Continuous-Time Piecewise-Linear Recurrent Neural Networks

• URL: http://arxiv.org/abs/2602.15649v1
• Date: Tue, 17 Feb 2026 15:16:12 GMT
• Title: Continuous-Time Piecewise-Linear Recurrent Neural Networks
• Authors: Alena Brändle, Lukas Eisenmann, Florian Götz, Daniel Durstewitz,
• Abstract summary: We aim to learn a generative surrogate model which approximates the underlying, data-generating DS.<n>In scientific and medical areas, these models need to be mechanistically tractable.
• Score: 10.4029480932728
• License: http://creativecommons.org/licenses/by/4.0/
• 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 (cPLRNNs): We present a novel algorithm for training and simulating such models, bypassing numerical integration by efficiently exploiting their PL structure. We further demonstrate how important topological objects like equilibria or limit cycles can be determined semi-analytically in trained models. We compare cPLRNNs to both their discrete-time cousins as well as Neural ODEs on DSR benchmarks, including systems with discontinuities which come with hard thresholds.

Related papers

• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs)<n>We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations.<n> Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process.
  arXiv  Detail & Related papers  (2025-04-16T10:39:43Z)
• Contextualizing MLP-Mixers Spatiotemporally for Urban Data Forecast at Scale [54.15522908057831]
  We propose an adapted version of the computationally-Mixer for STTD forecast at scale. Our results surprisingly show that this simple-yeteffective solution can rival SOTA baselines when tested on several traffic benchmarks. Our findings contribute to the exploration of simple-yet-effective models for real-world STTD forecasting.
  arXiv  Detail & Related papers  (2023-07-04T05:19:19Z)
• On the Dynamics of Learning Time-Aware Behavior with Recurrent Neural Networks [2.294014185517203]
  We introduce a family of supervised learning tasks dependent on hidden temporal variables. We train RNNs to emulate temporal flipflops that emphasize the need for time-awareness over long-term memory. We show that these RNNs learn to switch between periodic orbits that encode time modulo the period of the transition rules.
  arXiv  Detail & Related papers  (2023-06-12T14:01:30Z)
• How neural networks learn to classify chaotic time series [77.34726150561087]
  We study the inner workings of neural networks trained to classify regular-versus-chaotic time series. We find that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models.
  arXiv  Detail & Related papers  (2023-06-04T08:53:27Z)
• Brain-Inspired Spiking Neural Network for Online Unsupervised Time Series Prediction [13.521272923545409]
  We present a novel Continuous Learning-based Unsupervised Recurrent Spiking Neural Network Model (CLURSNN) CLURSNN makes online predictions by reconstructing the underlying dynamical system using Random Delay Embedding. We show that the proposed online time series prediction methodology outperforms state-of-the-art DNN models when predicting an evolving Lorenz63 dynamical system.
  arXiv  Detail & Related papers  (2023-04-10T16:18:37Z)
• Online Evolutionary Neural Architecture Search for Multivariate Non-Stationary Time Series Forecasting [72.89994745876086]
  This work presents the Online Neuro-Evolution-based Neural Architecture Search (ONE-NAS) algorithm. ONE-NAS is a novel neural architecture search method capable of automatically designing and dynamically training recurrent neural networks (RNNs) for online forecasting tasks. Results demonstrate that ONE-NAS outperforms traditional statistical time series forecasting methods.
  arXiv  Detail & Related papers  (2023-02-20T22:25:47Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Effects of VLSI Circuit Constraints on Temporal-Coding Multilayer Spiking Neural Networks [2.5234156040689237]
  spiking neural network (SNN) has been attracting considerable attention not only as a mathematical model for the brain, but also as an energy-efficient information processing model for real-world applications. In this study, we investigated the effects of the time discretization and/or weight quantization on the performance of SNNs.
  arXiv  Detail & Related papers  (2021-06-18T22:51:58Z)
• CARRNN: A Continuous Autoregressive Recurrent Neural Network for Deep Representation Learning from Sporadic Temporal Data [1.8352113484137622]
  In this paper, a novel deep learning-based model is developed for modeling multiple temporal features in sporadic data. The proposed model, called CARRNN, uses a generalized discrete-time autoregressive model that is trainable end-to-end using neural networks modulated by time lags. It is applied to multivariate time-series regression tasks using data provided for Alzheimer's disease progression modeling and intensive care unit (ICU) mortality rate prediction.
  arXiv  Detail & Related papers  (2021-04-08T12:43:44Z)
• Neural ODE Processes [64.10282200111983]
  We introduce Neural ODE Processes (NDPs), a new class of processes determined by a distribution over Neural ODEs. We show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points.
  arXiv  Detail & Related papers  (2021-03-23T09:32:06Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)
• Industrial Forecasting with Exponentially Smoothed Recurrent Neural Networks [0.0]
  We present a class of exponential smoothed recurrent neural networks (RNNs) which are well suited to modeling non-stationary dynamical systems arising in industrial applications. Application of exponentially smoothed RNNs to forecasting electricity load, weather data, and stock prices highlight the efficacy of exponential smoothing of the hidden state for multi-step time series forecasting.
  arXiv  Detail & Related papers  (2020-04-09T17:53:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.