Graph Metanetworks for Processing Diverse Neural Architectures (2312.04501v2)

Abstract: Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks - neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures.

• The paper introduces Graph Metanetworks that extend processing from MLPs and CNNs to complex architectures using graph representations.
• It proves GMNs’ equivariance and expressivity to parameter permutation symmetries, ensuring robust network predictions.
• Empirical tests on diverse classifiers show GMNs outperform conventional methods, enabling unified and scalable neural architecture analysis.

Overview of Graph Metanetworks for Processing Diverse Neural Architectures

The paper "Graph Metanetworks for Processing Diverse Neural Architectures" by Lim et al. introduces an approach called Graph Metanetworks (GMNs) for processing diverse neural architectures. The approach leverages graph neural networks (GNNs) to handle neural architectures as data, addressing challenges in representing diverse neural network parameters equitably. This research offers significant theoretical and empirical insights into metanetwork design and performance.

Key Contributions

1. Generalization to Diverse Architectures: The GMNs are designed to generalize beyond simple architectures such as MLPs and CNNs, extending compatibility to more complex structures like multi-head attention layers, normalization layers, and residual networks. The authors meticulously construct graphs for these diverse architectures and process them through GNNs.
2. Equivariance and Expressivity: A major theoretical contribution is the proof of GMNs' expressivity and equivariance to parameter permutation symmetries. The authors utilize neural DAG automorphisms to show that GMNs respect the inherent symmetries of neural network parameter spaces. This generalizes known results for simpler architectures and is pivotal for ensuring accurate metanetwork predictions and transformations.
3. Empirical Validation: The paper provides a comprehensive evaluation of GMNs on various metanetwork tasks using datasets of image classifiers from architectures including CNNs, DeepSets, ResNets, and Vision Transformers. The GMNs outperform existing metanetwork methods, showing robust generalization in predicting network accuracy across disparate architectures and layer configurations.

Implications and Future Direction

This work has several practical and theoretical implications:

• Unified Framework for Neural Architecture Processing: By converting neural network architectures into graphs, the proposed framework offers a unified methodology for analyzing and manipulating networks, paving the way for more generalized and adaptable metanetwork applications.
• Scalability and Complexity Handling: The efficiency of GMNs in handling parameter-sharing layers (e.g., convolutions in CNNs and attention mechanisms) without substantial computational overhead suggests potential scalability to larger networks. However, the extension to billion-parameter networks remains an open challenge.
• Expanding Theory to Parameter Graphs: The diversity in parameter sharing techniques across modern architectures suggests further theoretical exploration in parameter graph design. This could extend the existing theory of neural DAG automorphisms beyond computation graphs, solidifying the general applicability of GMNs.
• Applications in Neural Network Analysis and Optimization: GMNs could be instrumental in advanced applications such as neural architecture search, federated learning with heterogenous architectures, and potentially augmenting neural architecture optimization tasks.

Overall, this paper introduces a significant advancement in metanetwork science, providing a robust method for neural architecture analysis and manipulation that is both theoretically grounded and empirically validated. The adoption of graph-based methods for neural networks could lead to new insights and capabilities in neural network design and efficiency.