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arXiv Machine Learning

Contrastive Neural Algorithmic Reasoning for Graph Coloring

arXiv:2606. 03923v1 Announce Type: new Abstract: Graph coloring seeks to assigns colors to a graph's nodes so that adjacent nodes receive different colors, using as few colors as possible.

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arXiv Machine Learning
Oct 12

The Expressive Power of Random-Feature MPNNs Across Graph Sizes

The paper investigates how continuous random node features affect the expressivity of message‑passing neural networks (MPNNs). It introduces a population‑level framework for size‑uniform approximation, showing that continuous random features can be quantized to finitely many colors with negligible error, allowing transfer of finite‑color distinguishability limits to size‑uniform approximation. The authors prove that such MPNNs are not size‑uniformly universal, analyze expressivity gains from colors and independent trials, establish incomparability with higher‑order Weisfeiler‑Leman methods, and provide finite‑color MPNN constructions for tree subgraph isomorphism and a local minimum spanning tree task.

By Robert R. Nerem, Mitchell Black, Antonis Vasileiou, Christopher Morris, Yusu Wang
efficiency
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arXiv AI
Aug 25

Which Algorithms Can Graph Neural Networks Learn?

arXiv:2602.13106v2 Announce Type: replace-cross Abstract: In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a li...

By Solveig Wittig, Antonis Vasileiou, Robert R. Nerem, Timo Stoll, Floris Geerts, Yusu Wang, Christopher Morris
efficiency
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arXiv Machine Learning
Oct 28

EnerGNN: Learning Optimization-Compatible Energy Functions for Exact Constrained Combinatorial Inference

EnerGNN is a framework that learns energy functions over complete binary configurations and performs exact constrained inference via mixed integer programming. It combines a graph neural network encoder, an optimization‑compatible readout, and a nonlinear energy head, and is trained with an optimality‑aware contrastive loss to reflect solution quality and constraint violations. In experiments on Quadratic Knapsack, Combinatorial Auctions, and a personalized cell therapy supply chain problem, EnerGNN achieves near‑optimal solutions with 100% feasibility, a 0.05% mean primal gap, and a 17.4× speedup over a monolithic MIP, while also generalizing to larger instances and supporting zero‑shot constraint injection.

By Niki Triantafyllou, Maria M. Papathanasiou
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arXiv Machine Learning
Oct 3

Reformulation-Contrastive Learning for Mixed Integer Programs

The paper introduces ReMILP, a reformulation‑contrastive learning framework that uses self‑supervision from equivalent formulations of mixed‑integer linear programs (MILPs). By distinguishing re‑descriptions and substitutions, the method trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables, achieving invariance and equivariance without solver‑derived labels. The learned representations prove useful for tasks such as binary solution, constraint activity, and integrality gap prediction, and serve as a strong initialization for fine‑tuning.

By Ousema Bouaneni, Mathis Le Bail, Cl\'ement Elliker, Ma\"el Jenny, Sonia Vanier
ragfine-tuning
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arXiv Machine Learning
Oct 7

Neural Algorithmic Reasoning for Graph Saddle Point Problems

The paper introduces “GraphPDHG,” a message‑passing neural network that aligns with the Chambolle‑Pock Primal–Dual Hybrid Gradient algorithm to solve general graph saddle‑point problems. The authors prove that “GraphPDHG” can efficiently simulate PDHG and can learn an accelerated version of the algorithm. Experiments demonstrate that the learned warm start improves second‑order optimizers and that alignment with PDHG yields better size generalization compared to standard GNN baselines.

By Samantha Chen, Jesse He, Coleman Clougherty, Gal Mishne, Chester Holtz
safety
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