论文标题
两层神经网络的训练精度：使用随机数据集的估计和理解
The training accuracy of two-layer neural networks: its estimation and understanding using random datasets
论文作者
论文摘要
尽管神经网络（NN）技术在机器学习中起着重要的作用，但了解NN模型的机制和深度学习的透明度仍然需要更多的基础研究。在这项研究中，我们提出了一种基于空间分配的新理论，以估计随机数据集上两层神经网络的近似训练精度，而无需训练。似乎没有其他研究提出了一种方法来估计训练准确性的方法，而无需使用输入数据和/或训练有素的模型。我们的方法仅使用三个参数估算两层随机数据集上两层完全连接的神经网络的训练精度：输入（d）的维度，输入（n）的数量（n）和隐藏层中的神经元数（L）。我们已经在实验中使用实际训练精度验证了我们的方法。结果表明该方法将适用于任何维度，并且所提出的理论也可以扩展以估计更深的NN模型。本文的主要目的是通过估计培训准确性的方法来了解NN模型的机制，而不是分析其概括或在实际应用中的性能。这项研究可能为研究人员在理解深度学习的困难问题上取得进展的新方法提供了一个起点。
Although the neural network (NN) technique plays an important role in machine learning, understanding the mechanism of NN models and the transparency of deep learning still require more basic research. In this study, we propose a novel theory based on space partitioning to estimate the approximate training accuracy for two-layer neural networks on random datasets without training. There appear to be no other studies that have proposed a method to estimate training accuracy without using input data and/or trained models. Our method estimates the training accuracy for two-layer fully-connected neural networks on two-class random datasets using only three arguments: the dimensionality of inputs (d), the number of inputs (N), and the number of neurons in the hidden layer (L). We have verified our method using real training accuracies in our experiments. The results indicate that the method will work for any dimension, and the proposed theory could extend also to estimate deeper NN models. The main purpose of this paper is to understand the mechanism of NN models by the approach of estimating training accuracy but not to analyze their generalization nor their performance in real-world applications. This study may provide a starting point for a new way for researchers to make progress on the difficult problem of understanding deep learning.
