{"slug": "the-expressive-power-of-random-feature-mpnns-across-graph-sizes", "title": "The Expressive Power of Random-Feature MPNNs Across Graph Sizes", "summary": "A new arXiv paper (2610.12809v1) proves that message-passing neural networks (MPNNs) using continuous random node features are not size-uniformly universal, meaning they cannot approximate all functions across graph sizes. The authors develop a population-level framework for size-uniform approximation and show that continuous random features can be quantized to finitely many colors with arbitrarily small uniform error for MPNNs with a graph-size-independent Lipschitz bound, including standard mean, max, and order-normalized sum architectures. The paper also establishes incomparability between random-color MPNNs and higher-order Weisfeiler-Leman methods and gives finite-color MPNN constructions for tree subgraph isomorphism via color coding and a local MST task.", "body_md": "arXiv:2610.12809v1 Announce Type: new \nAbstract: Continuous random node features increase the expressivity of message-passing neural networks (MPNNs), but existing theoretical analyses are not fine-grained enough to capture their limitations, particularly in approximating functions across graph sizes or under a fixed number of random bits. We develop a population-level framework for size-uniform approximation. For MPNNs with a graph-size-independent Lipschitz bound in their initial features, including standard mean, max, and order-normalized sum architectures, we show that continuous random features can be quantized to finitely many colors with arbitrarily small uniform error in expected output. This reduction lets us transfer limitations on finite-color distinguishability to limitations on size-uniform approximation with continuous random features. We use this framework to prove that these MPNNs are not size-uniformly universal, analyze the expressivity gains from colors and independent trials, and establish incomparability between random-color MPNNs and higher-order Weisfeiler-Leman methods. We also give finite-color MPNN constructions for tree subgraph isomorphism via color coding and a local MST task.", "url": "https://wpnews.pro/news/the-expressive-power-of-random-feature-mpnns-across-graph-sizes", "canonical_source": "https://www.machinebrief.com/news/the-expressive-power-of-random-feature-mpnns-across-graph-si-5e2g", "published_at": "2026-10-12 04:00:00+00:00", "updated_at": "2026-10-12 05:08:05.982620+00:00", "lang": "en", "topics": ["machine-learning", "neural-networks", "ai-research"], "entities": ["arXiv", "MPNNs", "Weisfeiler-Leman"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/the-expressive-power-of-random-feature-mpnns-across-graph-sizes", "markdown": "https://wpnews.pro/news/the-expressive-power-of-random-feature-mpnns-across-graph-sizes.md", "text": "https://wpnews.pro/news/the-expressive-power-of-random-feature-mpnns-across-graph-sizes.txt", "jsonld": "https://wpnews.pro/news/the-expressive-power-of-random-feature-mpnns-across-graph-sizes.jsonld"}}