Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers

Fuente: arXiv
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Main Authors: Huang, Zekai, Liang, Yingyu, Shi, Zhenmei, Song, Zhao, Zhuang, Zhen
Format: Preprint
Published: 2025
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author Huang, Zekai
Liang, Yingyu
Shi, Zhenmei
Song, Zhao
Zhuang, Zhen
author_facet Huang, Zekai
Liang, Yingyu
Shi, Zhenmei
Song, Zhao
Zhuang, Zhen
contents Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize graphs by modeling higher-order relationships among multiple entities, enabling richer representations but introducing significant computational challenges. In this work, we extend the Loop Transformer architecture's neural algorithmic reasoning capability to simulate hypergraph algorithms, addressing the gap between neural networks and combinatorial optimization over hypergraphs. Specifically, we propose a novel degradation mechanism for reducing hypergraphs to graph representations, enabling the simulation of graph-based algorithms, such as Dijkstra's shortest path. Furthermore, we introduce a hyperedge-aware encoding scheme to simulate hypergraph-specific algorithms, exemplified by Helly's algorithm. We establish theoretical guarantees for these simulations, demonstrating the feasibility of processing high-dimensional and combinatorial data using Loop Transformers. This work highlights the potential of Transformers as general-purpose algorithmic solvers for structured data.
format Preprint
id arxiv_https___arxiv_org_abs_2501_10688
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers
Huang, Zekai
Liang, Yingyu
Shi, Zhenmei
Song, Zhao
Zhuang, Zhen
Machine Learning
Artificial Intelligence
Computational Complexity
Computation and Language
Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize graphs by modeling higher-order relationships among multiple entities, enabling richer representations but introducing significant computational challenges. In this work, we extend the Loop Transformer architecture's neural algorithmic reasoning capability to simulate hypergraph algorithms, addressing the gap between neural networks and combinatorial optimization over hypergraphs. Specifically, we propose a novel degradation mechanism for reducing hypergraphs to graph representations, enabling the simulation of graph-based algorithms, such as Dijkstra's shortest path. Furthermore, we introduce a hyperedge-aware encoding scheme to simulate hypergraph-specific algorithms, exemplified by Helly's algorithm. We establish theoretical guarantees for these simulations, demonstrating the feasibility of processing high-dimensional and combinatorial data using Loop Transformers. This work highlights the potential of Transformers as general-purpose algorithmic solvers for structured data.
title Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers
topic Machine Learning
Artificial Intelligence
Computational Complexity
Computation and Language
url https://arxiv.org/abs/2501.10688