  It is common practice in deep learning to represent a measurement of the
world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying
signal represented by these measurements is often continuous, e.g. the scene
depicted in an image. A powerful continuous alternative is then to represent
these measurements using an implicit neural representation, a neural function
trained to output the appropriate measurement value for any input spatial
location. In this paper, we take this idea to its next level: what would it
take to perform deep learning on these functions instead, treating them as
data? In this context we refer to the data as functa, and propose a framework
for deep learning on functa. This view presents a number of challenges around
efficient conversion from data to functa, compact representation of functa, and
effectively solving downstream tasks on functa. We outline a recipe to overcome
these challenges and apply it to a wide range of data modalities including
images, 3D shapes, neural radiance fields (NeRF) and data on manifolds. We
demonstrate that this approach has various compelling properties across data
modalities, in particular on the canonical tasks of generative modeling, data
imputation, novel view synthesis and classification. Code:
https://github.com/deepmind/functa
