Eigenbasis-Independent Learnable Spectral Positional Encodings for Directed Graphs via Hermitian Block Krylov Subspaces

arXiv:2607.07032 · cs.LG, stat.ML · Submitted 2026-07-08 · Read on arXiv

Jiaqing Xie, Yuxin Wang

cs.LG, stat.ML

Submitted: 2026-07-08

Comments: 8 pages main, theorem and type fixed

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 26× in this paper · explained in 1 episode
• Benchmark — 13× in this paper · explained in 2 episodes
• Transformer — 7× in this paper · explained in 2 episodes
• Equivariance — 6× in this paper · explained in 3 episodes
• Parameterization — 5× in this paper · explained in 2 episodes
• Transformers — 4× in this paper · explained in 2 episodes
• Ablation — 2× in this paper · explained in 1 episode
• GNNs — 2× in this paper · explained in 2 episodes
• Neural Operators — 2× in this paper · explained in 2 episodes
• Overfitting — 2× in this paper · explained in 2 episodes
• Spectral Gap — 2× in this paper · explained in 6 episodes
• Weight Decay — 2× in this paper · explained in 2 episodes
• AUC — 1× in this paper · explained in 2 episodes
• Editor — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Gauge Invariance — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 14 episodes
• Linear Complexity — 1× in this paper · explained in 2 episodes
• Permutation Equivariance — 1× in this paper · explained in 2 episodes
• Representation Learning — 1× in this paper · explained in 3 episodes

Sources

• A Generalization of Transformer Networks to Graphs
• GIST: Gauge-Invariant Spectral Transformers for Scalable Graph Neural Operators

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