Graph Neural Networks for Learning Equivariant Representations of Neural Networks (2403.12143v3)

Abstract: Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However, existing approaches either overlook the inherent permutation symmetry in the neural network or rely on intricate weight-sharing patterns to achieve equivariance, while ignoring the impact of the network architecture itself. In this work, we propose to represent neural networks as computational graphs of parameters, which allows us to harness powerful graph neural networks and transformers that preserve permutation symmetry. Consequently, our approach enables a single model to encode neural computational graphs with diverse architectures. We showcase the effectiveness of our method on a wide range of tasks, including classification and editing of implicit neural representations, predicting generalization performance, and learning to optimize, while consistently outperforming state-of-the-art methods. The source code is open-sourced at https://github.com/mkofinas/neural-graphs.

• The paper presents a novel method that models neural networks as graphs to capture permutation symmetries and inherent structural properties.
• It leverages graph neural networks and transformers with edge features and positional embeddings to process heterogeneous architectures effectively.
• Empirical validation shows the approach outperforms state-of-the-art methods in tasks such as CNN performance prediction and implicit neural representation editing.

Neural Graphs: A Graph-Based Framework for Analyzing Neural Network Parameters

Introduction

Neural networks have been widely applied in various domains, offering impressive performance across a vast range of tasks. As these models evolve, there is an increasing interest in developing methods that can analyze, interpret, and manipulate the parameters of these neural networks themselves. This paper introduces a novel approach by representing neural networks as computational graphs, termed neural graphs, and applying graph neural networks (GNNs) and transformers to analyze and manipulate these neural graphs.

Neural Networks as Neural Graphs

The core idea behind our approach is the representation of neural networks as graphs, where nodes represent neurons and edges represent connections between these neurons. The weights and biases of the neural network are assigned as features to the respective edges and nodes in the graph. This representation naturally aligns with the computation graph underlying neural networks, thereby preserving structural and functional aspects of the original network while also accommodating the inherent permutation symmetries.

For Multi-Layer Perceptrons (MLPs), we construct neural graphs by treating biases as node features and weights as edge features. This construction extends to Convolutional Neural Networks (CNNs) by representing convolutional operations with appropriate edge features and incorporating mechanisms to handle architectural components like residual connections and normalization layers.

Processing Heterogeneous Architectures

A significant advantage of the neural graph representation is its ability to process neural networks with diverse architectures using a single model. This flexibility is achieved without the need for architectural changes or manual adaptations. The representation can handle varying layer dimensions, non-linearities, and connectivity patterns, including residual connections, by encoding these variations within the graph structure.

Learning with Neural Graphs

To process neural graphs, we adapt graph neural networks and transformers to incorporate edge features and positional embeddings, ensuring that the models are equivariant to the permutation symmetries of the neural graphs. This allows for powerful models capable of learning from neural graphs with diverse architectures. The architecture of the adapted models incorporates mechanisms to update both node and edge features, facilitating effective learning and manipulation of neural graph representations.

Empirical Validation

We validate our approach across a range of tasks, including classification and editing of implicit neural representations (INRs), predicting generalization performance of CNNs, and learning to optimize neural networks. The neural graph-based models consistently outperform existing state-of-the-art methods, demonstrating the effectiveness of our approach. Notably, the method's ability to handle heterogeneous architectures unlocks new avenues for analysis and manipulation of neural networks.

Implications and Future Developments

The research presents a novel paradigm for analyzing and manipulating neural networks through the lens of graph theory. Future developments may explore extending the neural graph representation to other types of neural network architectures, further improving model performance, and applying the approach to a broader spectrum of tasks within the field of neural network analysis and optimization.

In conclusion, the introduction of neural graphs and the development of corresponding GNN and transformer models represent a significant step forward in the capabilities of models to analyze, interpret, and manipulate neural networks based on their parameters. This approach not only addresses existing challenges in processing neural networks with varying architectures but also opens up new possibilities for research and application in the field of deep learning.