LASE - Learned Adjacency Spectral Embeddings - 图神经网络中基于算法展开的设计与应用

Aug 5, 2026

LASE提出一种基于图输入的神经架构，用于学习节点的邻接谱嵌入（Adjacency Spectral Embeddings, ASE）。该方法结合梯度下降与算法展开，将每次梯度迭代截断并重解释为图神经网络（GNN）中的层，从而训练参数化模型以逼近ASE。模型得到的嵌入具备可解释性、参数高效性，并能在存在未观测边的输入下保持鲁棒，同时在推理阶段可控复杂度。LASE层融合GCN与全连接GAT以表征所需图特征，并通过稀疏注意力与解耦层参数等改进实现更优的误差-计算权衡，性能可优于高度优化的特征分解例程；同时可无缝集成到更大的（半）监督图表示学习流水线，用于判别式ASE并在链路预测与节点分类任务中取得领先表现。

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages31

Reading Time1 h 18 min

AccessFree to download

Introduction

Graph representation learning and node embeddings

Spectral embeddings and limitations of eigendecomposition

Objectives: learned ASE via neural architecture

LASE: Learned Adjacency Spectral Embeddings Sofía Pé[rez Casulo](rez Casulo sperez@fing. edu.uy)[ sperez@fing. edu.uy](rez Casulo sperez@fing. edu.uy) Facultad de Ingeniería Universidad de la República [Marcelo Fiori](Marcelo Fiori mfiori@fing. edu.uy)[ mfiori@fing. edu.uy](Marcelo Fiori mfiori@fing. edu.uy) Facultad de Ingeniería Universidad de la República [Federico Larroca](Federico Larroca flarroca@fing. edu.uy)[ flarroca@fing. edu.uy](Federico Larroca flarroca@fing. edu.uy) Facultad de Ingeniería Universidad de la República Gonzalo Mateos [gmateosb@ece. rochester. edu](gmateosb@ece. rochester. edu) Department of Electrical and Computer Engineering University of Rochester Reviewed on OpenReview: [https: // openreview. net/ forum? id= J65NBLWrmh](https: // openreview. net/ forum? id= J65NBLWrmh) Abstract We put forth a principled design of a neural architecture to learn nodal Adjacency Spectral Embeddings (ASE) from graph inputs. By bringing to bear the gradient descent (GD) method and leveraging the technique of algorithm unrolling, we truncate and re-interpret each GD iteration as a layer in a graph neural network (GNN) that is trained to approximate the ASE. Accordingly, we call the resulting embeddings and our parametric model Learned ASE (LASE), which is interpretable, parameter efficient, robust to inputs with unobserved edges, and offers controllable complexity during inference. LASE layers combine Graph Convolutional Network (GCN) and fully-connected Graph Attention Network (GAT) modules, which is intuitively pleasing since GCN-based local aggregations alone are insufficient to express the sought graph eigenvectors. We propose several refinements to the unrolled LASE architecture (such as sparse attention in the GAT module and decoupled layerwise parameters) that offer favorable approximation error versus computation tradeoffs; even outperforming heavily-optimized eigendecomposition routines from scientific computing libraries. Because LASE is a differentiable function with respect to its parameters as well as its graph input, we can seamlessly integrate it as a trainable module within a larger (semi-)supervised graph representation learning pipeline. The resulting end-to-end system effectively learns “discriminative ASEs” that exhibit competitive performance in supervised link prediction and node classification tasks, outperforming a GNN even when the latter is endowed with open loop, meaning task-agnostic, precomputed spectral positional encodings. 1 Introduction Graphs are natural models of relational data, spanning domains as diverse as social networks, molecular biology, recommender systems, and knowledge graphs. Graph representation learning (GRL) has emerged as a powerful framework for extracting meaningful patterns from such structured data, enabling downstream machine learning tasks. At its core, this approach seeks to encode nodes (also edges, or entire subgraphs) into low-dimensional vectors –known as node embeddings– that capture both local and global graph structural properties. These learned representations facilitate scalable, flexible, and effective learning, driving advancements in applications such as drug discovery, fraud detection, and personalized recommendations. Objectives, context, and motivating challenges. Here we revisit spectral node embeddings derived from the eigendecomposition of the graph’s adjacency matrix; see e.g., (Lim et al., 2023) and note extensions to Laplacian embeddings are straightforward. Spectral embeddings are central to unsupervised node clustering methods (von Luxburg, 2007), which intuitively motivates why information encoded in the graph eigenvectors may be used to specify vertex positions in latent space. This intuition is further justified if we assume that the graph’s structure stems from a Random Dot Product Graph (RDPG) (Athreya et al., 2017), a generative model that subsumes the classic Stochastic Block Model (SBM) and which has cl

FAQs

什么是LASE（Learned ASE）？

LASE是一种参数化神经架构，用于从图输入中学习节点的邻接谱嵌入（ASE），并以层级化的方式逼近谱嵌入。

LASE如何将梯度下降与图神经网络联系起来？

通过算法展开思路，将每次梯度下降迭代截断并重解释为GNN中的一层，从而把逼近ASE的目标转化为可训练的网络结构。

LASE相较于直接做邻接矩阵特征分解有哪些优势？

特征分解在边部分缺失或归纳式设置需要重算时会带来不可行或高计算成本问题；LASE能避免该开销，并保持对未观测边输入的鲁棒性。

Aug 5, 2026

Upload by Seraphina