Related papers: Neural Oscillators are Universal
Fourier neural operators (FNOs) have recently been proposed as an effective framework for learning operators that map between infinite-dimensional spaces. We prove that FNOs are universal, in the sense that they can approximate any…
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as…
We present the Input-Connected Multilayer Perceptron (IC-MLP), a feedforward neural network architecture in which each hidden neuron receives, in addition to the outputs of the preceding layer, a direct affine connection from the raw input.…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…
The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that need not generalize, while the latter considers classes that…
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
Complex networks are ubiquitous to several Computer Science domains. Centrality measures are an important analysis mechanism to uncover vital elements of complex networks. However, these metrics have high computational costs and…
We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude…
Neural approximate computing gains enormous energy-efficiency at the cost of tolerable quality-loss. A neural approximator can map the input data to output while a classifier determines whether the input data are safe to approximate with…
Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish…
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we…
We propose the idea of using Kuramoto models (including their higher-dimensional generalizations) for machine learning over non-Euclidean data sets. These models are systems of matrix ODE's describing collective motions (swarming dynamics)…
Neural algorithmic reasoners are parallel processors. Teaching them sequential algorithms contradicts this nature, rendering a significant share of their computations redundant. Parallel algorithms however may exploit their full…
We propose o1Neuro, a new neural network model built on sparse indicator activation neurons, with two key statistical properties. (1) Constructive universal approximation: At the population level, a deep o1Neuro can approximate any…
Causal machine learning (ML) offers flexible, data-driven methods for predicting treatment outcomes including efficacy and toxicity, thereby supporting the assessment and safety of drugs. A key benefit of causal ML is that it allows for…
We present a novel general model that unifies the kinematics of constant curvature and constant twist continuum manipulators. Combining this kinematics with energy-based physics, we derive a linear mapping from actuator configuration to…
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…
Resistor networks have recently been studied as analog computing platforms for machine learning, particularly due to their compatibility with the Equilibrium Propagation training framework. In this work, we explore the computational…
Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been developed to approximate their solutions. Although these…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…