mlsanityData to 7 Oct 2026

Log Neural Controlled Differential Equations: The Lie Brackets Make a Difference

arXiv 2402.18512 ↗First posted 28 Feb 2024cs.LGcited by 34

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Abstract (arXiv)

The vector field of a controlled differential equation (CDE) describes the relationship between a control path and the evolution of a solution path. Neural CDEs (NCDEs) treat time series data as observations from a control path, parameterise a CDE's vector field using a neural network, and use the solution path as a continuously evolving hidden state. As their formulation makes them robust to irregular sampling rates, NCDEs are a powerful approach for modelling real-world data. Building on neural rough differential equations (NRDEs), we introduce Log-NCDEs, a novel, effective, and efficient method for training NCDEs. The core component of Log-NCDEs is the Log-ODE method, a tool from the study of rough paths for approximating a CDE's solution. Log-NCDEs are shown to outperform NCDEs, NRDEs, the linear recurrent unit, S5, and MAMBA on a range of multivariate time series datasets with up to 50,000 observations.

Key facts. Cited by 34 papers in the map (data through 7 Oct 2026). Builds on 10 of its 33 references that are in the map. First posted on arXiv 28 Feb 2024.

Builds on

10 of 33 references.

References · 10

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  3. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
  4. 2022Simplified State Space Layers for Sequence Modelingcited by 776
  5. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  6. 2023Resurrecting Recurrent Neural Networks for Long Sequencescited by 397
  7. 2022On Neural Differential Equationscited by 264
  8. 2017Spectral Norm Regularization for Improving the Generalizability of Deep Learningcited by 178
  9. 2020Neural Rough Differential Equations for Long Time Seriescited by 140
  10. 2016A Primer on the Signature Method in Machine Learningcited by 100

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 12; 2026: 19.

34 papers.

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  1. 2024Theoretical Foundations of Deep Selective State-Space Modelscited by 73
  2. 2024Oscillatory State-Space Modelscited by 35
  3. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  4. 2024Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patchingcited by 16
  5. 2025Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Modelscited by 16
  6. 2025Structured Sparse Transition Matrices to Enable State Tracking in State-Space Modelscited by 15
  7. 2025Parallelization of Non-linear State-Space Models: Scaling Up Liquid-Resistance Liquid-Capacitance Networks for Efficient Sequence Modelingcited by 10
  8. 2025Learning to Dissipate Energy in Oscillatory State-Space Modelscited by 7
  9. 2025Learning long range dependencies through time reversal symmetry breakingcited by 6
  10. 2025Weight-Space Linear Recurrent Neural Networkscited by 5
  11. 2025Random Feature Representation Boostingcited by 4
  12. 2026Strong Stochastic Flow Mapscited by 4
22 more
  1. 2025Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learningcited by 3
  2. 2026Data-Driven Open-Loop Simulation for Digital-Twin Operator Decision Support in Wastewater Treatmentcited by 2
  3. 2025Autonomous-Flow-Based Generationcited by 1
  4. 2026Efficient Neural Controlled Differential Equations via Attentive Kernel Smoothingcited by 1
  5. 2026Why Depth Matters in Parallelizable Sequence Models: A Lie Algebraic Viewcited by 1
  6. 2025BioOSS: A Bio-Inspired Oscillatory State System with Spatio-Temporal Dynamicscited by 0
  7. 2025ASecond-Order SpikingSSM for Wearablescited by 0
  8. 2026Rotation-free Online Handwritten Character Recognition Using Linear Recurrent Unitscited by 0
  9. 2026U-Former ODE: Fast Probabilistic Forecasting of Irregular Time Seriescited by 0
  10. 2026From Path Signatures to Sequential Modeling: Incremental Signature Contributions for Offline RLcited by 0
  11. 2026Extending SSMs with the Exponentially Weighted Signaturecited by 0
  12. 2026Scalable Memristive-Friendly Reservoir Computing for Time Series Classificationcited by 0
  13. 2026TIDES: Implicit Time-Awareness in Selective State Space Modelscited by 0
  14. 2026Reshape and Recur: Improving SSMs with Input Reshaping and Depth Recurrencecited by 0
  15. 2026Flash PD-SSM: Memory-Optimized Structured Sparse State-Space Modelscited by 0
  16. 2026Faithful Embeddings of Irregular and Asynchronous Data for Online Log-NCDEscited by 0
  17. 2026Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solverscited by 0
  18. 2026Learning Manifold and Ito Dynamics with Branched Neural Rough Differential Equationscited by 0
  19. 2026INDEQS: Informed Neural controlled Differential EQuationScited by 0
  20. 2026Liquid Gated Attentioncited by 0
  21. 2026Riccati State Space Models: Non-iterative Parallelization for Nonlinear Sequence Modelingcited by 0
  22. 2026CAMOS: Coupled Oscillatory State-Space Model for Multimodal Clinical Time-Seriescited by 0

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  1. 2025Symbolic Neural Ordinary Differential Equations
  2. 2026Diff-MN: Diffusion Parameterized MoE-NCDE for Continuous Time Series Generation with Irregular Observations
  3. 2026LogSig-SSM: Time-Series Modelling with Multi-Scale Log-Signature Compression for State-Space Models
  4. 2024DeNOTS: Stable Deep Neural ODEs for Time Series
  5. 2024Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems
  6. 2022Neural Ordinary Differential Equations for Nonlinear System Identification
  7. 2025Neuro-Symbolic AI for Analytical Solutions of Differential Equations
  8. 2025Hierarchical Stochastic Differential Equation Models for Latent Manifold Learning in Neural Time Series