PLGC: Pseudo-Labeled Graph Condensation

TL;DR

PLGC tackles the problem of graph condensation in settings with scarce or noisy labels by introducing a self-supervised framework that learns latent pseudo-labels from node embeddings and alternates pseudo-label construction with condensed-graph optimization. It replaces ground-truth supervision with a prototype-based pseudo-labeling scheme, using swapped-assignment and balanced Sinkhorn-based updates to form a stable assignment matrix, and aligns condensed graphs to these pseudo-labels via an MMD-like representation objective. The authors provide theoretical guarantees showing pseudo-labels concentrate around latent centers and preserve cluster separation under mild assumptions, along with explicit sample-complexity bounds. Empirically, PLGC achieves competitive performance with state-of-the-art supervised condensation on clean data and substantially outperforms under label noise, with strong generalization in few-shot and multi-source scenarios, and transferability to link prediction. Overall, the work bridges self-supervised representation learning and graph condensation, enabling robust, label-free condensation for scalable graph learning.

Abstract

Large graph datasets make training graph neural networks (GNNs) computationally costly. Graph condensation methods address this by generating small synthetic graphs that approximate the original data. However, existing approaches rely on clean, supervised labels, which limits their reliability when labels are scarce, noisy, or inconsistent. We propose Pseudo-Labeled Graph Condensation (PLGC), a self-supervised framework that constructs latent pseudo-labels from node embeddings and optimizes condensed graphs to match the original graph's structural and feature statistics -- without requiring ground-truth labels. PLGC offers three key contributions: (1) A diagnosis of why supervised condensation fails under label noise and distribution shift. (2) A label-free condensation method that jointly learns latent prototypes and node assignments. (3) Theoretical guarantees showing that pseudo-labels preserve latent structural statistics of the original graph and ensure accurate embedding alignment. Empirically, across node classification and link prediction tasks, PLGC achieves competitive performance with state-of-the-art supervised condensation methods on clean datasets and exhibits substantial robustness under label noise, often outperforming all baselines by a significant margin. Our findings highlight the practical and theoretical advantages of self-supervised graph condensation in noisy or weakly-labeled environments.

Figures (6)

• Figure 1: Proposed self-supervised graph condensation framework to condense the original (unlabeled) graphs from different distributed sources within a small memory that can be used for training or finetuning for downstream tasks with limited supervision.
• Figure 2: Overview of the proposed PLGC framework. The method alternates between two coupled optimization steps: (I) Pseudo-Label Learning — multiple graph augmentations are generated from the original graph, processed through a shared GNN encoder to obtain node embeddings, and assigned to the pseudo-labels using an entropy-regularized Sinkhorn optimization. The resulting assignments and pseudo-labels are updated via a swapped-assignment view prediction loss. (II) Condensed Graph Optimization — the condensed graph is passed through the same shared encoder, and its node embeddings are aligned with the learned pseudo-labels using an MSE-based representation matching loss. Together, these steps iteratively refine pseudo-labels and the condensed graph so that the synthetic graph preserves the latent structure of the original graph without relying on ground-truth labels.
• Figure 3: Single-Source with Label Noise for Node classification: By leveraging the self-supervised condensed graphs, PLGC achieves better performance at lesser number of clean labelled nodes during funetuning stage, and demonstrates faster convergence compared to the 'full-finetune' baselines.
• Figure 4: Single-Source with Label Noise for Node classification: The superiority of our PLGC method is clearly visible as node-level label noises are increased, producing a robust, stable accuracy compared to the supervised GCond and SFGC methods.
• Figure 5: Multi-Source with Label Noise for Node classification: The superiority of our PLGC method is clearly visible as node-level label noises are increased, producing a robust, stable accuracy compared to the supervised GCond and SFGC methods.

Theorems & Definitions (8)

• Lemma 1: Existence of a $1/2$-net on unit sphere
• proof
• Lemma 2: Directional concentration via Chernoff
• proof
• Lemma 3: Stationarity Condition of pseudo-labels
• proof
• Theorem 1: Pseudo-labels Concentration and Interior Point recovery
• proof