# ATLAS: Adaptive Topology-based Learning at Scale for Homophilic and Heterophilic Graphs

arXiv: https://arxiv.org/abs/2512.14908 · HTML: https://mlsanity.com/paper/2512.14908/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 63 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 30 of 44)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [On Explainability of Graph Neural Networks via Subgraph Explorations](https://mlsanity.com/paper/2102.05152/) (2021)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1911.07323/) (2019)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)

## Abstract (arXiv)

Graph neural networks (GNNs) excel on homophilic graphs where connected nodes share labels, but struggle with heterophilic graphs where edges do not imply similarity. Moreover, iterative message passing limits scalability due to neighborhood expansion overhead. We introduce ATLAS (Adaptive Topology-based Learning at Scale), a propagation-free framework that encodes graph structure through multi-resolution community features rather than message passing. We first prove that community refinement involves a fundamental trade-off: finer partitions increase label-community mutual information but also increase entropy. We formalize when refinement improves normalized mutual information, explaining why intermediate granularities are often most predictive. ATLAS employs modularity-guided adaptive search to automatically identify informative community scales, which are one-hot encoded, projected into learnable embeddings, and concatenated with node attributes for MLP classification. This enables standard mini-batch training and adjacency-free inference after one-time preprocessing. Across 13 benchmarks including million-node graphs, ATLAS achieves competitive or superior accuracy, up to 20-point gains over GCN on heterophilic datasets and 12-point gains over MLPs on homophilic graphs. By treating topology as explicit features, ATLAS adapts intelligently: leveraging structure when informative, remaining robust when weakly aligned, and avoiding propagation when structure misleads, providing both scalable performance and interpretable structural insights.