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Wavelet-Induced Rotary Encodings: RoPE Meets Graphs

Created by
  • Haebom

Author

Isaac Reid, Arijit Sehanobish, Cederik H ofs, Bruno Mlodozeniec, Leonhard Vulpius, Federico Barbero, Adrian Weller, Krzysztof Choromanski, Richard E. Turner, Petar Veli\v{c}kovi c

WIRE: Wavelet-Induced Rotary Encodings

Outline

This paper introduces Wavelet-Induced Rotary Encodings (WIRE), an extension of Rotary Position Encodings (RoPE), a widely used algorithm in LLM and ViT, to graph-structured data. WIRE is more general than RoPE and demonstrates that it can recover RoPE in the special case of grid graphs. It also possesses desirable theoretical properties, such as isovariance under node reordering, compatibility with linear attention, and asymptotic dependence on graph-resistance distance under certain conditions. WIRE has been tested on a variety of synthetic and real-world tasks, including monochromatic subgraph identification, semantic segmentation of point clouds, and other standard graph benchmarks. It demonstrates effective performance in settings where graph structure is important.

Takeaways, Limitations

We present a novel encoding method that extends RoPE to allow it to be applied to graph data.
A more general methodology than RoPE, restoring RoPE from a grid graph
It has theoretical advantages such as isovariance for node order changes and compatibility with linear attention.
Performance verification by applying to various graph-related tasks
If the graph structure is not important, performance degradation may occur.
Dependence on resistance distance under certain assumptions, requires further research.
In practical applications, hyperparameter tuning is required for optimal performance.
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