  Recent vision transformers, large-kernel CNNs and MLPs have attained
remarkable successes in broad vision tasks thanks to their effective
information fusion in the global scope. However, their efficient deployments,
especially on mobile devices, still suffer from noteworthy challenges due to
the heavy computational costs of self-attention mechanisms, large kernels, or
fully connected layers. In this work, we apply conventional convolution theorem
to deep learning for addressing this and reveal that adaptive frequency filters
can serve as efficient global token mixers. With this insight, we propose
Adaptive Frequency Filtering (AFF) token mixer. This neural operator transfers
a latent representation to the frequency domain via a Fourier transform and
performs semantic-adaptive frequency filtering via an elementwise
multiplication, which mathematically equals to a token mixing operation in the
original latent space with a dynamic convolution kernel as large as the spatial
resolution of this latent representation. We take AFF token mixers as primary
neural operators to build a lightweight neural network, dubbed AFFNet.
Extensive experiments demonstrate the effectiveness of our proposed AFF token
mixer and show that AFFNet achieve superior accuracy and efficiency trade-offs
compared to other lightweight network designs on broad visual tasks, including
visual recognition and dense prediction tasks.
