{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/neural-controlled-differential-equations-for-1","title":"Neural Controlled Differential Equations for Online Prediction Tasks","arxiv_id":"2106.11028","date":"2021-06-21","proceeding":null,"authors":["James Morrill","Patrick Kidger","Lingyi Yang","Terry Lyons"],"abstract":"Neural controlled differential equations (Neural CDEs) are a continuous-time extension of recurrent neural networks (RNNs), achieving state-of-the-art (SOTA) performance at modelling functions of irregular time series. In order to interpret discrete data in continuous time, current implementations rely on non-causal interpolations of the data. This is fine when the whole time series is observed in advance, but means that Neural CDEs are not suitable for use in \\textit{online prediction tasks}, where predictions need to be made in real-time: a major use case for recurrent networks. Here, we show how this limitation may be rectified. First, we identify several theoretical conditions that interpolation schemes for Neural CDEs should satisfy, such as boundedness and uniqueness. Second, we use these to motivate the introduction of new schemes that address these conditions, offering in particular measurability (for online prediction), and smoothness (for speed). Third, we empirically benchmark our online Neural CDE model on three continuous monitoring tasks from the MIMIC-IV medical database: we demonstrate improved performance on all tasks against ODE benchmarks, and on two of the three tasks against SOTA non-ODE benchmarks.","url_abs":"https://arxiv.org/abs/2106.11028v1","url_pdf":"https://arxiv.org/pdf/2106.11028v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"neural-controlled-differential-equations-for-1","repo_url":"https://github.com/jambo6/online-neural-cdes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"neural-controlled-differential-equations-for-1","repo_url":"https://github.com/patrick-kidger/torchcde","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"irregular-time-series","task_name":"Irregular Time Series"},{"task_slug":"prediction","task_name":"Prediction"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2106.11028","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2106.11028"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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