Scaling the Scattering Transform: Deep Hybrid Networks (1703.08961v2)

Abstract: We use the scattering network as a generic and fixed ini-tialization of the first layers of a supervised hybrid deep network. We show that early layers do not necessarily need to be learned, providing the best results to-date with pre-defined representations while being competitive with Deep CNNs. Using a shallow cascade of 1 x 1 convolutions, which encodes scattering coefficients that correspond to spatial windows of very small sizes, permits to obtain AlexNet accuracy on the imagenet ILSVRC2012. We demonstrate that this local encoding explicitly learns invariance w.r.t. rotations. Combining scattering networks with a modern ResNet, we achieve a single-crop top 5 error of 11.4% on imagenet ILSVRC2012, comparable to the Resnet-18 architecture, while utilizing only 10 layers. We also find that hybrid architectures can yield excellent performance in the small sample regime, exceeding their end-to-end counterparts, through their ability to incorporate geometrical priors. We demonstrate this on subsets of the CIFAR-10 dataset and on the STL-10 dataset.

• The paper introduces the use of fixed scattering transforms as initial layers in deep hybrid networks to preserve discriminative features and geometric invariance.
• It achieves performance comparable to AlexNet on ImageNet, with a combined scattering and ResNet model reaching an 11.4% top-5 error rate while reducing complexity.
• The hybrid approach offers substantial benefits in low-data scenarios, outperforming end-to-end models on datasets like CIFAR-10 and STL-10.

Scaling the Scattering Transform: Deep Hybrid Networks

The paper "Scaling the Scattering Transform: Deep Hybrid Networks" by Oyallon et al. presents an innovative approach to image classification that leverages the scattering transform as a foundational element of deep hybrid networks. The main thrust of the research is to investigate whether the initial stages of deep neural networks can be effectively initialized with fixed, non-learned layers, specifically using the scattering transform, which preserves geometric invariances.

Key Findings and Contributions

The authors propose using the scattering network as a fixed initialization for the first layers in a hybrid deep learning model. By introducing this pre-defined transformation, they demonstrate that early layers of the network can maintain discriminative features while offering inherent invariance to rotation and translation, without the need for end-to-end training of these layers.

Performance on Large-Scale Datasets:

• Using a concise set of operations through shallow cascades of $1 \times 1$ convolutions, the authors achieve performance on par with AlexNet on the ImageNet ILSVRC2012 dataset.
• A combined scattering and ResNet approach obtains a single-crop top 5 error rate of 11.4% on ImageNet, comparable with larger architectures such as ResNet-18, yet with reduced model complexity consisting of only 10 layers.

Advantages in Limited Data Scenarios:

• The hybrid architectures exhibit notable performance improvements in settings characterized by limited data availability. When evaluated on subsets of CIFAR-10 and the STL-10 datasets, the model surpasses end-to-end trained counterparts by effectively integrating geometric priors.
• This finding emphasizes the practicality of utilizing pre-defined representations in scenarios where acquiring large datasets is infeasible, enabling robust performance with fewer training samples.

Methodological Implications

The paper re-evaluates the role of pre-defined features in modern deep learning, suggesting that leveraging such features can facilitate the creation of more interpretable and theoretically grounded models. Employing scattering transforms allows for a structured approach in the network’s initial layers, aligning with known geometrical properties and providing a stable initialization.

The integration of scattering transforms advances the understanding of how networks can capture and utilize invariances inherent in certain tasks, potentially reducing the necessity for extensive data in training deep models. The structured approach also aids in mitigating the challenges associated with learning from scratch, particularly in the early layers where geometrical invariances can be encoded directly through the scattering representation.

Future Research Directions

The implications of this research suggest several possible future directions:

• Enhanced Theoretical Foundations: Developing a deeper theoretical framework to understand the interactions between learned and pre-defined layers could elucidate further improvements in the hybrid model’s architecture and efficiency.
• Broader Applications and Extensions: Extending the use of scattering transforms to other domains and applications within computer vision and beyond, testing its efficacy in tasks like object detection and segmentation, is warranted.
• Optimization and Hyperparameter Tuning: Exploring optimized training regimes and hyperparameter selection specifically tailored for hybrid networks could unlock further practical benefits, as the current learning strategies are heavily adapted from end-to-end deep learning frameworks.

In conclusion, Oyallon et al. contribute a compelling case for reconsidering the use of pre-defined transformations within deep neural networks, offering a fresh perspective on the integration of classical signal processing techniques with modern deep learning paradigms. The exploration of such hybrid networks offers promising potential for improved performance across a variety of domains, particularly where data limitations pose significant challenges.