  We introduce a modality-agnostic neural compression algorithm based on a
functional view of data and parameterised as an Implicit Neural Representation
(INR). Bridging the gap between latent coding and sparsity, we obtain compact
latent representations non-linearly mapped to a soft gating mechanism. This
allows the specialisation of a shared INR network to each data item through
subnetwork selection. After obtaining a dataset of such latent representations,
we directly optimise the rate/distortion trade-off in a modality-agnostic space
using neural compression. Variational Compression of Implicit Neural
Representations (VC-INR) shows improved performance given the same
representational capacity pre quantisation while also outperforming previous
quantisation schemes used for other INR techniques. Our experiments demonstrate
strong results over a large set of diverse modalities using the same algorithm
without any modality-specific inductive biases. We show results on images,
climate data, 3D shapes and scenes as well as audio and video, introducing
VC-INR as the first INR-based method to outperform codecs as well-known and
diverse as JPEG 2000, MP3 and AVC/HEVC on their respective modalities.
