Related papers: Linking Microscopic and Macroscopic Models for Evo…

We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that…

Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under…

The issue of data-driven neural network model construction is one of the core problems in the domain of Artificial Intelligence. A standard approach assumes a fixed architecture with trainable weights. A conceptually more advanced…

Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings…

This work presents a novel means for understanding learning dynamics and scaling relations in neural networks. We show that certain measures on the spectrum of the empirical neural tangent kernel, specifically entropy and trace, yield…

Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…

Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…

We investigate the capacity of transformers to learn algorithms involving their context while solely being trained using next token prediction. We set up Markov chains with random transition matrices and we train transformers to predict the…

Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov…

Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief…

Associative networks theory is increasingly providing tools to interpret update rules of artificial neural networks. At the same time, deriving neural learning rules from a solid theory remains a fundamental challenge. We make some steps in…

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…

The learning dynamics of biological brains and artificial neural networks are of interest to both neuroscience and machine learning. A key difference between them is that neural networks are often trained from a randomly initialized state…

An artificial neural network architecture, parameterization networks, is proposed for simulating extrapolated dynamics beyond observed data in dynamical systems. Parameterization networks are used to ensure the long term integrity of…

Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…

We develop a framework for the compression of reversible Markov chains with rigorous error control. Given a subset of selected states, we construct reduced dynamics that can be lifted to an approximation of the full dynamics, and we prove…

Deep neural networks have emerged as the workhorse for a large section of robotics and control applications, especially as models for dynamical systems. Such data-driven models are in turn used for designing and verifying autonomous…

Machine learning algorithms have been applied to predict agent behaviors in real-world dynamic systems, such as advertiser behaviors in sponsored search and worker behaviors in crowdsourcing. The behavior data in these systems are generated…

We study the evolution of interacting groups of agents in two-dimensional geometries. We introduce a microscopic stochastic model that includes floor fields modeling the global flow of individual groups as well as local interaction rules.…