Recurrently Predicting Hypergraphs

by   David W. Zhang, et al.

This work considers predicting the relational structure of a hypergraph for a given set of vertices, as common for applications in particle physics, biological systems and other complex combinatorial problems. A problem arises from the number of possible multi-way relationships, or hyperedges, scaling in π’ͺ(2^n) for a set of n elements. Simply storing an indicator tensor for all relationships is already intractable for moderately sized n, prompting previous approaches to restrict the number of vertices a hyperedge connects. Instead, we propose a recurrent hypergraph neural network that predicts the incidence matrix by iteratively refining an initial guess of the solution. We leverage the property that most hypergraphs of interest are sparsely connected and reduce the memory requirement to π’ͺ(nk), where k is the maximum number of positive edges, i.e., edges that actually exist. In order to counteract the linearly growing memory cost from training a lengthening sequence of refinement steps, we further propose an algorithm that applies backpropagation through time on randomly sampled subsequences. We empirically show that our method can match an increase in the intrinsic complexity without a performance decrease and demonstrate superior performance compared to state-of-the-art models.


page 1

page 2

page 3

page 4

βˆ™ 01/19/2021

Learning over Families of Sets – Hypergraph Representation Learning for Higher Order Tasks

Graph representation learning has made major strides over the past decad...
βˆ™ 09/21/2020

Connected Fair Detachments of Hypergraphs

Let 𝒒 be a hypergraph whose edges are colored. An (Ξ±,n)-detachment of 𝒒 ...
βˆ™ 03/29/2023

On the Ξ±-spectral radius of hypergraphs

For real α∈ [0,1) and a hypergraph G, the α-spectral radius of G is the ...
βˆ™ 07/07/2019

A spectral bound on hypergraph discrepancy

Let H be a t-regular hypergraph on n vertices and m edges. Let M be the ...
βˆ™ 10/09/2022

Hypergraph-based Multi-Robot Task and Motion Planning

We present a multi-robot task and motion planning method that, when appl...
βˆ™ 02/25/2021

Random hypergraphs and property B

In 1964 ErdΕ‘s proved that (1+1)) ln(2)/4 k^2 2^k edges are sufficient to...

Please sign up or login with your details

Forgot password? Click here to reset