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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2402.18512 |
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| _version_ | 1866909864229339136 |
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| author | Walker, Benjamin McLeod, Andrew D. Qin, Tiexin Cheng, Yichuan Li, Haoliang Lyons, Terry |
| author_facet | Walker, Benjamin McLeod, Andrew D. Qin, Tiexin Cheng, Yichuan Li, Haoliang Lyons, Terry |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log Neural Controlled Differential Equations: The Lie Brackets Make a Difference Walker, Benjamin McLeod, Andrew D. Qin, Tiexin Cheng, Yichuan Li, Haoliang Lyons, Terry Machine Learning 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. |
| title | Log Neural Controlled Differential Equations: The Lie Brackets Make a Difference |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.18512 |