Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are trained on, or biologically adapted to, similar tasks. A standardized set of analysis tools is now needed to identify how network-level covariates -- such as architecture, anatomical brain region, and model organism -- impact neural representations (hidden layer activations). Here, we provide a rigorous foundation for these analyses by defining a broad family of metric spaces that quantify representational dissimilarity. Using this framework we modify existing representational similarity measures based on canonical correlation analysis to satisfy the triangle inequality, formulate a novel metric that respects the inductive biases in convolutional layers, and identify approximate Euclidean embeddings that enable network representations to be incorporated into essentially any off-the-shelf machine learning method. We demonstrate these methods on large-scale datasets from biology (Allen Institute Brain Observatory) and deep learning (NAS-Bench-101). In doing so, we identify relationships between neural representations that are interpretable in terms of anatomical features and model performance.

为了理解生物和人工神经网络的操作，研究者们需要一个标准化的工具集来量化其结构等因素对神经表征的影响，这篇论文提出了一族量化表征不同神经网络之间相似性的度量空间，利用这个框架使得神经网络表征可以整合进任意的机器学习方法中，然后利用大规模生物和深度学习数据集来验证这些方法，最终找出了神经表征之间与结构和性能之间的关系。

神经表征的广义形状度量