A Study of Changes in Prediction Performance
Influenced by Attractor Statein Oscillator Reservoir Computing
Kazuki Yasufuku, Yoko Uwate and Yoshifumi Nishio†Dept. of Electrical and Electronic Engineering, Tokushima University
2-1 Minami-Josanjima, Tokushima, Japan
Email: {yasufuku, uwate, nishio}@ ee.tokushima-u.ac.jp
Abstract— AI technologies have proven their capabilities in solving
complex problems, but they often require significant
computational resources and power. This study proposes areservoir computing (RC) model utilizing Bonhoeffer-van der Pol(BVP) oscillators, leveraging their chaotic dynamics to generatecomplex, high-dimensional internal states. The paper investigates
the impact of the attractor states of these oscillators on theprediction performance of a speech recognition task. Results
indicated that the asymmetric attractors led to lower Word Error
Rates (WER) compared to periodic ones, suggesting that thediversity of circuit responses is beneficial for RC performance.
Keywords; oscillator, reservoir computing, synchronization,chaosI.
INTRODUCTION
In recent years, artificial intelligence technologies such as
deep learning and recurrent neural networks have rapidly
developed and demonstrated their capabilities in various
domains. These techniques excel particularly in their ability toprovide highly accurate solutions to complex problems such asimage recognition, natural language processing, and financial
forecasting. However, these algorithms are challenged by thelarge amount of computational resources required and theassociated increase in power consumption [1]. One approach toovercome this challenge is reservoir computing (RC), a type of
RNN whose internal state is randomly initialized and fixedduring the training process [2]. This allows for fast learning by
optimizing only some parameters, which is expected to reduce
power consumption. We specifically proposed RC with theBonhoeffer-Van der Pol (BVP) oscillator, which we considered
to represent a high-dimensional and complex state space byusing the chaotic dynamics of the BVP to generate internal states,
resulting in high prediction performance [3]. In this study, weinvestigate the attractor states of these chaotic dynamics in RC
with BVP and the accuracy of speech recognition using them.
A. Reservoir configuration
Figure 1 shows a networked reservoir using the proposed
oscillation circuit.

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Figure 1. Configuration of the proposed oscillator reservoir.

The oscillation circuit used a BVP. The circuit equation isshown below.
𝑁𝑑𝐴𝑛
1𝐶= −𝑖𝐿 − 𝑖𝐺 − ∑ (𝑣𝐴𝑛 − 𝑣𝐴𝑘 )
𝑑𝑡
𝑅
𝑘=1

𝑑𝐵𝑛
1(1)
𝐶= 𝑖𝐿 − 𝑣𝐵
𝑑𝑡
𝑅𝑑𝑖 𝐿𝑛𝐶= 𝑣𝐴 − 𝑣𝐵{
𝑑𝑡
The normalized circuit equations are described as follows.
𝑁𝑑𝑥𝑛= 𝜀𝑥𝑛 (1 − 𝑥𝑛 2 ) − 𝑧𝑛 + ∑ 𝐾(𝑥𝑘 − 𝑥𝑛 )𝑑𝜏
𝑘=1{𝑑𝑦𝑛= 𝑧𝑛 − 𝜎𝑑𝜏𝑑𝑧𝑛= 𝑧𝑛 − 𝑦𝑛𝑑𝜏(2)B. Simulation Methods
This study evaluated speech recognition using oscillator
reservoirs. A total of 500 data samples consisting of recordingsof five different speakers pronouncing each of the numbers 0
through 9, repeated 10 times, were used for the input data set.
The input data used in this study was based on an application of
Lyon's auditory model. After removing the silent parts, thespeech signal is converted to a cochlear-type speech signal. Thistransformation yields time series data with dimensionscorresponding to different frequency channels. In this study, thecochleagram data is characterized by 77 dimensions that reflect
the spectral characteristics of the speech signal. Half of thedataset, containing five pronunciations of each number spoken
by five speakers, was allocated for training and the remaining
data for testing [4]. The initial transient response of 10,000τ was259

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ignored. The simulation was performed using the Runge-Kutta
method. Signals were input by varying the coupling strength
between the input node and the reservoir layer over time. Thevoltage difference between each oscillator and the reference
oscillator was used as the output, which was trained by linear
learning. The Word Error Rate (WER) was used to evaluate theaccuracy of speech recognition.
II.

SIMULATION RESULTS

In this section, we check the accuracy of speech recognition
and the oscillator's attractor at that time. The results werechecked when the coupling probability P was varied and when
the coupling strength K was varied, respectively.
A. When the connection probability P is varied
When P is varied, the error in speech recognition varies asshown in Figs. 2 and 3. The attractors of the oscillators at thistime are shown below, with the attractor of one circuit out of 100
placed as representative.

Figure 2. WER when P is varied.

Figure 3. Attractor when P is varied.

Figure 5. Attractor when K is varied.

Figures 2, 3 and 4, 5 show that WER is lower when theattractor is asymmetric rather than periodic. This is thought tobe a good physical property for reservoirs as the response of thecircuit is more diverse.

III. CONCLUSION
This study proposed and evaluated the use of a reservoir
computing (RC) model based on Bonhoeffer-van der Pol (BVP)
oscillators for speech recognition tasks. The study utilized theinherent chaotic dynamics of BVP oscillators to generatecomplex, high-dimensional internal states within the reservoir,
aiming to improve prediction performance. The results indicatedthat the oscillators' attractor states significantly influence thespeech recognition accuracy. Specifically, it was found thatasymmetric attractors resulted in lower Word Error Rates(WER) as compared to periodic ones. This outcome suggeststhat asymmetric attractors lead to greater diversity in the circuit
response, enhancing the RC's performance in processing andpredicting complex, non-linear data such as speech signals. This
research offers promising insights into the design of more
efficient and powerful RC models. Investigating other types ofoscillators and their attractor states might also be beneficial.
Additionally, the impacts of varying other parameters could beexamined more closely. This could lead to a more nuanced
understanding of the dynamics of RCs, potentially informing thedesign of more effective and energy-efficient RC models forcomplex tasks like speech recognition and beyond.

B. When the connection strength K is varied
The attractors of the oscillator as K is varied are shown inFigs. 4 and 5, one attractor out of 100 circuits is placed as arepresentative.

REFERENCES
[1]

[2]

[3]

[4]
Figure 4. WER when K is varied.

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