This paper introduces a structured, adaptive-length deep representation called Neural Eigenmap. Unlike prior spectral methods such as Laplacian Eigenmap that operate in a nonparametric manner, Neural Eigenmap leverages NeuralEF to parametrically model eigenfunctions using a neural network. We show that, when the eigenfunction is derived from positive relations in a data augmentation setup, applying NeuralEF results in an objective function that resembles those of popular self-supervised learning methods, with an additional symmetry-breaking property that leads to \emph{structured} representations where features are ordered by importance. We demonstrate using such representations as adaptive-length codes in image retrieval systems. By truncation according to feature importance, our method requires up to $16\times$ shorter representation length than leading self-supervised learning ones to achieve similar retrieval performance. We further apply our method to graph data and report strong results on a node representation learning benchmark with more than one million nodes.

翻译：本文提出了一种名为神经特征映射的结构化自适应长度深度表示方法。与拉普拉斯特征映射等先验谱方法采用非参数化方式不同，神经特征映射利用神经EF（NeuralEF）通过神经网络参数化建模特征函数。我们证明，当特征函数来源于数据增强设置中的正关系时，应用神经EF会导致一个与流行自监督学习方法相似的目标函数，并具备额外的对称破缺特性，从而得到按重要性排序的结构化表示。我们通过将此类表示作为图像检索系统中的自适应长度编码来展示其效用。根据特征重要性进行截断后，我们的方法在达到相似检索性能时，所需表示长度比领先的自监督学习方法短达16倍。我们进一步将该方法应用于图数据，并在包含超过一百万个节点的节点表示学习基准测试中取得了显著成果。