# Adaptive Graph Mixture of Residual Experts: Unsupervised Learning on Diverse Graphs with Heterogeneous Specialization

arXiv: https://arxiv.org/abs/2510.21207 · HTML: https://mlsanity.com/paper/2510.21207/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE for time series and graphs, one of 12 directions in Mixture-of-experts.
- Builds on 36 of its 54 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Placed in

- Mixture-of-experts / [MoE for time series and graphs](https://mlsanity.com/moe/moe-for-time-series-and-graphs/)

## Builds on (most cited first, 30 of 36)

- [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)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Learning Factored Representations in a Deep Mixture of Experts](https://mlsanity.com/paper/1312.4314/) (2013)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Graph Barlow Twins: A self-supervised representation learning framework for graphs](https://mlsanity.com/paper/2106.02466/) (2021)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)
- [Graph Mixture of Experts: Learning on Large-Scale Graphs with Explicit Diversity Modeling](https://mlsanity.com/paper/2304.02806/) (2023)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [Generalized Graph Prompt: Toward a Unification of Pre-Training and Downstream Tasks on Graphs](https://mlsanity.com/paper/2311.15317/) (2023)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [Non-Homophilic Graph Pre-Training and Prompt Learning](https://mlsanity.com/paper/2408.12594/) (2024)
- [Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs](https://mlsanity.com/paper/2306.07608/) (2023)
- [FAITH: Few-Shot Graph Classification with Hierarchical Task Graphs](https://mlsanity.com/paper/2205.02435/) (2022)
- [Graph Classification by Mixture of Diverse Experts](https://mlsanity.com/paper/2103.15622/) (2021)
- [Single-Pass Contrastive Learning Can Work for Both Homophilic and Heterophilic Graph](https://mlsanity.com/paper/2211.10890/) (2022)

## Abstract (arXiv)

Graph Neural Networks (GNNs) face a fundamental adaptability challenge: their fixed message-passing architectures struggle with the immense diversity of real-world graphs, where optimal computational strategies vary by local structure and task. While Mixture-of-Experts (MoE) offers a promising pathway to adaptability, existing graph MoE methods remain constrained by their reliance on supervised signals and instability when training heterogeneous experts. We introduce ADaMoRE (Adaptive Mixture of Residual Experts), a principled framework that enables robust, fully unsupervised training of heterogeneous MoE on graphs. ADaMoRE employs a backbone-residual expert architecture where foundational encoders provide stability while specialized residual experts capture diverse computational patterns. A structurally-aware gating network performs fine-grained node routing. The entire architecture is trained end-to-end using a unified unsupervised objective, which integrates a primary reconstruction task with an information-theoretic diversity regularizer to explicitly enforce functional specialization among the experts. Theoretical analysis confirms our design improves data efficiency and training stability. Extensive evaluation across 16 benchmarks validates ADaMoRE's state-of-the-art performance in unsupervised node classification and few-shot learning, alongside superior generalization, training efficiency, and faster convergence on diverse graphs and tasks.