A Generative Model for Sampling High-Performance and Diverse Weights for Neural Networks

Abstract: Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork, mapping a latent vector into high-performance (low-loss) weight vectors, generalizing recent findings of mode connectivity to higher dimensional manifolds. We formulate the training objective as a compromise between accuracy and diversity, where the diversity takes into account trivial symmetry transformations of the target network. We demonstrate how to reduce the number of parameters in the hypernetwork by parameter sharing. Once learned, the hypernetwork allows for a computationally efficient, ancestral sampling of neural network weights, which we recruit to form large ensembles. The improvement in classification accuracy obtained by this ensembling indicates that the generated manifold extends in dimensions other than directions implied by trivial symmetries. For computational efficiency, we distill an ensemble into a single classifier while retaining generalization.

• The paper introduces a hypernetwork generative model to sample diverse, high-performance neural network weights.
• It employs latent variable techniques and mode connectivity principles to navigate high-dimensional weight manifolds.
• Experimental results demonstrate improved classification accuracy and robustness through ensembles of varied network configurations.

A Generative Model for Neural Networks: An Authoritative Summary

Introduction

This paper explores a hypernetwork approach for generating neural network weights that achieve high performance while maintaining diversity in configuration. It extends the concept of mode connectivity in neural networks' loss landscapes to a higher dimensional manifold. By employing a hypernetwork, represented as a generative model, it constructs a manifold in the weight space where diverse, high-performance configurations can coexist.

Methodology

The central component of this approach is the hypernetwork, a neural network that outputs weights for a target network given latent input. The training objective optimizes for a balance between high accuracy and network diversity. The diversity term integrates trivial symmetries into its calculation, thereby enhancing the meaningful representation of generated network diversity.

Figure 1: Architecture block diagram of the hypernetwork with latent variable $z$, extractor $E$, codes $c$, weight-generators $W$, and generated weights $\theta$.

The hypernetwork architecture involves parameter sharing, leveraging convolutional layers to effectively manage the size of the hypernetwork relative to the target network. The architecture of the hypernetwork consists of several sub-networks: an extractor and weight-generators, each with distinct roles in managing and processing the latent representations to produce diverse network configurations.

Results and Evaluation

Experimentation demonstrates that the hypernetwork can generate weights placed on a complex manifold in the space of possible configurations. The diversity of generated networks is illustrated through PCA scatter plots, which display non-trivial manifold structures across layers.

Figure 2: Scatter plots of the generated weights for a specific second layer filter, in PCA space. The $(i,j)$ scatter plot has principal component $i$ against principal component $j$.

The ability of the hypernetwork to create ensembles of networks is evidenced by improvements in classification accuracy, suggesting the manifold extends into non-trivial dimensions beyond simple symmetries. The hypernetwork's capability to encompass various sub-optimal configurations further justifies the diversity-oriented design.

Comparison to Related Work

By not relying on a probabilistic output for the target network, this approach widens its applicability beyond Bayesian settings. Its loss function includes a hyperparameter that controls the trade-off between accuracy and diversity, a flexibility not present in traditional VI-based hypernetworks. This method's facilitation of ancestral sampling positions it as a viable alternative for exploratory and optimization tasks in high-dimensional neural network landscapes.

Implementation Considerations

The practical implementation requires careful calibration of the hyperparameter $\lambda$ to balance accuracy with diversity, without overwhelming the computational resources. The generator’s modularity—exemplified by the separation of extraction and weight generation tasks—indicates opportunities for optimization through reduced parameterization.

Conclusion

The paper introduces a novel generative model approach for sampling high-performance, diverse weights for neural networks. Future prospects include leveraging hypernetworks for tasks like transfer learning and efficient network compression. These avenues have practical implications for deploying robust, adaptable AI models capable of navigating complex decision landscapes in dynamic environments.