Then we follow recent works to pursue the weak approximate solutions.

This raises a challenging research question: How can we keep improving the systems when their capabilities have surpassed the levels of humans?

The omnipresence of NP-hard combinatorial optimization problems (COPs) compels domain experts to engage in trial-and-error heuristic design. The long-standing endeavor of design automation has gained new momentum with the rise of large language models (LLMs).

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge.

End-to-end backpropagation is the standard training method of neural networks.

End-to-end backpropagation is the standard training method of neural networks.

To this end, we introduce Poppy, a simple training procedure for populations.

In this paper we consider standard convex relaxations for such problems.

Optimisation problems on the Stiefel manifold occur for example in spectral relaxations of various combinatorial problems, such as graph matching, clustering, or permutation synchronisation. Although sparsity is a desirable property in such settings, it is mostly neglected in spectral formulations since existing solvers, e.g. based on eigenvalue decomposition, are unable to account for sparsity while at the same time maintaining global optimality guarantees.