# Reservoir Computing System

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A Reservoir Computing System is a Recurrent Neural Network System in which the input signal is fed into a reservoir and then mapped by readout mechanism to a desired output.

## References

### 2019a

• (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Reservoir_computing Retrieved:2019-10-27.
• Reservoir computing is a framework for computation that may be viewed as an extension of neural networks. [1] Typically an input signal is fed into a fixed (random) dynamical system called a reservoir and the dynamics of the reservoir map the input to a higher dimension. Then a simple readout mechanism is trained to read the state of the reservoir and map it to the desired output. The main benefit is that training is performed only at the readout stage and the reservoir is fixed. Liquid-state machines [2] and echo state networks [3] are two major types of reservoir computing. [4] One important feature of this system is that it can use the computational power of naturally available systems which is different from the neural networks and it reduces the computational cost.

### 2019d

Figure 1 Reservoir computing system based on diffusive memristor: a) Schematic of an RC system, showing the reservoir with internal dynamics and a readout function. The weight matrix connecting the reservoir state and the output needs to be trained. b) Equivalent schematic of a simplified system where the reservoir is populated with nodes with recurrent connections having a magnitude less than 1 (...)

### 2018a

Figure 1. Illustration of the reservoir computer architecture. Figure credit: Daniel J. Gauthier

### 2018b

Figure 3: (a) Reservoir architecture with input state of the two images at time $t$ denoted by $\vec{u}(t)$, reservoir state at a single time by $\vec{r}(t)$ and output state by $\vec{y}(t)$. (b) shows one image pair from the rotated 90o category of the MNIST dataset split vertically and fed into the reservoir in columns of 1 pixel width, shown to be larger here for ease of visualization.

### 2017b

Figure 1. Reservoir computing system based on a memristor array. a) Schematic of an RC system, showing the reservoir with internal dynamics and a readout function. Only the weight matrix $\theta$ connecting the reservoir state $x(t)$ and the output $y(t)$ needs to be trained. b) Response of a typical WOx memristor to a pulse stream with different time intervals between pulses. Inset: image of the memristor array wired-bonded to a chip carrier and mounted on a test board. c) Schematic of the RC system with pulse streams as the inputs, the memristor reservoir and a readout network. For the simple digit recognition task of 5 × 4 images, the reservoir consists of 5 memristors. d) An example of digit 2 used in the simple digit analysis.

### 2008

1. Schrauwen, Benjamin, David Verstraeten, and Jan Van Campenhout. "An overview of reservoir computing: theory, applications, and implementations." Proceedings of the European Symposium on Artificial Neural Networks ESANN 2007, pp. 471-482.
2. Mass, Wolfgang, T. Nachtschlaeger, and H. Markram. "Real-time computing without stable states: A new framework for neural computation based on perturbations." Neural Computation 14(11): 2531–2560 (2002).
3. Jaeger, Herbert, "The echo state approach to analyzing and training recurrent neural networks." Technical Report 154 (2001), German National Research Center for Information Technology.
4. Echo state network, Scholarpedia
 Author Gouhei Tanaka +, Toshiyuki Yamane +, Jean Benoit HÃ©roux +, Ryosho Nakane +, Naoki Kanazawa +, Seiji Takeda +, Hidetoshi Numata +, Daiju Nakano +, Akira Hirose +, Rivu Midya +, Zhongrui Wang +, Shiva Asapu +, Xumeng Zhang +, Mingyi Rao +, Wenhao Song +, Ye Zhuo +, Navnidhi Upadhyay +, Qiangfei Xia +, J. Joshua Yang +, Sanjukta Krishnagopal +, Yiannis Aloimonos +, Michelle Girvan +, Chao Du +, Fuxi Cai +, Mohammed A. Zidan +, Wen Ma +, Seung Hwan Lee +, Wei D. Lu + and Ali Rodan + year 2019 +, 2018 +, 2017 + and 2012 +