Self-Similarity Priors: Neural Collages as Differentiable Fractal Representations
This work addresses the challenge of efficiently leveraging self-similarity in natural and artificial patterns for tasks like data compression and generation, representing an incremental advancement in neural representation methods.
The paper tackled the problem of automated discovery and utilization of self-similarity in data by introducing Neural Collages, which represent data as parameters of self-referential transformations using hypernetworks. The result includes image compressors that are orders of magnitude faster than other self-similarity-based algorithms during encoding and offer competitive compression rates with implicit methods.
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.