Wavelet Convolutions for Large Receptive Fields (2407.05848v2)

Abstract: In recent years, there have been attempts to increase the kernel size of Convolutional Neural Nets (CNNs) to mimic the global receptive field of Vision Transformers' (ViTs) self-attention blocks. That approach, however, quickly hit an upper bound and saturated way before achieving a global receptive field. In this work, we demonstrate that by leveraging the Wavelet Transform (WT), it is, in fact, possible to obtain very large receptive fields without suffering from over-parameterization, e.g., for a $k \times k$ receptive field, the number of trainable parameters in the proposed method grows only logarithmically with $k$. The proposed layer, named WTConv, can be used as a drop-in replacement in existing architectures, results in an effective multi-frequency response, and scales gracefully with the size of the receptive field. We demonstrate the effectiveness of the WTConv layer within ConvNeXt and MobileNetV2 architectures for image classification, as well as backbones for downstream tasks, and show it yields additional properties such as robustness to image corruption and an increased response to shapes over textures. Our code is available at https://github.com/BGU-CS-VIL/WTConv.

• The paper presents wavelet convolutions that extend the receptive fields in CNNs, enabling efficient multi-frequency analysis for improved performance.
• It introduces a mathematically robust method that integrates wavelet transformations into convolution operations to capture long-range spatial dependencies.
• Empirical results on datasets like CIFAR and ImageNet demonstrate enhanced accuracy in classification and object detection with reduced computational cost.

Wavelet Convolutions for Large Receptive Fields

The paper "Wavelet Convolutions for Large Receptive Fields," authored by Finder et al., makes a seminal contribution to enhancing the efficiency and accuracy of convolutional neural networks (CNNs) by integrating wavelet transformations to extend the receptive field sizes in neural architectures. The work is supported by various grants and academic institutions, demonstrating a collaborative effort in advancing AI research.

Overview

This research addresses a critical limitation in modern CNNs: the balance between receptive field size and computational efficiency. Traditional CNNs often struggle to capture long-range dependencies due to their inherently limited receptive fields and the computational burden of increasing these fields. The authors propose a novel method leveraging wavelet transformations within convolutional layers to overcome this challenge. This technique allows CNNs to maintain large receptive fields without a proportional increase in computational complexity.

Methodology

The core innovation lies in the application of wavelet transformations to convolutions. The technique involves applying wavelet convolutions, enabling multi-frequency analysis and enhancing the network's capacity to capture spatial hierarchies. Specifically, wavelet convolutions expand the receptive field by incorporating multi-frequency information, which is typically not accessible in standard convolutions. This approach integrates seamlessly into existing CNN architectures, offering versatility and ease of adoption.

The methodological robustness is underpinned by a detailed mathematical formulation of the wavelet convolution operations. These operations are defined such that they preserve essential properties required for efficient neural computation. Alongside the theoretical framework, the authors provide algorithmic details to facilitate practical implementation.

Results

The paper presents extensive empirical evaluations to substantiate the efficacy of the proposed method. Across various benchmarks, the wavelet convolution approach demonstrates superior performance in tasks such as image classification and object detection. Key datasets utilized include CIFAR-10, CIFAR-100, and ImageNet, where the proposed method consistently outperforms baseline models while maintaining computational efficiency.

Significant numerical results include:

• Improved classification accuracy: The wavelet convolution models achieve a notable increase in top-1 and top-5 accuracies across diverse datasets.
• Enhanced object detection performance: The method provides substantial improvements in mean Average Precision (mAP) metrics over standard convolution models.
• Computational efficiency: Despite the enlarged receptive fields, the method achieves comparable, if not reduced, computational overhead relative to state-of-the-art CNN architectures.

Implications and Future Directions

The implications of this research are manifold. From a practical perspective, the integration of wavelet convolutions can significantly enhance the performance of deep learning models in various applications, including but not limited to image processing, medical imaging, and remote sensing. Theoretically, this work bridges concepts from signal processing and neural networks, offering a rich avenue for further exploration.

Future developments may focus on:

• Extending the wavelet convolution framework to other neural network architectures such as Recurrent Neural Networks (RNNs) and Transformers.
• Investigating the implications of wavelet convolutions in unsupervised and semi-supervised learning contexts.
• Further optimizing the computational aspects to harness the full potential of hardware accelerations like GPUs and TPUs.

In summary, the paper "Wavelet Convolutions for Large Receptive Fields" delivers a substantial contribution to the field of neural network research, offering a novel solution to a longstanding challenge. The method's ability to enhance receptive fields while maintaining computational efficiency paves the way for more advanced and capable AI systems.