# Unsupervised Ordering for Maximum Clique

arXiv: https://arxiv.org/abs/2503.21814 · HTML: https://mlsanity.com/paper/2503.21814/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 25 Mar 2025.

## Builds on (most cited first, 6 of 6)

- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2006.10643/) (2020)
- [Unsupervised Learning for Solving the Travelling Salesman Problem](https://mlsanity.com/paper/2303.10538/) (2023)
- [Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem?](https://mlsanity.com/paper/2206.01506/) (2022)
- [Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions](https://mlsanity.com/paper/2208.04055/) (2022)
- [HoTPP Benchmark: Are We Good at the Long Horizon Events Forecasting?](https://mlsanity.com/paper/2406.14341/) (2024)

## Built on by (most cited first, 1 of 1)

- [Structure As Search: Unsupervised Permutation Learning for Combinatorial Optimization](https://mlsanity.com/paper/2507.04164/) (2025)

## Abstract (arXiv)

We propose an unsupervised approach for learning vertex orderings for the maximum clique problem by framing it within a permutation-based framework. We transform the combinatorial constraints into geometric relationships such that the ordering of vertices aligns with the clique structures. By integrating this clique-oriented ordering into branch-and-bound search, we improve search efficiency and reduce the number of computational steps. Our results demonstrate how unsupervised learning of vertex ordering can enhance search efficiency across diverse graph instances. We further study the generalization across different sizes.