m-RevNet: Deep Reversible Neural Networks with Momentum (2108.05862v2)

Abstract: In recent years, the connections between deep residual networks and first-order Ordinary Differential Equations (ODEs) have been disclosed. In this work, we further bridge the deep neural architecture design with the second-order ODEs and propose a novel reversible neural network, termed as m-RevNet, that is characterized by inserting momentum update to residual blocks. The reversible property allows us to perform backward pass without access to activation values of the forward pass, greatly relieving the storage burden during training. Furthermore, the theoretical foundation based on second-order ODEs grants m-RevNet with stronger representational power than vanilla residual networks, which potentially explains its performance gains. For certain learning scenarios, we analytically and empirically reveal that our m-RevNet succeeds while standard ResNet fails. Comprehensive experiments on various image classification and semantic segmentation benchmarks demonstrate the superiority of our m-RevNet over ResNet, concerning both memory efficiency and recognition performance.

• The paper introduces momentum-Reversible Blocks (m-RevBlocks) that incorporate a velocity term to model second-order ODE dynamics for enhanced performance.
• The paper demonstrates improved accuracy with m-RevNet achieving lower top-1 error rates, such as 6.75% on CIFAR-10 and 23.4% on ImageNet compared to ResNet.
• The paper also highlights practical advantages, including reduced memory usage during training, which facilitates deeper networks and larger input resolutions.

An Overview of m-RevNet: Deep Reversible Neural Networks with Momentum

The paper introduces m-RevNet, a novel reversible neural network architecture characterized by the incorporation of momentum updates into residual blocks. The architecture leverages the connection between neural networks and differential equations, extending the widely known relationship between deep residual networks and first-order ordinary differential equations (ODEs) to second-order ODEs. This theoretical enhancement is utilized to achieve improved representational power and training efficiency over traditional ResNet architectures.

Theoretical Contributions

The core of m-RevNet lies in its conceptual grounding in second-order ODEs, which has been relatively underexplored in neural network design. The momentum-Reversible Blocks (m-RevBlocks) introduced in m-RevNet integrate a velocity term analogous to the first-order derivative in second-order ODEs. This theoretical linkage provides m-RevNet networks with enhanced modeling flexibility and expressive power. The paper provides a theoretical backdrop that indicates the capability of second-order ODEs to offer a stronger representation, theoretically supporting its superior performance over first-order ODE-based methods like ResNet.

Practical Advantages and Experimental Results

Practically, the reversible property of m-RevNet allows for a backward pass without retaining activation values from the forward pass, significantly reducing memory requirements during network training. This is a noteworthy advantage as it permits the training of deeper networks or larger input resolutions, which are often constrained by the GPU memory bottleneck. In experiments conducted on standard image classification benchmarks such as CIFAR-10, CIFAR-100, and ImageNet, m-RevNet consistently outperformed ResNet, demonstrating not only superior memory efficiency but also improved accuracy across different datasets.

The efficacy of m-RevNet extends to semantic segmentation tasks on datasets like Cityscapes and ADE20K, where its ability to manage memory more efficiently allows for the utilization of larger mini-batch sizes during training, resulting in enhanced performance compared to non-reversible architectures like ResNet.

Numerical Results and Claims

The paper presents compelling numerical results that highlight the effectiveness of m-RevNet. For instance, on CIFAR-10, m-RevNet-32 achieved a top-1 error of 6.75% compared to 7.14% by ResNet-32, and on ImageNet, m-RevNet-50 attained a top-1 error rate of 23.4%, outperforming ResNet-50’s 24.7%. These results illustrate the promising benefits of adopting a second-order ODE-inspired neural network design.

Future Directions and Implications

The research opens up new avenues for exploiting higher-order ODEs in neural network architecture design, suggesting potential future developments that can leverage this deeper integration between continuous dynamical systems and discrete neural models. As AI technology continues to evolve, further exploration in this direction might yield even more efficient and powerful architectures, enhancing a multitude of applications including but not limited to image classification, semantic segmentation, and beyond.

In conclusion, this paper presents a meaningful advancement in the field of deep learning architectures. By bridging the gap between neural network design and second-order ODEs, m-RevNet provides a novel perspective on how momentum concepts can be intricately integrated into network layers to yield both practical and theoretical improvements. The proposed architecture not only achieves efficient memory usage but also pushes the performance boundaries of contemporary neural networks.