HLRPF驱动的混沌神经网络：模式分类新策略

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本文主要探讨了在混沌神经网络（Chaos Neural Networks, CNN）的背景下，如何通过引入被动遗忘（Passive Forgetting, HLRPF）的学习规则来提升模式分类性能。Hebbian学习规则是一种基于神经元活动同步性增强连接强度的自组织学习策略，而被动遗忘则是对这一过程的一种补充，它在一定程度上控制了神经元之间的不必要或过时联系的削弱，有助于提高网络的泛化能力和效率。作者们首先提出了一种结合Hebbian学习规则和被动遗忘机制的新型学习算法，这种方法旨在优化CNN在处理模糊模式分类任务时的表现。传统的Hebbian学习可能由于过度学习或噪音干扰导致网络过拟合，而HLRPF则提供了一个动态调整连接权重的有效途径，使得网络能够更好地适应不断变化的数据分布。在设计过程中，他们采用了欧几里得距离作为评估权重演变的标准，这种距离度量方法可以直观地反映网络内部结构的变化，帮助分析和理解网络学习过程中的模式识别过程。通过数值模拟，研究者展示了在适当外部刺激下，CNN应用了HLRPF学习规则后，其模式分类能力显著优于常规的CNN模型，这表明了学习规则和模式识别之间的相互作用，以及被动遗忘在优化网络性能方面的重要作用。此外，这项工作还揭示了在混沌系统中，学习规则的设计不仅影响网络的计算能力，还与系统的动态稳定性密切相关。通过在复杂且非线性的混沌环境中实现有效的模式分类，这项研究为进一步探索混沌神经网络在实际问题中的应用提供了新的理论支持，如信号处理、图像识别和时间序列预测等领域。这篇论文对混沌神经网络的学习机制进行了深入研究，特别是在模式分类任务中的学习策略创新，为改进神经网络模型的性能和理解学习与认知过程之间的关系提供了重要的科学依据。

Author's personal copy

Physics Letters A 376 (2012) 412–417

Contents lists available at SciVerse ScienceDirect

Physics Letters A

www.elsevier.com/locate/pla

Learning-induced pattern classiﬁcation in a chaotic neural network

Yang Li

a,b

,PingZhu

, Xiaoping Xie

, Guoguang He

a,∗

, Kazuyuki Aihara

Department of Physics, Faculty of Science, Zhejiang University, Hangzhou 310027, PR China

Key Laboratory of Infrared Imaging Materials and Detectors, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083,PRChina

Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan

article info abstract

Article history:

Received 1 April 2011

Received in revised form 21 September

2011

Accepted 25 October 2011

Availableonline23November2011

Communicated by A.R. Bishop

Keywords:

Pattern classiﬁcation

Learning rule

Passive forgetting

Chaotic neural networks

In this Letter, we propose a Hebbian learning rule with passive forgetting (HLRPF) for use in a chaotic

neural network (CNN). We then deﬁne the indices based on the Euclidean distance to investigate the

evolution of the weights in a simpliﬁed way. Numerical simulations demonstrate that, under suitable

external stimulations, the CNN with the proposed HLRPF acts as a fuzzy-like pattern classiﬁer that

performs much better than an ordinary CNN. The results imply relationship between learning and

recognition.

1. Introduction

In the past three decades, different artiﬁcial neural network

models have been proposed and investigated because of their po-

tential application to ﬂexible intelligent information processing

[1–3]. Along with the discovery of chaotic behavior in biological

systems, artiﬁcial neural network models that exhibit chaotic dy-

namics have been drawing increasing attention [4–7].Onesuch

chaotic neural network (CNN) model was proposed [4] on the ba-

sis of electrophysiological experiments on squid giant axons [8,9].

Both the network and its single constituent neuron take on chaotic

dynamics when suitable values of the parameters are chosen [4,

10]. Further, intensive studies demonstrated that the CNN model is

a promising approach to tasks such as memory retrieval, pattern

recognition, combinational optimization, and multistable percep-

tion, and so on [10–17].

In application to associative memory, the synaptic weights be-

tween individual neurons in an ordinary CNN are usually deter-

mined by a symmetric auto-associative matrix [10].Severalbasal

patterns are embedded in the constant synaptic weights, and the

output of the CNN wanders chaotically among all these stored pat-

terns. Furthermore, the widely known phenomena of synaptic plas-

ticity provide powerful models to studies on CNNs with changeable

synapses [18–20]. Generally speaking, these studies fall into two

categories. One analyzes successive learning strategies that enable

Corresponding author.

E-mail address: gghe@zju.edu.cn (G. He).

a CNN to gain new memories, whereas the other considers the

mechanism of dynamic synapses with no memory update but im-

provement in the network’s information processing ability. For ex-

ample, Watanabe et al. [18] proposed a fully local algorithm by

which the CNN can detect and learn an unknown pattern auto-

matically; Wang et al. [20] incorporated synaptic depression into

the original CNN and found that the reﬁned model becomes a pe-

culiar pattern recognition system. However, the learning-induced

function of pattern recognition or classiﬁcation in a CNN has not

been widely reported.

The main aim of this Letter is to reveal the fact that learning in

a CNN can enhance its pattern classiﬁcation ability. We proposed

a variant Hebbian learning rule with passive forgetting for weights

updating, and deﬁned indices for the weight projection to inves-

tigate the weights evolution. Thereafter, we carried out numerical

simulations to investigate the retrieval properties of the proposed

model. In Section 2, the CNN model and its associative memory

are brieﬂy discussed. The proposed learning rule and observation

method are presented in Section 3, followed by the simulation

results in Section 4. The conclusion and discussion are given in

Section 5.

2. The chaotic neural network model

A chaotic neuron model was derived with a continuous out-

put function and relative refractoriness to model responses of a

biological neuron. Using this kind of chaotic neuron, a CNN is con-

structed by considering the spatiotemporal summation of both the

external inputs and the feedback inputs [4]. The structure of the

doi:10.1016/j.physleta.2011.10.062

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