mlsanityData to 7 Oct 2026

Neural Oscillators are Universal

arXiv 2305.08753 ↗First posted 15 May 2023cs.NE cs.LGcited by 16

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Abstract (arXiv)

Coupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation learning and in physical neural networks that are used in analog ML devices. We introduce an abstract class of neural oscillators that encompasses these architectures and prove that neural oscillators are universal, i.e, they can approximate any continuous and casual operator mapping between time-varying functions, to desired accuracy. This universality result provides theoretical justification for the use of oscillator based ML systems. The proof builds on a fundamental result of independent interest, which shows that a combination of forced harmonic oscillators with a nonlinear read-out suffices to approximate the underlying operators.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 19 of its 39 references that are in the map. First posted on arXiv 15 May 2023.

Builds on

19 of 39 references.

References · 19

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  6. 2014Deep Visual-Semantic Alignments for Generating Image Descriptionscited by 966
  7. 2021Offline Reinforcement Learning as One Big Sequence Modeling Problemcited by 636
  8. 2020HiPPO: Recurrent Memory with Optimal Polynomial Projectionscited by 600
  9. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
  10. 2021Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systemscited by 125
  11. 2022Graph-Coupled Oscillator Networkscited by 123
  12. 2022How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projectionscited by 121
7 more
  1. 2018Echo state networks are universalcited by 86
  2. 2020Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependenciescited by 81
  3. 2020On Second Order Behaviour in Augmented Neural ODEscited by 68
  4. 2021UnICORNN: A recurrent model for learning very long time dependenciescited by 56
  5. 2017Vowel recognition with four coupled spin-torque nano-oscillatorscited by 22
  6. 2019Risk bounds for reservoir computingcited by 22
  7. 2021Oscillatory Fourier Neural Network: A Compact and Efficient Architecture for Sequential Processingcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 7; 2025: 5; 2026: 2.

16 papers.

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  1. 2024Operator Learning: Algorithms and Analysiscited by 84
  2. 2024Oscillatory State-Space Modelscited by 35
  3. 2024Mixtures of Neural Operators Reduce Active Complexity in Operator Learningcited by 16
  4. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  5. 2023Neural oscillators for generalization of physics-informed machine learningcited by 9
  6. 2024Input-to-State Stable Coupled Oscillator Networks for Closed-form Model-based Control in Latent Spacecited by 7
  7. 2025Learning to Dissipate Energy in Oscillatory State-Space Modelscited by 7
  8. 2025Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamicscited by 6
  9. 2023Neural oscillators for magnetic hysteresis modelingcited by 1
  10. 2024Systematic construction of continuous-time neural networks for linear dynamical systemscited by 1
  11. 2025Learning Visually Interpretable Oscillator Networks for Soft Continuum Robots from Videocited by 1
  12. 2025Upper Approximation Bounds for Neural Oscillatorscited by 1
4 more
  1. 2026EML Trees Are Universal Approximatorscited by 1
  2. 2024GLAudio Listens to the Sound of the Graphcited by 0
  3. 2025BioOSS: A Bio-Inspired Oscillatory State System with Spatio-Temporal Dynamicscited by 0
  4. 2026Upper Generalization Bounds for Neural Oscillatorscited by 0