A tensor network approach for chaotic time series prediction

• URL: http://arxiv.org/abs/2505.17740v1
• Date: Fri, 23 May 2025 11:03:35 GMT
• Title: A tensor network approach for chaotic time series prediction
• Authors: Rodrigo Martínez-Peña, Román Orús,
• Abstract summary: This paper explores the application of a previously proposed tensor network model for predicting chaotic time series.<n>It shows its advantages in terms of accuracy and computational efficiency compared to conventional echo state networks.<n>Using a state-of-the-art tensor network approach, we bridge the gap between the tensor network and reservoir computing communities.
• Score: 1.03590082373586
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems without requiring extensive parameter tuning. However, selecting and optimizing reservoir architectures remains an open problem. Next-generation reservoir computing simplifies this problem by employing nonlinear vector autoregression based on truncated Volterra series, thereby reducing hyperparameter complexity. Nevertheless, the latter suffers from exponential parameter growth in terms of the maximum monomial degree. Tensor networks offer a promising solution to this issue by decomposing multidimensional arrays into low-dimensional structures, thus mitigating the curse of dimensionality. This paper explores the application of a previously proposed tensor network model for predicting chaotic time series, demonstrating its advantages in terms of accuracy and computational efficiency compared to conventional echo state networks. Using a state-of-the-art tensor network approach enables us to bridge the gap between the tensor network and reservoir computing communities, fostering advances in both fields.

Related papers

• Dynamics-Informed Reservoir Computing with Visibility Graphs [0.0]
  Reservoir computing offers a computationally efficient alternative to traditional deep learning.<n>Despite its advantages, the largely random reservoir graph architecture often results in suboptimal networks with poorly understood dynamics.<n>We propose a novel Dynamics-Informed Reservoir Computing framework that systematically infers the reservoir network structure directly from the input training sequence.
  arXiv  Detail & Related papers  (2025-07-25T08:07:17Z)
• Optimal Depth of Neural Networks [2.1756081703276]
  This paper introduces a formal theoretical framework to address Determining the optimal depth of a neural network.<n>We model the layer-by-layer evolution of hidden representations as a sequential decision process.<n>We propose a novel and practical regularization term, $mathcalL_rm depth$, that encourages the network to learn representations amenable to efficient, early exiting.
  arXiv  Detail & Related papers  (2025-06-20T09:26:01Z)
• MesaNet: Sequence Modeling by Locally Optimal Test-Time Training [67.45211108321203]
  We introduce a numerically stable, chunkwise parallelizable version of the recently proposed Mesa layer.<n>We show that optimal test-time training enables reaching lower language modeling perplexity and higher downstream benchmark performance than previous RNNs.
  arXiv  Detail & Related papers  (2025-06-05T16:50:23Z)
• Temporal Convolution Derived Multi-Layered Reservoir Computing [5.261277318790788]
  We propose a new mapping of input data into the reservoir's state space. We incorporate this method in two novel network architectures increasing parallelizability, depth and predictive capabilities of the neural network. For the chaotic time series, we observe an error reduction of up to $85.45%$ compared to Echo State Networks and $90.72%$ compared to Gated Recurrent Units.
  arXiv  Detail & Related papers  (2024-07-09T11:40:46Z)
• Optimization Guarantees of Unfolded ISTA and ADMM Networks With Smooth Soft-Thresholding [57.71603937699949]
  We study optimization guarantees, i.e., achieving near-zero training loss with the increase in the number of learning epochs. We show that the threshold on the number of training samples increases with the increase in the network width.
  arXiv  Detail & Related papers  (2023-09-12T13:03:47Z)
• Iterative Soft Shrinkage Learning for Efficient Image Super-Resolution [91.3781512926942]
  Image super-resolution (SR) has witnessed extensive neural network designs from CNN to transformer architectures. This work investigates the potential of network pruning for super-resolution iteration to take advantage of off-the-shelf network designs and reduce the underlying computational overhead. We propose a novel Iterative Soft Shrinkage-Percentage (ISS-P) method by optimizing the sparse structure of a randomly network at each and tweaking unimportant weights with a small amount proportional to the magnitude scale on-the-fly.
  arXiv  Detail & Related papers  (2023-03-16T21:06:13Z)
• Scalable Spatiotemporal Graph Neural Networks [14.415967477487692]
  Graph neural networks (GNNs) are often the core component of the forecasting architecture. In most pretemporal GNNs, the computational complexity scales up to a quadratic factor with the length of the sequence times the number of links in the graph. We propose a scalable architecture that exploits an efficient encoding of both temporal and spatial dynamics.
  arXiv  Detail & Related papers  (2022-09-14T09:47:38Z)
• Deep recurrent networks predicting the gap evolution in adiabatic quantum computing [0.0]
  We explore the potential of deep learning for discovering a mapping from the parameters that fully identify a problem Hamiltonian to the parametric dependence of the gap. We show that a long short-term memory network succeeds in predicting the gap when the parameter space scales linearly with system size. Remarkably, we show that once this architecture is combined with a convolutional neural network to deal with the spatial structure of the model, the gap evolution can even be predicted for system sizes larger than the ones seen by the neural network during training.
  arXiv  Detail & Related papers  (2021-09-17T12:08:57Z)
• DeepSplit: Scalable Verification of Deep Neural Networks via Operator Splitting [70.62923754433461]
  Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non- optimization problem. We propose a novel method that can directly solve a convex relaxation of the problem to high accuracy, by splitting it into smaller subproblems that often have analytical solutions.
  arXiv  Detail & Related papers  (2021-06-16T20:43:49Z)
• Non-Gradient Manifold Neural Network [79.44066256794187]
  Deep neural network (DNN) generally takes thousands of iterations to optimize via gradient descent. We propose a novel manifold neural network based on non-gradient optimization.
  arXiv  Detail & Related papers  (2021-06-15T06:39:13Z)
• Tensor-Train Networks for Learning Predictive Modeling of Multidimensional Data [0.0]
  A promising strategy is based on tensor networks, which have been very successful in physical and chemical applications. We show that the weights of a multidimensional regression model can be learned by means of tensor networks with the aim of performing a powerful compact representation. An algorithm based on alternating least squares has been proposed for approximating the weights in TT-format with a reduction of computational power.
  arXiv  Detail & Related papers  (2021-01-22T16:14:38Z)
• 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)

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.