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Motivated by the recent trend towards the usage of larger receptive fields for more context-aware neural networks in vision applications, we aim to investigate how large these receptive fields really need to be. To facilitate such study, several challenges need to be addressed, most importantly: (i) We need to provide an effective way for models to learn large filters (potentially as large as the input data) without increasing their memory consumption during training or inference, (ii) the study of filter sizes has to be decoupled from other effects such as the network width or number of learnable parameters, and (iii) the employed convolution operation should be a plug-and-play module that can replace any conventional convolution in a Convolutional Neural Network (CNN) and allow for an efficient implementation in current frameworks. To facilitate such models, we propose to learn not spatial but frequency representations of filter weights as neural implicit functions, such that even infinitely large filters can be parameterized by only a few learnable weights. The resulting neural implicit frequency CNNs are the first models to achieve results on par with the state-of-the-art on large image classification benchmarks while executing convolutions solely in the frequency domain and can be employed within any CNN architecture. They allow us to provide an extensive analysis of the learned receptive fields. Interestingly, our analysis shows that, although the proposed networks could learn very large convolution kernels, the learned filters practically translate into well-localized and relatively small convolution kernels in the spatial domain.
Fix your downsampling ASAP! Be natively more robust via Aliasing and Spectral Artifact free Pooling
(2023)
Convolutional neural networks encode images through a sequence of convolutions, normalizations and non-linearities as well as downsampling operations into potentially strong semantic embeddings. Yet, previous work showed that even slight mistakes during sampling, leading to aliasing, can be directly attributed to the networks' lack in robustness. To address such issues and facilitate simpler and faster adversarial training, [12] recently proposed FLC pooling, a method for provably alias-free downsampling - in theory. In this work, we conduct a further analysis through the lens of signal processing and find that such current pooling methods, which address aliasing in the frequency domain, are still prone to spectral leakage artifacts. Hence, we propose aliasing and spectral artifact-free pooling, short ASAP. While only introducing a few modifications to FLC pooling, networks using ASAP as downsampling method exhibit higher native robustness against common corruptions, a property that FLC pooling was missing. ASAP also increases native robustness against adversarial attacks on high and low resolution data while maintaining similar clean accuracy or even outperforming the baseline.
State-of-the-art models for pixel-wise prediction tasks such as image restoration, image segmentation, or disparity estimation, involve several stages of data resampling, in which the resolution of feature maps is first reduced to aggregate information and then sequentially increased to generate a high-resolution output. Several previous works have investigated the effect of artifacts that are invoked during downsampling and diverse cures have been proposed that facilitate to improve prediction stability and even robustness for image classification. However, equally relevant, artifacts that arise during upsampling have been less discussed. This is significantly relevant as upsampling and downsampling approaches face fundamentally different challenges. While during downsampling, aliases and artifacts can be reduced by blurring feature maps, the emergence of fine details is crucial during upsampling. Blurring is therefore not an option and dedicated operations need to be considered. In this work, we are the first to explore the relevance of context during upsampling by employing convolutional upsampling operations with increasing kernel size while keeping the encoder unchanged. We find that increased kernel sizes can in general improve the prediction stability in tasks such as image restoration or image segmentation, while a block that allows for a combination of small-size kernels for fine details and large-size kernels for artifact removal and increased context yields the best results.