Log Neural Controlled Differential Equations: The Lie Brackets Make A Difference
Authors: Benjamin Walker, Andrew Donald Mcleod, Tiexin Qin, Yichuan Cheng, Haoliang Li, Terry Lyons
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 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. |
| Researcher Affiliation | Academia | 1Mathematical Institute, University of Oxford, UK 2Department of Electrical Engineering, City University of Hong Kong. |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | 1https://github.com/Benjamin-Walker/ Log-Neural-CDEs |
| Open Datasets | Yes | We construct a toy dataset of 100,000 time series with 6 channels and 100 regularly spaced samples each. |
| Dataset Splits | Yes | Following Morrill et al. (2021), the original train and test cases are combined and resplit into new random train, validation, and test cases using a 70 : 15 : 15 split. |
| Hardware Specification | Yes | In order to compare the models, 1000 steps of training were run on an NVIDIA RTX 4090 with each model using the hyperparameters obtained from the hyperparameter optimisation. |
| Software Dependencies | No | The paper mentions 'Jax s vmap' and 'Adam' but does not provide specific version numbers for these or other software dependencies. |
| Experiment Setup | Yes | On the toy dataset, all models use a hidden state of dimension 64 and Adam with a learning rate of 0.0001 (Kingma & Ba, 2017). Full details on the hyperparameter grid search are in Appendix C.4. |