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Parameter-Free Hypergraph Neural Network for Few-Shot Node Classification

Chaewoon Bae, Doyun Choi, Jaehyun Lee, Jaemin Yoo

TL;DR

ZEN tackles few-shot node classification on hypergraphs with a fully linear, parameter-free architecture. By linearizing HNNs into a single propagation matrix and a weight matrix, and then deriving a tractable closed-form for the weight while applying redundancy-aware propagation to remove self-information, it achieves strong generalization with minimal computation. The method yields state-of-the-art average performance across 11 real hypergraphs and delivers substantial speedups over nonlinear baselines, while offering interpretable class-feature relations through its linear decision process. This approach significantly improves scalability for hypergraph learning in low-label regimes and opens avenues for broader, training-free graph-based reasoning. $\text{Key ideas include: a unified linearization of HNNs, a closed-form weight solution, and a 2-hop redundancy-aware propagation design.}$

Abstract

Few-shot node classification on hypergraphs requires models that generalize from scarce labels while capturing high-order structures. Existing hypergraph neural networks (HNNs) effectively encode such structures but often suffer from overfitting and scalability issues due to complex, black-box architectures. In this work, we propose ZEN (Zero-Parameter Hypergraph Neural Network), a fully linear and parameter-free model that achieves both expressiveness and efficiency. Built upon a unified formulation of linearized HNNs, ZEN introduces a tractable closed-form solution for the weight matrix and a redundancy-aware propagation scheme to avoid iterative training and to eliminate redundant self information. On 11 real-world hypergraph benchmarks, ZEN consistently outperforms eight baseline models in classification accuracy while achieving up to 696x speedups over the fastest competitor. Moreover, the decision process of ZEN is fully interpretable, providing insights into the characteristic of a dataset. Our code and datasets are fully available at https://github.com/chaewoonbae/ZEN.

Parameter-Free Hypergraph Neural Network for Few-Shot Node Classification

TL;DR

ZEN tackles few-shot node classification on hypergraphs with a fully linear, parameter-free architecture. By linearizing HNNs into a single propagation matrix and a weight matrix, and then deriving a tractable closed-form for the weight while applying redundancy-aware propagation to remove self-information, it achieves strong generalization with minimal computation. The method yields state-of-the-art average performance across 11 real hypergraphs and delivers substantial speedups over nonlinear baselines, while offering interpretable class-feature relations through its linear decision process. This approach significantly improves scalability for hypergraph learning in low-label regimes and opens avenues for broader, training-free graph-based reasoning.

Abstract

Few-shot node classification on hypergraphs requires models that generalize from scarce labels while capturing high-order structures. Existing hypergraph neural networks (HNNs) effectively encode such structures but often suffer from overfitting and scalability issues due to complex, black-box architectures. In this work, we propose ZEN (Zero-Parameter Hypergraph Neural Network), a fully linear and parameter-free model that achieves both expressiveness and efficiency. Built upon a unified formulation of linearized HNNs, ZEN introduces a tractable closed-form solution for the weight matrix and a redundancy-aware propagation scheme to avoid iterative training and to eliminate redundant self information. On 11 real-world hypergraph benchmarks, ZEN consistently outperforms eight baseline models in classification accuracy while achieving up to 696x speedups over the fastest competitor. Moreover, the decision process of ZEN is fully interpretable, providing insights into the characteristic of a dataset. Our code and datasets are fully available at https://github.com/chaewoonbae/ZEN.
Paper Structure (29 sections, 10 theorems, 43 equations, 13 tables, 1 algorithm)

This paper contains 29 sections, 10 theorems, 43 equations, 13 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem definition and related work
  3. Problem definition
  4. Related work
  5. Proposed method: ZEN
  6. General form of a linearized HNN
  7. Tractable closed-form solution for the weight matrix $\mathbf{W}$
  8. Redundancy-aware propagation for eliminating self-information
  9. Summary of ZEN and its computational complexity
  10. Experiments
  11. Experimental setup
  12. Classification accuracy
  13. Running time
  14. Interpretability
  15. Ablation study
  16. ...and 14 more sections

Key Result

Lemma 1

Given a linear HNN $\hat{\mathbf{Y}} = \mathbf{P}\mathbf{X}\mathbf{W}$ and the SSE loss $\mathcal{L_\mathrm{SSE}} = \| \mathbf{D}_\mathrm{trn}\hat{\mathbf{Y}} - \mathbf{D}_\mathrm{trn} \mathbf{Y}\|_\mathrm{F}^2$, the closed-form solution $\mathbf{W}^*$ that minimizes $\mathcal{L_\mathrm{SSE}}$ is gi where $\dagger$ denotes the Moore-Penrose inverse (or the pseudoinverse) of a matrix.

Theorems & Definitions (21)

  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Definition 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • ...and 11 more