Latent-shift: gradient of entropy helps neural codecs

End-to-end image/video codecs are getting competitive compared to traditional compression techniques that have been developed through decades of manual engineering efforts. These trainable codecs have many advantages over traditional techniques such as easy adaptation on perceptual distortion metrics and high performance on specific domains thanks to their learning ability. However, state of the art neural codecs does not take advantage of the existence of gradient of entropy in decoding device. In this paper, we theoretically show that gradient of entropy (available at decoder side) is correlated with the gradient of the reconstruction error (which is not available at decoder side). We then demonstrate experimentally that this gradient can be used on various compression methods, leading to a 1-2% rate savings for the same quality. Our method is orthogonal to other improvements and brings independent rate savings.