Neural Algorithmic Reasoning for Hypergraphs with Looped Transformers

TL;DR

This paper extends Loop Transformers to hypergraphs, enabling neural algorithmic reasoning for complex higher-order structures through novel encoding schemes and theoretical guarantees.

Contribution

It introduces a hyperedge-aware encoding and a degradation mechanism to adapt Loop Transformers for hypergraph algorithms, bridging neural networks and combinatorial optimization.

Findings

Successfully simulated hypergraph algorithms like Helly's algorithm.

Provided theoretical guarantees for hypergraph algorithm simulation.

Demonstrated potential of Transformers as general-purpose structured data solvers.

Abstract

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.