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arXiv 1902.08043cs.LGcond-mat.dis-nn
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二元感知器问题中的主动在线学习

Active online learning in the binary perceptron problem

Institute of Theoretical Physics, Chinese Academy of Sciences(中国科学院理论物理研究所);University of Chinese Academy of Sciences(中国科学院大学)

Hai-Jun Zhou

摘要:

二进制感知器是由$N$输入设备和一个输出单元形成的最简单的人工神经网络,其中神经状态和突触权重都被限制为$\pm 1$值。教师-学生场景中的任务是通过对一组标记模式进行训练来推断隐藏的权重向量。先前对被动学习模式的研究表明,从独立的随机模式中学习是非常低效的。在这里,我们考虑主动的在线学习模式,学生设计每一个新的伊辛训练模式。我们证明,它是数学上可以实现完美的(无错误)推理,只使用$N$设计的训练模式,但这是计算上不可行的大型系统。然后,我们研究了两个贝叶斯统计设计协议,这需要$2.3 N$和$1.9 N$训练模式,分别实现无错推理。如果训练模式是通过演绎推理设计的,则使用$N\!+\!\log_{2}\!N$样本可以实现完美的推理。贝叶斯和演绎设计策略之间的性能差距可能会缩短在未来的工作中,考虑到遍历打破的二进制感知器的版本空间的可能性。

英文摘要:

The binary perceptron is the simplest artificial neural network formed by $N$ input units and one output unit, with the neural states and the synaptic weights all restricted to $\pm 1$ values. The task in the teacher--student scenario is to infer the hidden weight vector by training on a set of labeled patterns. Previous efforts on the passive learning mode have shown that learning from independent random patterns is quite inefficient. Here we consider the active online learning mode in which the student designs every new Ising training pattern. We demonstrate that it is mathematically possible to achieve perfect (error-free) inference using only $N$ designed training patterns, but this is computationally unfeasible for large systems. We then investigate two Bayesian statistical designing protocols, which require $2.3 N$ and $1.9 N$ training patterns, respectively, to achieve error-free inference. If the training patterns are instead designed through deductive reasoning, perfect inference is achieved using $N\!+\!\log_{2}\!N$ samples. The performance gap between Bayesian and deductive designing strategies may be shortened in future work by taking into account the possibility of ergodicity breaking in the version space of the binary perceptron.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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