From data to functa: Your data point is a function and you can treat it like one

TL;DR

This paper introduces a novel framework for deep learning directly on implicit neural representations of data, called functa, enabling improved generative modeling, data imputation, view synthesis, and classification across various data types.

Contribution

It proposes a comprehensive method to perform deep learning on neural function data, addressing challenges in conversion, representation, and task execution, applicable to multiple data modalities.

Findings

Effective deep learning on functa improves generative modeling.

The approach enhances data imputation and view synthesis capabilities.

Applicable across images, 3D shapes, NeRF, and manifolds.

Abstract

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