Computing optimal discrete readout weights in reservoir computing is NP-hard

Hadaeghi, Fatemeh; Jaeger, Herbert

doi:10.1016/j.neucom.2019.02.009

Cited by 11 publications

(4 citation statements)

References 15 publications

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“…In our setting we, however, might additionally postulate that we work below the overparametrization barrier due to the Boolean entries of W DMD (k), which brings substantial rigidity into play. The price one pays is making the problem harder from a computational optimization viewpoint [26].…”

Section: Resultsmentioning

confidence: 99%

Boolean learning under noise-perturbations in hardware neural networks

et al. 2020

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AbstractA high efficiency hardware integration of neural networks benefits from realizing nonlinearity, network connectivity and learning fully in a physical substrate. Multiple systems have recently implemented some or all of these operations, yet the focus was placed on addressing technological challenges. Fundamental questions regarding learning in hardware neural networks remain largely unexplored. Noise in particular is unavoidable in such architectures, and here we experimentally and theoretically investigate its interaction with a learning algorithm using an opto-electronic recurrent neural network. We find that noise strongly modifies the system’s path during convergence, and surprisingly fully decorrelates the final readout weight matrices. This highlights the importance of understanding architecture, noise and learning algorithm as interacting players, and therefore identifies the need for mathematical tools for noisy, analogue system optimization.

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Section: Resultsmentioning

confidence: 99%

Boolean learning under noise-perturbations in hardware neural networks

et al. 2020

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“…The second type of node is based on a sigmoid function. Sigmoid functions are common in neural network studies [22], although the form of our node is not the same as the most commonly used sigmoid function. The form of the nonlinearities in these two node types is different enough that our results should be general for different types of reservoir computers.…”

Section: S(t)mentioning

confidence: 99%

Network structure effects in reservoir computers

Carroll

Pecora

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition or control of robotic systems. Typically a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network, driving the nodes with an input signal and using the node outputs to fit a training signal. In this work, we set up reservoirs where the edges (or connections) between all the network nodes are either +1 or 0, and proceed to alter the network structure by flipping some of these edges from +1 to -1. We use this simple network because it turns out to be easy to characterize; we may use the fraction of edges flipped as a measure of how much we have altered the network. In some cases, the network can be rearranged in a finite number of ways without changing its structure; these rearrangements are symmetries of the network, and the number of symmetries is also useful for characterizing the network. We find that changing the number of edges flipped in the network changes the rank of the covariance of a matrix consisting of the time series from the different nodes in the network, and speculate that this rank is important for understanding the reservoir computer performance. * Electronic address: thomas.carroll@nrl.navy.mil † Electronic address: louis.pecora@nrl.navy.mil

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“…However, for on-chip learning, the weights will be physically realized by states of electronic synapses, which currently can be reliably set only to a very small number of discrete values. It has been recently proved that computing optimal discrete readout weights in reservoir computing is NP-hard and approximate (or heuristic) methods must be exploited to obtain high-quality solutions in reasonable time for practical uses [30]. The spike-based learning algorithm proposed by [31] is an example of such approximate solutions for FPGA implementations.…”

Section: Rc On Digital Neuromorphic Processorsmentioning

confidence: 99%

Neuromorphic Electronic Systems for Reservoir Computing

Hadaeghi¹

2019

Preprint

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This chapter provides a comprehensive survey of the researches and motivations for hardware implementation of reservoir computing (RC) on neuromorphic electronic systems. Due to its computational efficiency and the fact that training amounts to a simple linear regression, both spiking and non-spiking implementations of reservoir computing on neuromorphic hardware have been developed. Here, a review of these experimental studies is provided to illustrate the progress in this area and to address the technical challenges which arise from this specific hardware implementation. Moreover, to deal with challenges of computation on such unconventional substrates, several lines of potential solutions are presented based on advances in other computational approaches in machine learning.

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Computing optimal discrete readout weights in reservoir computing is NP-hard

Cited by 11 publications

References 15 publications

Boolean learning under noise-perturbations in hardware neural networks

Boolean learning under noise-perturbations in hardware neural networks

Network structure effects in reservoir computers

Neuromorphic Electronic Systems for Reservoir Computing

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