Neural Eigenfunctions Are Structured Representation Learners
This work addresses the need for efficient and structured representations in machine learning, particularly for image retrieval and graph data, though it builds incrementally on prior spectral and self-supervised methods.
The paper tackles the problem of learning structured, adaptive-length representations by introducing Neural Eigenmap, which parametrically models eigenfunctions using a neural network. The result is a method that requires up to 16× shorter representation lengths than leading self-supervised learning approaches to achieve similar retrieval performance, with strong results on large-scale graph benchmarks.
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.