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Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…

Recurrent neural network (RNN)'s architecture is a key factor influencing its performance. We propose algorithms to optimize hidden sizes under running time constraint. We convert the discrete optimization into a subset selection problem.…

To be effective in sequential data processing, Recurrent Neural Networks (RNNs) are required to keep track of past events by creating memories. While the relation between memories and the network's hidden state dynamics was established over…

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Echo state networks represent a special type of recurrent neural networks. Recent papers stated that the echo state networks maximize their computational performance on the transition between order and chaos, the so-called edge of chaos.…

Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap…

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…

Machine Learning techniques have been used to teach computer programs how to play games as complicated as Chess and Go. These were achieved using powerful tools such as Neural Networks and Parallel Computing on Supercomputers. In this…

We consider evolutionary dynamics for population games in which players have a continuum of strategies at their disposal. Models in this setting amount to infinite-dimensional differential equations evolving on the manifold of probability…

Recording simultaneous activity of hundreds of neurons is now possible. Existing methods can model such population activity, but do not directly reveal the computations used by the brain. We present a fully unsupervised method that models…

A new approach for the study of social games and communications is proposed. Games are simulated between cognitive players who build the opponent's internal model and decide their next strategy from predictions based on the model. In this…

We consider the following learning problem: Given sample pairs of input and output signals generated by an unknown nonlinear system (which is not assumed to be causal or time-invariant), we wish to find a continuous-time recurrent neural…

Direct reciprocity facilitates the evolution of cooperation when individuals interact repeatedly. Most previous studies on direct reciprocity implicitly assume compulsory interactions. Yet, interactions are often voluntary in human…

Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs,…

We use system-theoretic passivity methods to study evolutionary Nash equilibria learning in large populations of agents engaged in strategic, non-cooperative interactions. The agents follow learning rules (rules for short) that capture…

This paper considers a game-theoretic framework for distributed machine learning problems over networks where the information acquisition at a node is modeled as a rational choice of a player. In the proposed game, players decide both the…

Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an…

Recent research demonstrate that prediction of time series by predictive recurrent neural networks based on the noisy input generates a smooth anticipated trajectory. We examine influence of the noise component in both the training data…

We consider a stochastic model for evolution of group-structured populations in which interactions between group members correspond to the Prisoner's Dilemma or the Hawk-Dove game. Selection operates at two organization levels: individuals…

Feed-forward convolutional neural networks (CNNs) are currently state-of-the-art for object classification tasks such as ImageNet. Further, they are quantitatively accurate models of temporally-averaged responses of neurons in the primate…