Related papers: Neural Oscillators are Universal
In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
This paper proposes a specific type of Local Linear Model, the Shuffled Linear Model (SLM), that can be used as a universal approximator. Local operating points are chosen randomly and linear models are used to approximate a function or…
We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition and separation structures, and covers both finite-dimensional…
Despite the fact that generative models are extremely successful in practice, the theory underlying this phenomenon is only starting to catch up with practice. In this work we address the question of the universality of generative models:…
Pattern classification architectures leveraging the physics of coupled nano-oscillators have been demonstrated as promising alternative computing approaches, but lack effective learning algorithms. In this work, we propose a nano-oscillator…
Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving…
The enormous energy demand of artificial intelligence is driving the development of alternative hardware for deep learning. Physical neural networks try to exploit physical systems to perform machine learning more efficiently. In…
Model Predictive Controllers (MPC) are widely used for controlling cyber-physical systems. It is an iterative process of optimizing the prediction of the future states of a robot over a fixed time horizon. MPCs are effective in practice,…
The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task.…
Coupled oscillator-based networks are an attractive approach for implementing hardware neural networks based on emerging nanotechnologies. However, the readout of the state of a coupled oscillator network is a difficult challenge in…
Machine Learning (ML) techniques, such as Neural Network, are widely used in today's applications. However, there is still a big gap between the current ML systems and users' requirements. ML systems focus on improving the performance of…
Neural networks are dynamical systems that compute with their dynamics. One example is the Hopfield model, forming an associative memory which stores patterns as global attractors of the network dynamics. From studies of dynamical networks…
Hysteresis is a ubiquitous phenomenon in science and engineering; its modeling and identification are crucial for understanding and optimizing the behavior of various systems. We develop an ordinary differential equation-based recurrent…
In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…
It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…
Neural networks (NNs) are known for their high predictive accuracy in complex learning problems. Beside practical advantages, NNs also indicate favourable theoretical properties such as universal approximation (UA) theorems. Binarized…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
Different collective behaviors emerging from the unknown have been examined in networks of mobile agents in recent years. Mobile systems, far from being limited to modeling and studying various natural and artificial systems in motion and…
Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous…