Orthogonal Jacobian Regularization for Unsupervised Disentanglement in Image Generation (2108.07668v1)

Abstract: Unsupervised disentanglement learning is a crucial issue for understanding and exploiting deep generative models. Recently, SeFa tries to find latent disentangled directions by performing SVD on the first projection of a pre-trained GAN. However, it is only applied to the first layer and works in a post-processing way. Hessian Penalty minimizes the off-diagonal entries of the output's Hessian matrix to facilitate disentanglement, and can be applied to multi-layers.However, it constrains each entry of output independently, making it not sufficient in disentangling the latent directions (e.g., shape, size, rotation, etc.) of spatially correlated variations. In this paper, we propose a simple Orthogonal Jacobian Regularization (OroJaR) to encourage deep generative model to learn disentangled representations. It simply encourages the variation of output caused by perturbations on different latent dimensions to be orthogonal, and the Jacobian with respect to the input is calculated to represent this variation. We show that our OroJaR also encourages the output's Hessian matrix to be diagonal in an indirect manner. In contrast to the Hessian Penalty, our OroJaR constrains the output in a holistic way, making it very effective in disentangling latent dimensions corresponding to spatially correlated variations. Quantitative and qualitative experimental results show that our method is effective in disentangled and controllable image generation, and performs favorably against the state-of-the-art methods. Our code is available at https://github.com/csyxwei/OroJaR

• The paper presents OroJaR, a novel method that enforces orthogonal gradients in latent dimensions to achieve improved disentangled representations.
• It outperforms Hessian Penalty by holistically constraining spatially correlated variations, as validated by metrics like PPL and VP across multiple datasets.
• The approach adapts to pre-trained models and multiple layers, paving the way for enhanced interpretability and controllable image synthesis.

Orthogonal Jacobian Regularization for Unsupervised Disentanglement in Image Generation

The paper "Orthogonal Jacobian Regularization for Unsupervised Disentanglement in Image Generation," authored by Yuxiang Wei et al., proposes a novel approach for enhancing unsupervised disentanglement in deep generative models, specifically targeting complex spatial variations in image generation tasks. Disentanglement learning is crucial for understanding generative models, enabling interpretability and controllable image synthesis without relying on labeled data.

Core Contributions

The authors introduce Orthogonal Jacobian Regularization (OroJaR)—a method designed to encourage the learning of disentangled representations by making changes in output orthogonal when perturbations occur in different latent dimensions. OroJaR operates by focusing on the Jacobian matrix, which represents the change in output with respect to each latent variable. The orthogonality constraint imposed on the Jacobian aims to ensure each latent dimension influences the output independently, thus promoting disentanglement.

Compared to Hessian Penalty, which minimizes off-diagonal entries of the Hessian matrix, OroJaR is advantageous as it constrains the output holistically, which is particularly beneficial for disentangling spatially correlated variations such as shape, size, and rotation. Furthermore, OroJaR can apply to multiple layers of the generative model, providing more flexibility and effectiveness in representation learning.

Experimental Evaluation

The research presents extensive experiments across various datasets, including Edges+Shoes, CLEVR, and Dsprites, demonstrating OroJaR's ability to achieve superior disentangled representations compared to existing methods such as SeFa and GAN-based techniques. Measures such as Perceptual Path Length (PPL) and Variation Predictability (VP) indicate that OroJaR outperforms competitors in smoothness and predictability of latent factor variations.

Additionally, OroJaR is applied to pre-trained models like BigGAN, showing its adaptability to identify meaningful directions in latent space without the need for retraining. This feature is particularly useful for practical cases where existing models need fine-tuning or editing capabilities.

Implications and Future Work

The implications of this work are significant for generative modeling in AI, particularly where model interpretability and control are crucial. OroJaR's ability to tackle spatially correlated factors of variation makes it applicable to a broad range of computer vision tasks, such as style transfer, domain adaptation, and interactive image generation.

Furthermore, the approach opens avenues for extending disentanglement techniques to other model architectures like VAEs and boosting the computational efficiency of these models. Future developments could explore integrating OroJaR with additional generative frameworks, further refining disentanglement capabilities.

Conclusion

In summary, the paper presents a robust method for disentanglement learning, addressing limitations present in prior techniques and expanding the utility of generative models in unsupervised scenarios. OroJaR stands out for its simplicity, adaptability, and effectiveness, offering a promising direction for researchers focusing on deep generative models and disentangled representations.