Invertible Residual Networks (1811.00995v3)

Abstract: We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple normalization step during training, already available in standard frameworks. Invertible ResNets define a generative model which can be trained by maximum likelihood on unlabeled data. To compute likelihoods, we introduce a tractable approximation to the Jacobian log-determinant of a residual block. Our empirical evaluation shows that invertible ResNets perform competitively with both state-of-the-art image classifiers and flow-based generative models, something that has not been previously achieved with a single architecture.

• The paper introduces a novel modification to standard ResNets that enforces invertibility using a fixed-point iteration and Lipschitz constraints.
• It bridges discriminative and generative modeling by approximating the Jacobian log-determinant with a scalable power series method.
• Empirical results show competitive performance on MNIST, CIFAR10, and CIFAR100, streamlining unified architectures for multiple tasks.

Invertible Residual Networks

The paper "Invertible Residual Networks" introduces a novel approach to enhance the utility of standard ResNet architectures by making them invertible. This development facilitates a unified framework capable of handling classification, density estimation, and generative tasks within a single model architecture. The authors' primary contribution lies in proposing a simple modification to conventional ResNets, obviating the need for dimension partitioning or restrictive architectural constraints typically associated with invertible networks.

Key Concepts and Methodology

The core technique involves integrating a normalization step during training, which enforces the Lipschitz condition necessary for invertibility. This approach simplifies implementation as it leverages standard machine learning libraries. By viewing ResNets through the lens of Euler discretization of Ordinary Differential Equations (ODEs), the authors ensure invertibility by maintaining a Lipschitz constant less than one for the residual blocks. The invertibility is solved through a fixed-point iteration approach, offering stability and uniqueness in the mapping.

The construction of these invertible ResNets allows them to function as generative models. For density estimation, the paper introduces a scalable approximation to compute the Jacobian log-determinant of residual blocks—necessary for evaluating likelihoods—using a power series expansion. This tractable method enables the application of invertible ResNets in generative modeling while maintaining competitiveness with existing image classifiers.

Empirical Results

The empirical evaluations demonstrate that invertible ResNets match the performance of state-of-the-art classifiers on datasets such as MNIST, CIFAR10, and CIFAR100. The authors highlight that their model also performs competitively with existing flow-based generative models without the previously required complex constraints. The paper identifies that the proposed architectures offer stability in forward and inverse mappings, challenging prior architectures focused solely on either discriminative or generative tasks.

Implications and Future Directions

The implications of this research are significant for developing general-purpose architectures in machine learning. By bridging generative and discriminative tasks through a unified architecture, invertible ResNets present an efficient solution for practitioners aiming to leverage unsupervised learning techniques in supervised settings.

Future research directions may explore further refinement of the Lipschitz constraints and extending this methodology to broader domains such as adversarial training. Additionally, enhancing the unbiased estimation of log-determinant calculations could improve model accuracy and applicability.

Conclusion

Overall, the paper contributes a streamlined methodology for crafting invertible neural networks that maintain competitive performance across diverse tasks. This advancement in neural architecture design highlights the potential for creating versatile and efficient machine learning models, reinforcing the interplay between dynamical systems and deep learning. The invertible ResNet framework is a step towards unified architecture paradigms, offering robust solutions for both classification and generative modeling.