# Aligning the Spectrum: Hybrid Graph Pre-training and Prompt Tuning across Homophily and Heterophily

arXiv: https://arxiv.org/abs/2508.11328 · HTML: https://mlsanity.com/paper/2508.11328/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 45 references that are in the map.
- First posted on arXiv 15 Aug 2025.

## Builds on (most cited first, 30 of 35)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [LLaGA: Large Language and Graph Assistant](https://mlsanity.com/paper/2402.08170/) (2024)
- [SimGRACE: A Simple Framework for Graph Contrastive Learning without Data Augmentation](https://mlsanity.com/paper/2202.03104/) (2022)
- [GraphPrompt: Unifying Pre-Training and Downstream Tasks for Graph Neural Networks](https://mlsanity.com/paper/2302.08043/) (2023)
- [All in One: Multi-task Prompting for Graph Neural Networks](https://mlsanity.com/paper/2307.01504/) (2023)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [Self-supervised Learning on Graphs: Deep Insights and New Direction](https://mlsanity.com/paper/2006.10141/) (2020)
- [Universal Prompt Tuning for Graph Neural Networks](https://mlsanity.com/paper/2209.15240/) (2022)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [AFEC: Active Forgetting of Negative Transfer in Continual Learning](https://mlsanity.com/paper/2110.12187/) (2021)
- [Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrum](https://mlsanity.com/paper/2210.02330/) (2022)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [Automated Self-Supervised Learning for Recommendation](https://mlsanity.com/paper/2303.07797/) (2023)
- [Non-Homophilic Graph Pre-Training and Prompt Learning](https://mlsanity.com/paper/2408.12594/) (2024)
- [ProG: A Graph Prompt Learning Benchmark](https://mlsanity.com/paper/2406.05346/) (2024)

## Abstract (arXiv)

Graph ``pre-training and prompt-tuning'' aligns downstream tasks with pre-trained objectives to enable efficient knowledge transfer under limited supervision. However, current methods typically rely on single-filter backbones (e.g., low-pass), whereas real-world graphs exhibit inherent spectral diversity. Our theoretical textitSpectral Specificity principle reveals that effective knowledge transfer requires alignment between pre-trained spectral filters and the intrinsic spectrum of downstream graphs. This identifies two fundamental limitations: (1) Knowledge Bottleneck: single-filter models suffer from irreversible information loss by suppressing signals from other frequency bands (e.g., high-frequency); (2) Utilization Bottleneck: spectral mismatches between pre-trained filters and downstream spectra lead to significant underutilization of pre-trained knowledge. To bridge this gap, we propose HS-GPPT. We utilize a hybrid spectral backbone to construct an abundant knowledge basis. Crucially, we introduce Spectral-Aligned Prompt Tuning to actively align the downstream graph's spectrum with diverse pre-trained filters, facilitating comprehensive knowledge utilization across both homophily and heterophily. Extensive experiments validate the effectiveness under both transductive and inductive learning settings.