- Transport in the calculation of reservoirs(arXiv)
Author : G Manjunath, Juan-Pablo Ortega
Summary : Reservoir computer systems are built using a driven dynamic system in which external inputs can alter the evolving states of a system. These paradigms are used in information processing, machine learning and computation. A fundamental question that needs to be addressed in this framework is the statistical relationship between the input and the states of the system. This paper provides conditions that guarantee the existence and uniqueness of asymptotically invariant measures for driven systems and shows that their dependence on the input process is continuous when the set of input and output is endowed with the Wasserstein distance. The main tool of these developments is the characterization of these invariant measures as fixed points of naturally defined Foias operators which appear in this context and which have been extensively studied in the article. These fixed points are obtained by imposing a newly introduced stochastic state contractivity on the trained system which is easily verifiable in examples. Stochastic state contractivity can be satisfied by systems that are not state contractive, which is a need generally discussed to ensure the echo state property in reservoir computation. As a result, it may actually be satisfied even if the echo state property is not present.
2. Calculation of reservoir induced by quantum noise(arXiv)
Author : Tomoyuki Kubota, Yudai Suzuki, Shumpei Kobayashi, Quoc Hoan Tran, Naoki Yamamoto, Kohei Nakajima
Summary : Quantum computing has moved from a theoretical phase to a practical phase, presenting daunting challenges in implementing physical qubits, which are subject to noise from the surrounding environment. These quantum noises are ubiquitous in quantum devices and generate detrimental effects in the quantum computing model, leading to extensive research on their correction and mitigation techniques. But do these quantum noises always have drawbacks? We address this problem by proposing a framework called quantum noise-induced reservoir computation and show that some abstract quantum noise models can induce useful information processing capabilities for temporal input data. We demonstrate this capability in several typical benchmarks and investigate the information processing capability to clarify the framework’s processing mechanism and memory profile. We have verified our view by implementing the framework in a number of IBM quantum processors and obtained similar characteristic memory profiles with model analyses. Surprisingly, the information processing capacity increased with the noise levels and higher error rates of quantum devices. Our study opens a new way to divert useful information from the noises of quantum computers to a more sophisticated information processor.
3.RcTorch: A PyTorch reservoir computation package with automated hyperparameter optimization (arXiv)
Author : Hayden Joy, Marios Mattheakis, Pavlos Protopapas
Summary : Reservoir (RC) computers are among the fastest to train of all neural networks, especially when compared to other recurrent neural networks. RC has this advantage while handling sequential data exceptionally well. However, the adoption of RC has lagged behind other neural network models due to the sensitivity of the model to its hyper-parameters (HP). A modern unified software package that automatically adjusts these parameters is missing from the literature. Manually setting these numbers is very difficult and the cost of traditional grid finding methods increases exponentially with the number of HP considered, discouraging the use of RC and limiting the complexity of RC models that can be designed. We address these issues by introducing RcTorch, a PyTorch-based RC neural network package with automated HP tuning. Here we demonstrate the utility of RcTorch by using it to predict the complex dynamics of a driven pendulum under the action of varying forces. This work includes coding examples. Sample Python Jupyter notebooks can be found on our GitHub repository https://github.com/blindedjoy/RcTorch and documentation can be found at https://rctorch.readthedocs.io/.
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