# Learning How Much to Think: Difficulty-Aware Dynamic MoEs for Graph Node Classification

arXiv: https://arxiv.org/abs/2604.11473 · HTML: https://mlsanity.com/paper/2604.11473/

## 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 24 of its 28 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## 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, 24 of 24)

- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [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)
- [Exphormer: Sparse Transformers for Graphs](https://mlsanity.com/paper/2303.06147/) (2023)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
- [SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations](https://mlsanity.com/paper/2306.10759/) (2023)
- [DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion](https://mlsanity.com/paper/2301.09474/) (2023)
- [Hierarchical Graph Transformer with Adaptive Node Sampling](https://mlsanity.com/paper/2210.03930/) (2022)
- [Graph Mixture of Experts: Learning on Large-Scale Graphs with Explicit Diversity Modeling](https://mlsanity.com/paper/2304.02806/) (2023)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approach](https://mlsanity.com/paper/2406.03464/) (2024)
- [DA-MoE: Addressing Depth-Sensitivity in Graph-Level Analysis through Mixture of Experts](https://mlsanity.com/paper/2411.03025/) (2024)
- [Mixture of Experts Meets Decoupled Message Passing: Towards General and Adaptive Node Classification](https://mlsanity.com/paper/2412.08193/) (2024)
- [Mixture of Scope Experts at Test: Generalizing Deeper Graph Neural Networks with Shallow Variants](https://mlsanity.com/paper/2409.06998/) (2024)

## Abstract (arXiv)

Mixture-of-Experts (MoE) architectures offer a scalable path for Graph Neural Networks (GNNs) in node classification tasks but typically rely on static and rigid routing strategies that enforce a uniform expert budget or coarse-grained expert toggles on all nodes. This limitation overlooks the varying discriminative difficulty of nodes and leads to under-fitting for hard nodes and redundant computation for easy ones. To resolve this issue, we propose D2MoE, a novel framework that shifts the focus from static expert selection to node-wise expert resource allocation. By using predictive entropy as a real-time proxy for difficulty, D2MoE employs a difficulty-driven top-p routing mechanism to adaptively concentrate expert resources on hard nodes while reducing overhead for easy ones, achieving continuous and fine-grained expert budget scaling for node classification. Experiments on 13 benchmarks demonstrate that D2MoE achieves consistent state-of-the-art performance, surpassing leading baselines by up to 7.92% in accuracy on heterophilous graphs. Notably, on large-scale graphs, it reduces memory consumption by up to 73.07% and training time by 46.53% compared to the best-performing Graph MoE, thereby validating its superior efficiency.