Related papers: Neural Integration of Continuous Dynamics
We propose neural-symbolic integration for abstract concept explanation and interactive learning. Neural-symbolic integration and explanation allow users and domain-experts to learn about the data-driven decision making process of large…
Neural networks have become a widely adopted tool for modeling nonlinear dynamical systems from data. However, the choice of training strategy remains a key design decision, particularly for simulation tasks. This paper compares two…
Capsules are the multidimensional analogue to scalar neurons in neural networks, and because they are multidimensional, much more complex routing schemes can be used to pass information forward through the network than what can be used in…
Neurotechnology has made great strides in the last 20 years. However, we still have a long way to go to commercialize many of these technologies as we lack a unified framework to study cyber-neural systems (CNS) that bring the hardware,…
This paper proposes a class of neural ordinary differential equations parametrized by provably input-to-state stable continuous-time recurrent neural networks. The model dynamics are defined by construction to be input-to-state stable (ISS)…
Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we…
Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…
We investigate the dynamics of a network consisting of an array of identical cortical units with nearest neighbor interactions under periodic arousal. Each unit consists of two interconnected populations of neurons tuned to a state in which…
Differentiable programming is the combination of classical neural networks modules with algorithmic ones in an end-to-end differentiable model. These new models, that use automatic differentiation to calculate gradients, have new learning…
We report a novel approach for the efficient computation of solutions of a broad class of large-scale systems of non-linear ordinary differential equations, describing aggregation kinetics. The method is based on a new take on the…
Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models;…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
To address Quantum Artificial Neural Networks as quantum dynamical computing systems, a formalization of quantum artificial neural networks as dynamical systems is developed, expanding the concept of unitary map to the neural computation…
Regardless of the marked differences between biological and artificial neural systems, one fundamental similarity is that they are essentially dynamical systems that can learn to imitate other dynamical systems, without knowing their…
A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Learning continuous-time dynamics on complex networks is crucial for understanding, predicting and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the…
A key step in many perceptual decision tasks is the integration of sensory inputs over time, but fundamental questions remain about how this is accomplished in neural circuits. One possibility is to balance decay modes of membranes and…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…