graphs, arise in machine learning, biology, social science, physics, and other applications. Newman [1] has noted the mathematical challenges of such networks. In this…
Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this…
We discuss a possibility that the entire universe on its most fundamental level is a neural network. We identify two different types of dynamical degrees of freedom: "trainable" variables (e.g. bias vector or weight matrix) and "hidden"…
Current social networks are of extremely large-scale generating tremendous information flows at every moment. How information diffuse over social networks has attracted much attention from both industry and academics. Most of the existing…
Entrainment of randomly coupled oscillator networks by periodic external forcing applied to a subset of elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window…