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.

翻译：尽管神经网络技术在机器学习中扮演着重要角色，但理解神经网络模型的机制以及深度学习的透明性仍需更多基础研究。本研究提出了一种基于空间划分的新理论，用于在不进行训练的情况下估计双层神经网络在随机数据集上的近似训练精度。目前尚无其他研究提出无需使用输入数据和/或训练模型即可估计训练精度的方法。该方法仅需三个参数：输入维度（d）、输入数量（N）和隐藏层神经元数量（L），即可估计双层全连接神经网络在二分类随机数据集上的训练精度。我们通过实验中的实际训练精度验证了该方法，结果表明该方法适用于任意维度，且所提理论可进一步扩展以估计更深层神经网络模型。本文的主要目的是通过估计训练精度的途径理解神经网络模型机制，而非分析其泛化能力或在实际应用中的性能。该研究可能为研究人员在理解深度学习这一难题上提供新的起点。