论文标题
使用拓扑数据分析预测神经网络中的概括差距
Predicting the generalization gap in neural networks using topological data analysis
论文作者
论文摘要
了解神经网络在看不见的数据上如何概括对于设计更健壮和可靠的模型至关重要。在本文中，我们使用拓扑数据分析中的方法研究了神经网络的概括差距。为此，我们计算训练阶段后由神经元激活相关性构成的加权图的同源持久图，旨在捕获与网络的通用能力相关的模式。我们比较了持久图的不同数值摘要的有用性，并表明其中一些可以准确预测并部分解释概括差距而无需测试集。与最新方法进行比较时，对两项计算机视觉识别任务（CIFAR10和SVHN）的评估显示了竞争性的泛化差距预测。
Understanding how neural networks generalize on unseen data is crucial for designing more robust and reliable models. In this paper, we study the generalization gap of neural networks using methods from topological data analysis. For this purpose, we compute homological persistence diagrams of weighted graphs constructed from neuron activation correlations after a training phase, aiming to capture patterns that are linked to the generalization capacity of the network. We compare the usefulness of different numerical summaries from persistence diagrams and show that a combination of some of them can accurately predict and partially explain the generalization gap without the need of a test set. Evaluation on two computer vision recognition tasks (CIFAR10 and SVHN) shows competitive generalization gap prediction when compared against state-of-the-art methods.
