  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.
