# Learn from Global Correlations: Enhancing Evolutionary Algorithm via Spectral GNN

arXiv: https://arxiv.org/abs/2412.17629 · HTML: https://mlsanity.com/paper/2412.17629/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 60 references that are in the map.
- First posted on arXiv 23 Dec 2024.

## Builds on (most cited first, 19 of 19)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Large Language Models As Evolution Strategies](https://mlsanity.com/paper/2402.18381/) (2024)
- [Interpretable and Efficient Heterogeneous Graph Convolutional Network](https://mlsanity.com/paper/2005.13183/) (2020)
- [Self-supervised Heterogeneous Graph Pre-training Based on Structural Clustering](https://mlsanity.com/paper/2210.10462/) (2022)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Survey on Evolutionary Deep Learning: Principles, Algorithms, Applications and Open Issues](https://mlsanity.com/paper/2208.10658/) (2022)
- [MMES: Mixture Model based Evolution Strategy for Large-Scale Optimization](https://mlsanity.com/paper/2203.12675/) (2022)
- [SARF: Aliasing Relation Assisted Self-Supervised Learning for Few-shot Relation Reasoning](https://mlsanity.com/paper/2304.10297/) (2023)
- [Reviewing and Benchmarking Parameter Control Methods in Differential Evolution](https://mlsanity.com/paper/2010.01035/) (2020)
- [Assessing Ranking and Effectiveness of Evolutionary Algorithm Hyperparameters Using Global Sensitivity Analysis Methodologies](https://mlsanity.com/paper/2207.04820/) (2022)
- [Analyzing Evolutionary Optimization in Noisy Environments](https://mlsanity.com/paper/1311.4987/) (2013)

## Built on by (most cited first, 15 of 15)

- [Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning Large Language Models](https://mlsanity.com/paper/2505.16122/) (2025)
- [ReCreate: Reasoning and Creating Domain Agents Driven by Experience](https://mlsanity.com/paper/2601.11100/) (2026)
- [Task-Specific Efficiency Analysis: When Small Language Models Outperform Large Language Models](https://mlsanity.com/paper/2603.21389/) (2026)
- [DSPC: Dual-Stage Progressive Compression Framework for Efficient Long-Context Reasoning](https://mlsanity.com/paper/2509.13723/) (2025)
- [Research on Personalized Financial Product Recommendation by Integrating Large Language Models and Graph Neural Networks](https://mlsanity.com/paper/2506.05873/) (2025)
- [Rethinking LoRA for Privacy-Preserving Federated Learning in Large Models](https://mlsanity.com/paper/2602.19926/) (2026)
- [Out of the Memory Barrier: A Highly Memory Efficient Training System for LLMs with Million-Token Contexts](https://mlsanity.com/paper/2602.02108/) (2026)
- [Patient-Similarity Cohort Reasoning in Clinical Text-to-SQL](https://mlsanity.com/paper/2601.09876/) (2026)
- [Adaptive Debiasing Tsallis Entropy for Test-Time Adaptation](https://mlsanity.com/paper/2602.11743/) (2026)
- [Attribution-Guided Model Rectification of Unreliable Neural Network Behaviors](https://mlsanity.com/paper/2603.15656/) (2026)
- [FAST: A Synergistic Framework of Attention and State-space Models for Spatiotemporal Traffic Prediction](https://mlsanity.com/paper/2604.13453/) (2026)
- [Physics-Informed Evolution: An Evolutionary Framework for Solving Quantum Control Problems Involving the Schr"odinger Equation](https://mlsanity.com/paper/2502.05228/) (2025)
- [Sharpness-Aware Minimization for Generalized Embedding Learning in Federated Recommendation](https://mlsanity.com/paper/2603.11503/) (2026)
- [VigilFormer: Deformable Attention for Video Anomaly Detection with Causal Risk Inference](https://mlsanity.com/paper/2606.14724/) (2026)
- [Bridging Geographic Bias in Urban Streetscape Inference via Lifelong Learning with Visual-Semantic Pivoting](https://mlsanity.com/paper/2606.15055/) (2026)

## Abstract (arXiv)

Evolutionary algorithms (EAs) simulate natural selection but have two main limitations: (1) they rarely update individuals based on global correlations, limiting comprehensive learning; (2) they struggle with balancing exploration and exploitation, where excessive exploitation causes premature convergence, and excessive exploration slows down the search. Moreover, EAs often depend on manual parameter settings, which can disrupt the exploration-exploitation balance. To address these issues, we propose Graph Neural Evolution (GNE), a novel EA framework. GNE represents the population as a graph, where nodes represent individuals, and edges capture their relationships, enabling global information usage. GNE utilizes spectral graph neural networks (GNNs) to decompose evolutionary signals into frequency components, applying a filtering function to fuse these components. High-frequency components capture diverse global information, while low-frequency ones capture more consistent information. This explicit frequency filtering strategy directly controls global-scale features through frequency components, overcoming the limitations of manual parameter settings and making the exploration-exploitation control more interpretable and manageable. Tests on nine benchmark functions (e.g., Sphere, Rastrigin, Rosenbrock) show that GNE outperforms classical (GA, DE, CMA-ES) and advanced algorithms (SDAES, RL-SHADE) under various conditions, including noise-corrupted and optimal solution deviation scenarios. GNE achieves solutions several orders of magnitude better (e.g., 3.07e-20 mean on Sphere vs. 1.51e-07).