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GLAudio Listens to the Sound of the Graph

Aurelio Sulser, Johann Wenckstern, Clara Kuempel

TL;DR

GLAudio introduces a novel graph-learning paradigm that separates feature propagation from processing by propagating node features through a discrete wave equation $\ddot{\mathbf{X}}(t) = -\mathbf{L}\mathbf{X}(t)$ and decoding the resulting wave signal with sequence models. The paper provides a theoretical expressivity framework based on a vertex receptive field and shows Dirichlet energy is preserved, which helps mitigate over-smoothing; it also analyzes over-squashing within this wave-based setting. Empirically, GLAudio performs well on heterophilic graphs and benefits from deeper propagation, while gains on long-range molecular benchmarks depend on combining long-range emphasis with short-range models. Overall, the work establishes a principled separation of propagation and processing as a promising direction for robust graph learning with long-range dependencies.

Abstract

We propose GLAudio: Graph Learning on Audio representation of the node features and the connectivity structure. This novel architecture propagates the node features through the graph network according to the discrete wave equation and then employs a sequence learning architecture to learn the target node function from the audio wave signal. This leads to a new paradigm of learning on graph-structured data, in which information propagation and information processing are separated into two distinct steps. We theoretically characterize the expressivity of our model, introducing the notion of the receptive field of a vertex, and investigate our model's susceptibility to over-smoothing and over-squashing both theoretically as well as experimentally on various graph datasets.

GLAudio Listens to the Sound of the Graph

TL;DR

GLAudio introduces a novel graph-learning paradigm that separates feature propagation from processing by propagating node features through a discrete wave equation and decoding the resulting wave signal with sequence models. The paper provides a theoretical expressivity framework based on a vertex receptive field and shows Dirichlet energy is preserved, which helps mitigate over-smoothing; it also analyzes over-squashing within this wave-based setting. Empirically, GLAudio performs well on heterophilic graphs and benefits from deeper propagation, while gains on long-range molecular benchmarks depend on combining long-range emphasis with short-range models. Overall, the work establishes a principled separation of propagation and processing as a promising direction for robust graph learning with long-range dependencies.

Abstract

We propose GLAudio: Graph Learning on Audio representation of the node features and the connectivity structure. This novel architecture propagates the node features through the graph network according to the discrete wave equation and then employs a sequence learning architecture to learn the target node function from the audio wave signal. This leads to a new paradigm of learning on graph-structured data, in which information propagation and information processing are separated into two distinct steps. We theoretically characterize the expressivity of our model, introducing the notion of the receptive field of a vertex, and investigate our model's susceptibility to over-smoothing and over-squashing both theoretically as well as experimentally on various graph datasets.
Paper Structure (13 sections, 3 theorems, 16 equations, 1 figure, 4 tables)

This paper contains 13 sections, 3 theorems, 16 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. GLAudio
  3. Wave Signal Encodes Features and Graph Structure
  4. Model Architecture
  5. Expressivity of GLAudio
  6. Experiments
  7. Node Classification on Network Graphs
  8. Graph Regression on ZINC Dataset
  9. Long Range Graph Benchmark: Peptides-struct
  10. Conclusion
  11. Proof of Theorem \ref{['thm:GraphEncoding']}
  12. Proof of Theorem \ref{['thm:Universality']}
  13. Further Experiment and Training Details

Key Result

Theorem 2.1

Given two graphs $G, H$ on the same vertex set with initial features $\mathbf{x}_{G}, \mathbf{x}_{H}$, then we have for the two corresponding wave signals $\mathbf{X}_{G}(t), \mathbf{X}_{H}(t),$$\forall t > 0$

Figures (1)

  • Figure 1: Test accuracy for varying numbers of time steps $N$. Accuracies are averaged over 10 random initializations.

Theorems & Definitions (5)

  • Theorem 2.1
  • Theorem 2.2: schafer2006recurrent
  • Theorem 2.3
  • Definition 2.4
  • proof : Proof of the claim.