mlsanityData to 7 Oct 2026

Lecture notes on rough paths and applications to machine learning

arXiv 2404.06583 ↗First posted 9 Apr 2024cs.LG math.PR math.STcited by 13

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Abstract (arXiv)

These notes expound the recent use of the signature transform and rough path theory in data science and machine learning. We develop the core theory of the signature from first principles and then survey some recent popular applications of this approach, including signature-based kernel methods and neural rough differential equations. The notes are based on a course given by the two authors at Imperial College London.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 12 of its 97 references that are in the map. First posted on arXiv 9 Apr 2024.

Builds on

12 of 97 references.

References · 12

  1. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  2. 2022On Neural Differential Equationscited by 264
  3. 2021Neural SDEs as Infinite-Dimensional GANscited by 159
  4. 2020Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPUcited by 45
  5. 2018The iisignature library: efficient calculation of iterated-integral signatures and log signaturescited by 38
  6. 2020Metrizing Weak Convergence with Maximum Mean Discrepanciescited by 35
  7. 2021Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processescited by 27
  8. 2023Global universal approximation of functional input maps on weighted spacescited by 19
  9. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  10. 2013Sparse arrays of signatures for online character recognitioncited by 17
  11. 2021SK-Tree: a systematic malware detection algorithm on streaming trees via the signature kernelcited by 16
  12. 2023A Neural RDE approach for continuous-time non-Markovian stochastic control problemscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 6; 2026: 2.

13 papers.

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  1. 2025Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Modelscited by 16
  2. 2024Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signalscited by 9
  3. 2024Sparse Signature Coefficient Recovery via Kernelscited by 5
  4. 2024Universal randomised signatures for generative time series modellingcited by 4
  5. 2024SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddingscited by 4
  6. 2025ParallelFlow: Parallelizing Linear Transformers via Flow Discretizationcited by 3
  7. 2024Infinite-dimensional Mahalanobis Distance with Applications to Kernelized Novelty Detectioncited by 1
  8. 2025Local regression on path spaces with signature metricscited by 1
  9. 2025Autonomous-Flow-Based Generationcited by 1
  10. 2026Conservative Continuous-Time Treatment Optimizationcited by 1
  11. 2025Detecting malignant dynamics on very few blood sample using signature coefficientscited by 0
  12. 2025Random Controlled Differential Equationscited by 0
1 more
  1. 2026Time series generation with spectrally aligned latent flow matchingcited by 0