arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2012.07881cs.LGcs.AI

感知机理论能够预测神经网络的准确率

Perceptron Theory Can Predict the Accuracy of Neural Networks

University of California, Berkeley(加州大学伯克利分校);Research Institutes of Sweden(瑞典研究院);University of Rome “La Sapienza”(罗马第一大学);Intel Labs(英特尔研究院)

Denis Kleyko, Antonello Rosato, E. Paxon Frady, Massimo Panella, Friedrich T. Sommer

AI总结:

本研究提出一种单层感知机统计理论,仅需输出神经元突触后总和分布的前两阶矩,即可预测多种架构神经网络的性能,在三类实验中表现优于同类无估计器训练的方法。

摘要:

多层神经网络在众多技术分类问题中代表了当前的最优水平,但从分析与性能预测的角度来看,这类网络本质上仍属于黑箱。本文提出了一种针对单层感知机的统计理论,并证明它能够预测种类惊人繁多、架构各异的神经网络的性能。我们通过推广一项现有理论,构建了通用的感知机分类理论——该现有理论用于分析储层计算模型,以及被称为向量符号架构的符号推理联结主义模型。我们的统计理论提供了三个利用信号统计特性的公式,其细节程度依次递增。这些公式在解析上难以求解,但可通过数值方式计算。其中细节最丰富的描述层级需要采用随机采样方法,而根据网络模型的不同,较为简单的公式已能实现很高的预测准确率。我们在三种实验场景中评估了该理论预测的质量:储层计算领域中回声状态网络(ESNs)的记忆任务、浅层随机连接网络的一组分类数据集,以及深度卷积神经网络对应的ImageNet数据集。研究发现,感知机理论的第二描述层级能够预测此前无法描述的各类ESN的性能;该理论还可通过应用于深度多层神经网络的输出层,实现对这类网络的性能预测。其他用于神经网络性能预测的方法通常需要训练一个估计器模型,而本文提出的理论仅需输出神经元中突触后总和分布的前两阶矩。与其他不依赖训练估计器模型的方法相比,该感知机理论表现更优。

英文摘要:

Multilayer neural networks set the current state of the art for many technical classification problems. But, these networks are still, essentially, black boxes in terms of analyzing them and predicting their performance. Here, we develop a statistical theory for the one-layer perceptron and show that it can predict performances of a surprisingly large variety of neural networks with different architectures. A general theory of classification with perceptrons is developed by generalizing an existing theory for analyzing reservoir computing models and connectionist models for symbolic reasoning known as vector symbolic architectures. Our statistical theory offers three formulas leveraging the signal statistics with increasing detail. The formulas are analytically intractable, but can be evaluated numerically. The description level that captures maximum details requires stochastic sampling methods. Depending on the network model, the simpler formulas already yield high prediction accuracy. The quality of the theory predictions is assessed in three experimental settings, a memorization task for echo state networks (ESNs) from reservoir computing literature, a collection of classification datasets for shallow randomly connected networks, and the ImageNet dataset for deep convolutional neural networks. We find that the second description level of the perceptron theory can predict the performance of types of ESNs, which could not be described previously. The theory can predict deep multilayer neural networks by being applied to their output layer. While other methods for prediction of neural networks performance commonly require to train an estimator model, the proposed theory requires only the first two moments of the distribution of the postsynaptic sums in the output neurons. The perceptron theory compares favorably to other methods that do not rely on training an estimator model.

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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