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[2602.15649] Continuous-Time Piecewise-Linear Recurrent Neural Networks
Summary
This article presents Continuous-Time Piecewise-Linear Recurrent Neural Networks (cPLRNNs), a novel approach to modeling dynamical systems that improves upon existing discrete-time models by accommodating irregular data intervals and enhancing tractability.
Why It Matters
The development of cPLRNNs addresses significant limitations in current dynamical systems modeling, particularly in scientific and medical fields where understanding underlying processes is crucial. By providing a continuous-time framework, this research enhances the applicability and performance of recurrent neural networks in real-world scenarios.
Key Takeaways
- cPLRNNs offer a continuous-time framework for recurrent neural networks, improving modeling of dynamical systems.
- The new algorithm allows for efficient training and simulation without relying on numerical integration.
- cPLRNNs can identify important topological features like equilibria and limit cycles semi-analytically.
- This approach outperforms both discrete-time PLRNNs and Neural ODEs in dynamical systems reconstruction benchmarks.
- The research is particularly relevant for applications in scientific and medical domains requiring mechanistic insights.
Computer Science > Machine Learning arXiv:2602.15649 (cs) [Submitted on 17 Feb 2026] Title:Continuous-Time Piecewise-Linear Recurrent Neural Networks Authors:Alena Brändle, Lukas Eisenmann, Florian Götz, Daniel Durstewitz View a PDF of the paper titled Continuous-Time Piecewise-Linear Recurrent Neural Networks, by Alena Br\"andle and 3 other authors View PDF HTML (experimental) Abstract:In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series. Specifically, we aim to learn a generative surrogate model which approximates the underlying, data-generating DS, and recreates its long-term properties (`climate statistics'). In scientific and medical areas, in particular, these models need to be mechanistically tractable -- through their mathematical analysis we would like to obtain insight into the recovered system's workings. Piecewise-linear (PL), ReLU-based RNNs (PLRNNs) have a strong track-record in this regard, representing SOTA DSR models while allowing mathematical insight by virtue of their PL design. However, all current PLRNN variants are discrete-time maps. This is in disaccord with the assumed continuous-time nature of most physical and biological processes, and makes it hard to accommodate data arriving at irregular temporal intervals. Neural ODEs are one solution, but they do not reach the DSR performance of PLRNNs and often lack their tractability. Here we develop theory for continuous-time PLRNNs (cPLRNN...
