用混沌系统提升分类准确率，加速训练且效果更优。
Enhancing classification accuracy through chaos
- 将数据升维后作为混沌系统初始条件演化，再输入分类器
- 相比标准softmax，分类准确率提升显著，训练速度加快
- 适用于需要快速高精度分类的场景，如小样本学习
我们提出一种新方法，利用混沌系统提升分类准确性。具体而言，待分类数据被视为向量，先升维至高维空间，再作为混沌动力系统在指定时间区间内的初始条件进行演化。演化后的状态输入可训练的softmax分类器，输出各类别概率。以中等维度（2至20）的随机扰动正交向量为样本，类别数等于向量维度，作为概念验证。结果表明，该方法显著加速训练过程，并优于仅升维但不演化的softmax分类器，也优于直接在原向量上运行的标准softmax分类器。我们还解释了性能提升的原因，并提出选择最优混沌演化时长的策略。
原文摘要 · Abstract (English)
We propose a novel approach which exploits chaos to enhance classification accuracy. Specifically, the available data that need to be classified are treated as vectors that are first lifted into a higher-dimensional space and then used as initial conditions for the evolution of a chaotic dynamical system for a prescribed temporal interval. The evolved state of the dynamical system is then fed to a trainable softmax classifier which outputs the probabilities of the various classes. As proof-of-concept, we use samples of randomly perturbed orthogonal vectors of moderate dimension (2 to 20), with a corresponding number of classes equal to the vector dimension, and show how our approach can both significantly accelerate the training process and improve the classification accuracy compared to a standard softmax classifier which operates on the original vectors, as well as a softmax classifier which only lifts the vectors to a higher-dimensional space without evolving them. We also provide an explanation for the improved performance of the chaos-enhanced classifier and a selection process for the optimal chaotic evolution interval.
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