Unfolding recurrence by Green's functions for optimized reservoir computing

• URL: http://arxiv.org/abs/2010.06247v2
• Date: Wed, 14 Oct 2020 07:08:39 GMT
• Title: Unfolding recurrence by Green's functions for optimized reservoir computing
• Authors: Sandra Nestler, Christian Keup, David Dahmen, Matthieu Gilson, Holger Rauhut and Moritz Helias
• Abstract summary: Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. We present a solvable recurrent network model that links to feed forward networks.
• Score: 3.7823923040445995
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the application of feed-forward networks and their theoretical understanding, it remains unclear how the interplay of recurrence and non-linearities in recurrent cortical networks contributes to their function. The purpose of this work is to present a solvable recurrent network model that links to feed forward networks. By perturbative methods we transform the time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels. The resulting analytical expressions allow us to build optimal time-series classifiers from random reservoir networks. Firstly, this allows us to optimize not only the readout vectors, but also the input projection, demonstrating a strong potential performance gain. Secondly, the analysis exposes how the second order stimulus statistics is a crucial element that interacts with the non-linearity of the dynamics and boosts performance.

Related papers

• ANCRe: Adaptive Neural Connection Reassignment for Efficient Depth Scaling [57.91760520589592]
  Scaling network depth has been a central driver behind the success of modern foundation models.<n>This paper revisits the default mechanism for deepening neural networks, namely residual connections.<n>We introduce adaptive neural connection reassignment (ANCRe), a principled and lightweight framework that parameterizes and learns residual connectivities from the data.
  arXiv  Detail & Related papers  (2026-02-09T18:54:18Z)
• Causal Convolutional Neural Networks as Finite Impulse Response Filters [3.268966882982408]
  Causal Convolutional Neural Networks (CNNs) capture spectral features implicitly and explicitly, offering enhanced interpretability for tasks involving dynamic systems.<n>We show that the entire network can be reduced to an equivalent single-layer filter resembling an FIR filter optimized via least-squares criteria.<n>This equivalence yields new insights into the spectral learning behavior of CNNs trained on signals with sparse frequency content.
  arXiv  Detail & Related papers  (2025-10-28T06:57:14Z)
• A tensor network approach for chaotic time series prediction [1.03590082373586]
  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.
  arXiv  Detail & Related papers  (2025-05-23T11:03:35Z)
• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs) We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations. 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)
• Fast Training of Recurrent Neural Networks with Stationary State Feedbacks [48.22082789438538]
  Recurrent neural networks (RNNs) have recently demonstrated strong performance and faster inference than Transformers. We propose a novel method that replaces BPTT with a fixed gradient feedback mechanism.
  arXiv  Detail & Related papers  (2025-03-29T14:45:52Z)
• Gradient-free training of recurrent neural networks [3.272216546040443]
  We introduce a computational approach to construct all weights and biases of a recurrent neural network without using gradient-based methods. The approach is based on a combination of random feature networks and Koopman operator theory for dynamical systems. In computational experiments on time series, forecasting for chaotic dynamical systems, and control problems, we observe that the training time and forecasting accuracy of the recurrent neural networks we construct are improved.
  arXiv  Detail & Related papers  (2024-10-30T21:24:34Z)
• Advancing Spatio-Temporal Processing in Spiking Neural Networks through Adaptation [6.233189707488025]
  In this article, we analyze the dynamical, computational, and learning properties of adaptive LIF neurons and networks thereof. We show that the superiority of networks of adaptive LIF neurons extends to the prediction and generation of complex time series.
  arXiv  Detail & Related papers  (2024-08-14T12:49:58Z)
• Learning Delays Through Gradients and Structure: Emergence of Spatiotemporal Patterns in Spiking Neural Networks [0.06752396542927405]
  We present a Spiking Neural Network (SNN) model that incorporates learnable synaptic delays through two approaches. In the latter approach, the network selects and prunes connections, optimizing the delays in sparse connectivity settings. Our results demonstrate the potential of combining delay learning with dynamic pruning to develop efficient SNN models for temporal data processing.
  arXiv  Detail & Related papers  (2024-07-07T11:55:48Z)
• Coding schemes in neural networks learning classification tasks [52.22978725954347]
  We investigate fully-connected, wide neural networks learning classification tasks. We show that the networks acquire strong, data-dependent features. Surprisingly, the nature of the internal representations depends crucially on the neuronal nonlinearity.
  arXiv  Detail & Related papers  (2024-06-24T14:50:05Z)
• Leveraging Low-Rank and Sparse Recurrent Connectivity for Robust Closed-Loop Control [63.310780486820796]
  We show how a parameterization of recurrent connectivity influences robustness in closed-loop settings. We find that closed-form continuous-time neural networks (CfCs) with fewer parameters can outperform their full-rank, fully-connected counterparts.
  arXiv  Detail & Related papers  (2023-10-05T21:44:18Z)
• 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)
• Implicit recurrent networks: A novel approach to stationary input processing with recurrent neural networks in deep learning [0.0]
  In this work, we introduce and test a novel implementation of recurrent neural networks into deep learning. We provide an algorithm which implements the backpropagation algorithm on a implicit implementation of recurrent networks. A single-layer implicit recurrent network is able to solve the XOR problem, while a feed-forward network with monotonically increasing activation function fails at this task.
  arXiv  Detail & Related papers  (2020-10-20T18:55:32Z)
• Continuous-in-Depth Neural Networks [107.47887213490134]
  We first show that ResNets fail to be meaningful dynamical in this richer sense. We then demonstrate that neural network models can learn to represent continuous dynamical systems. We introduce ContinuousNet as a continuous-in-depth generalization of ResNet architectures.
  arXiv  Detail & Related papers  (2020-08-05T22:54:09Z)
• Lipschitz Recurrent Neural Networks [100.72827570987992]
  We show that our Lipschitz recurrent unit is more robust with respect to input and parameter perturbations as compared to other continuous-time RNNs. Our experiments demonstrate that the Lipschitz RNN can outperform existing recurrent units on a range of benchmark tasks.
  arXiv  Detail & Related papers  (2020-06-22T08:44:52Z)
• 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)
• Link Prediction for Temporally Consistent Networks [6.981204218036187]
  Link prediction estimates the next relationship in dynamic networks. The use of adjacency matrix to represent dynamically evolving networks limits the ability to analytically learn from heterogeneous, sparse, or forming networks. We propose a new method of canonically representing heterogeneous time-evolving activities as a temporally parameterized network model.
  arXiv  Detail & Related papers  (2020-06-06T07:28:03Z)
• Input-to-State Representation in linear reservoirs dynamics [15.491286626948881]
  Reservoir computing is a popular approach to design recurrent neural networks. The working principle of these networks is not fully understood. A novel analysis of the dynamics of such networks is proposed.
  arXiv  Detail & Related papers  (2020-03-24T00:14:25Z)

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.