Multiscale Deep Equilibrium Models (2006.08656v2)

Abstract: We propose a new class of implicit networks, the multiscale deep equilibrium model (MDEQ), suited to large-scale and highly hierarchical pattern recognition domains. An MDEQ directly solves for and backpropagates through the equilibrium points of multiple feature resolutions simultaneously, using implicit differentiation to avoid storing intermediate states (and thus requiring only $O(1)$ memory consumption). These simultaneously-learned multi-resolution features allow us to train a single model on a diverse set of tasks and loss functions, such as using a single MDEQ to perform both image classification and semantic segmentation. We illustrate the effectiveness of this approach on two large-scale vision tasks: ImageNet classification and semantic segmentation on high-resolution images from the Cityscapes dataset. In both settings, MDEQs are able to match or exceed the performance of recent competitive computer vision models: the first time such performance and scale have been achieved by an implicit deep learning approach. The code and pre-trained models are at https://github.com/locuslab/mdeq .

• The paper introduces Multiscale Deep Equilibrium Models (MDEQ), a novel implicit neural network architecture that processes multiscale features simultaneously to achieve constant memory usage regardless of depth.
• Evaluations show MDEQ achieves competitive performance on tasks like ImageNet classification (77.5% top-1 accuracy) and Cityscapes segmentation (mIoU > 80%), demonstrating scalability and efficiency with over 60% memory reduction compared to explicit models.
• MDEQ challenges traditional stage-wise architectures and suggests a new paradigm for deep learning, inspiring future research in optimizing solvers, generalizing to other domains, and exploring hybrid model designs.

Overview of "Multiscale Deep Equilibrium Models"

The paper "Multiscale Deep Equilibrium Models" introduces a novel class of implicit neural network architectures designed to address key challenges in domains such as computer vision, where high-dimensional multiscale structures are prevalent. This approach, referred to as the Multiscale Deep Equilibrium Model (MDEQ), seeks to harness the power of implicit deep learning by resolving and backpropagating through equilibria at multiple feature resolutions concurrently.

In traditional explicit neural networks, memory usage grows linearly with the depth due to layer-wise forward computation and backpropagation. Implicit models, such as Deep Equilibrium Models (DEQs), overcome this limitation by simulating networks with "infinite" depth, achieving a constant memory footprint through implicit differentiation and root-finding algorithms. The MDEQ further expands upon standard DEQs by integrating multiscale processing directly into the implicit model. It uniquely maintains features of multiple resolutions simultaneously and optimizes them to reach a coherent equilibrium, requiring only $O(1)$ memory.

Approach and Contributions

MDEQ builds upon existing implicit models but introduces a significant advancement: it models different image feature scales simultaneously, rather than processing these scales in sequential layers as seen in typical hierarchical architectures. This model eschews the explicit multi-stage processing that characterizes conventional architectures such as ResNets and DenseNets, where information across resolutions flows from higher to lower stages or vice versa.

Key aspects of the MDEQ framework include:

• Transformation and Features: MDEQ uses shallow residual blocks and multiscale fusion layers to process and synchronize features across varying resolutions. The process is explicitly designed to efficiently merge and maintain information from multiple scales.
• Equilibrium Solver: The use of improved Broyden’s method, adapted for limited memory, facilitates finding equilibrium states in high-dimensional settings, which is crucial for handling image datasets with large inputs.
• Multi-task Learning: MDEQ’s architecture allows it to simultaneously handle diverse tasks by using different resolutions of equilibrium states to define task-specific losses. For example, low-resolution features may be suited for image classification while high-resolution features may excel at semantic segmentation.

Results and Evaluation

MDEQs were rigorously evaluated across several vision benchmarks, including CIFAR-10 for smaller datasets, and more challenging large-scale datasets like ImageNet for classification and Cityscapes for semantic segmentation. The results showcased that:

• ImageNet Classification: MDEQ models reach 77.5% top-1 accuracy, competing against well-established networks like ResNet-101, illustrating the capability of implicit models to rival explicit architectures in performance.
• Cityscapes Segmentation: Achieving mIoU scores above 80% for high-resolution semantic segmentation demonstrates MDEQ's applicability in scaling implicit models to larger datasets traditionally dominated by deeply-stacked networks.
• Efficiency: An advantage of MDEQ is its limited memory usage during training compared to explicit models, with over 60% reduction in some cases, although this comes with a modest increase in computational complexity during inference.

Implications and Future Directions

The MDEQ represents a potential paradigm shift in differentiable modeling by challenging the necessity of complex stage-wise architectures historically prevalent in machine learning. Its ability to process information across multiple scales implicitly could redefine approaches to many pattern recognition tasks.

The introduction of MDEQ could inspire further research along several vectors:

1. Efficiency and Convergence: Ongoing optimization of solvers like Broyden's method will be paramount in reducing runtime complexities, making implicit models more practical for real-time applications.
2. Generalization Across Domains: While MDEQ has proven successful in vision tasks, extending and adapting such architectures for other domains with multiscale challenges, such as audio and spatiotemporal data, could unlock new avenues for implicit models.
3. Hybrid Architectures: Exploring combinations of explicit and implicit model components may strike a balance between the efficiency of explicit models and the memory benefits of implicit solutions, catering to diverse application requirements.

In conclusion, "Multiscale Deep Equilibrium Models" presents an innovative methodology with the potential to impact both theoretical and practical aspects of neural network design, paving the way for further exploration and development in implicit deep learning paradigms.