  Most neural compression models are trained on large datasets of images or
videos in order to generalize to unseen data. Such generalization typically
requires large and expressive architectures with a high decoding complexity.
Here we introduce C3, a neural compression method with strong rate-distortion
(RD) performance that instead overfits a small model to each image or video
separately. The resulting decoding complexity of C3 can be an order of
magnitude lower than neural baselines with similar RD performance. C3 builds on
COOL-CHIC (Ladune et al.) and makes several simple and effective improvements
for images. We further develop new methodology to apply C3 to videos. On the
CLIC2020 image benchmark, we match the RD performance of VTM, the reference
implementation of the H.266 codec, with less than 3k MACs/pixel for decoding.
On the UVG video benchmark, we match the RD performance of the Video
Compression Transformer (Mentzer et al.), a well-established neural video
codec, with less than 5k MACs/pixel for decoding.
