Few-shot Implicit Function Generation via Equivariance

TL;DR

This paper introduces EquiGen, a novel framework for generating diverse implicit neural representations from limited data by leveraging weight permutation equivariance, enabling functional diversity with few examples.

Contribution

The paper proposes a new few-shot INR generation method using equivariance principles, contrastive learning, and diffusion processes to produce diverse, functionally consistent INRs.

Findings

Effective diversity in INR weights with few examples

Preservation of functional properties in generated INRs

Outperforms baseline methods in 2D and 3D tasks

Abstract

Implicit Neural Representations (INRs) have emerged as a powerful framework for representing continuous signals. However, generating diverse INR weights remains challenging due to limited training data. We introduce Few-shot Implicit Function Generation, a new problem setup that aims to generate diverse yet functionally consistent INR weights from only a few examples. This is challenging because even for the same signal, the optimal INRs can vary significantly depending on their initializations. To tackle this, we propose EquiGen, a framework that can generate new INRs from limited data. The core idea is that functionally similar networks can be transformed into one another through weight permutations, forming an equivariance group. By projecting these weights into an equivariant latent space, we enable diverse generation within these groups, even with few examples. EquiGen implements this through an equivariant encoder trained via contrastive learning and smooth augmentation, an equivariance-guided diffusion process, and controlled perturbations in the equivariant subspace. Experiments on 2D image and 3D shape INR datasets demonstrate that our approach effectively generates diverse INR weights while preserving their functional properties in few-shot scenarios.