Graph Few-Shot Learning via Adaptive Spectrum Experts and Cross-Set Distribution Calibration

TL;DR

GRACE tackles graph few-shot learning by addressing heterogeneity in local graph structure and distribution shift between support and query tasks. It introduces an adaptive spectrum expert framework (low-pass and high-pass experts) guided by a gating module to produce node-specific embeddings, coupled with a KDE-inspired cross-set calibration that refines class prototypes using query-density information. The approach is supported by a theoretical generalization bound that highlights benefits from expert diversity and reduced distribution shift, and empirically GRACE achieves state-of-the-art results across multiple FSNC benchmarks with robust ablations and analyses. This combination yields improved generalization and practical performance for rapid adaptation to new graph tasks.

Abstract

Graph few-shot learning has attracted increasing attention due to its ability to rapidly adapt models to new tasks with only limited labeled nodes. Despite the remarkable progress made by existing graph few-shot learning methods, several key limitations remain. First, most current approaches rely on predefined and unified graph filters (e.g., low-pass or high-pass filters) to globally enhance or suppress node frequency signals. Such fixed spectral operations fail to account for the heterogeneity of local topological structures inherent in real-world graphs. Moreover, these methods often assume that the support and query sets are drawn from the same distribution. However, under few-shot conditions, the limited labeled data in the support set may not sufficiently capture the complex distribution of the query set, leading to suboptimal generalization. To address these challenges, we propose GRACE, a novel Graph few-shot leaRning framework that integrates Adaptive spectrum experts with Cross-sEt distribution calibration techniques. Theoretically, the proposed approach enhances model generalization by adapting to both local structural variations and cross-set distribution calibration. Empirically, GRACE consistently outperforms state-of-the-art baselines across a wide range of experimental settings. Our code can be found here.

Figures (5)

• Figure 1: Diversity of local connectivity patterns in the Cora. Node colors indicate their class labels.
• Figure 2: Visualization of distributional discrepancy between support and query sets in the Cora.
• Figure 3: The overall framework of GRACE. (a) Illustration of episodic training. In each episode, an FSNC task is constructed by randomly sampling from the original graph. (b) Adaptive spectrum experts. By introducing multiple experts to capture the diverse frequency components of nodes, we employ a gating module to adaptively weight the spectrum experts. (c) Cross-set distribution calibration. We first compute class prototypes based on the support set. If classification is performed by directly assigning the query sample to the nearest prototype using Euclidean distance, it would be incorrectly assigned to the prototype $p_2$. However, after applying prototype calibration, the query sample can be correctly classified.
• Figure 4: Hyperparameter sensitivity analysis: (a) Model performance varies with the bandwidth $\sigma$. (b) Model performance varies with the gating temperature $\tau$.
• Figure 5: (a) Normalized low-pass expert weight across node homophily $d_v^{\text{hom}}$. (b) Normalized high-pass expert weight across node homophily $d_v^{\text{hom}}$. (c) Cross-set distribution calibration via KDE contours, showing support (stars), query (circles), and corrected prototypes (diamonds).

Theorems & Definitions (10)

• Theorem 5.1
• Corollary 5.2
• Lemma A.1: Expert Variance Bound
• proof
• Lemma A.2: Gating Error Propagation
• proof
• Lemma A.3: Distribution Calibration Error
• proof
• proof
• proof