Spectral Reversal: Counteracting Singular Value Bias for Graph Prompting

arXiv:2609.32143v1 Announce Type: new Abstract: Pre-training Graph Neural Networks (GNNs) via self-supervised learning has become a dominant paradigm, yet efficiently adapting frozen encoders remains a challenge. Graph prompting offers a parameter-efficient alternative to fine-tuning, but existing methods largely treat pre-trained models as opaque feature extractors, ignoring their internal spectral structure. In this work, we identify a systematic phenomenon in pre-trained GNNs, which we term spectral bias: optimization during pre-training disproportionately aligns representations with directions associated with large singular values, leaving low-energy directions under-explored. We show that these underutilized directions can encode complementary information that is beneficial for downstream adaptation, especially under distribution shift. To leverage this insight, we propose Spectral Reverse Prompt (SRP), a prompting framework that rebalances the spectral contributions of frozen GNN encoders. SRP applies a learnable soft-thresholding mask in the spectral domain to down-weight dominant directions while amplifying weaker ones. In addition, SRP incorporates a null-space augmentation module that captures variation in directions with minimal activation under the frozen encoder. Extensive experiments across multiple benchmarks demonstrate that SRP achieves state-of-the-art performance with minimal additional parameters, highlighting that reweighting spectral components is a principled and effective strategy for parameter-efficient graph adaptation.

Abstract:Pre-training Graph Neural Networks (GNNs) via self-supervised learning has become a dominant paradigm, yet efficiently adapting frozen encoders remains a challenge. Graph prompting offers a parameter-efficient alternative to fine-tuning, but existing methods largely treat pre-trained models as opaque feature extractors, ignoring their internal spectral structure. In this work, we identify a systematic phenomenon in pre-trained GNNs, which we term spectral bias: optimization during pre-training disproportionately aligns representations with directions associated with large singular values, leaving low-energy directions under-explored. We show that these underutilized directions can encode complementary information that is beneficial for downstream adaptation, especially under distribution shift. To leverage this insight, we propose Spectral Reverse Prompt (SRP), a prompting framework that rebalances the spectral contributions of frozen GNN encoders. SRP applies a learnable soft-thresholding mask in the spectral domain to down-weight dominant directions while amplifying weaker ones. In addition, SRP incorporates a null-space augmentation module that captures variation in directions with minimal activation under the frozen encoder. Extensive experiments across multiple benchmarks demonstrate that SRP achieves state-of-the-art performance with minimal additional parameters, highlighting that reweighting spectral components is a principled and effective strategy for parameter-efficient graph adaptation.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Social and Information Networks (cs.SI)

arXiv:2609.32143 [cs.LG]

(or arXiv:2609.32143v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.32143 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Spectral Reversal: Counteracting Singular Value Bias for Graph Prompting

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