Self-Similarity Priors: Neural Collages as Differentiable Fractal Representations

TL;DR

This paper introduces Neural Collages, a novel neural approach to model self-similarity in data, enabling fast compression, generation, and fractal art creation by leveraging structured self-referential transformations.

Contribution

The work presents Neural Collages, a new class of implicit operators using hypernetworks to efficiently learn and utilize self-similarity for various data tasks.

Findings

Neural Collages outperform traditional self-similarity algorithms in speed.

They achieve competitive compression rates with implicit methods.

Applications include fractal art and deep generative modeling.

Abstract

Many patterns in nature exhibit self-similarity: they can be compactly described via self-referential transformations. Said patterns commonly appear in natural and artificial objects, such as molecules, shorelines, galaxies and even images. In this work, we investigate the role of learning in the automated discovery of self-similarity and in its utilization for downstream tasks. To this end, we design a novel class of implicit operators, Neural Collages, which (1) represent data as the parameters of a self-referential, structured transformation, and (2) employ hypernetworks to amortize the cost of finding these parameters to a single forward pass. We investigate how to leverage the representations produced by Neural Collages in various tasks, including data compression and generation. Neural Collages image compressors are orders of magnitude faster than other self-similarity-based algorithms during encoding and offer compression rates competitive with implicit methods. Finally, we showcase applications of Neural Collages for fractal art and as deep generative models.