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Few-shot Implicit Function Generation via Equivariance

Suizhi Huang, Xingyi Yang, Hongtao Lu, Xinchao Wang

TL;DR

The paper addresses the challenge of generating diverse yet functionally consistent INR weights from limited data by introducing Few-shot Implicit Function Generation and the EquiGen framework. EquiGen leverages permutation-based weight-space equivariance through a three-stage pipeline: an equivariant encoder trained with contrastive learning, an equivariance-guided diffusion model, and controlled subspace perturbations for diversity during few-shot adaptation. Across 2D INR image datasets and 3D ShapeNet INRs, EquiGen delivers higher quality and greater diversity than strong baselines, demonstrating the value of exploiting weight-space symmetries for data-efficient INR generation. This work enables practical, data-efficient exploration of INR weight spaces with potential downstream benefits for 3D shape generation and flexible implicit representations.

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.

Few-shot Implicit Function Generation via Equivariance

TL;DR

The paper addresses the challenge of generating diverse yet functionally consistent INR weights from limited data by introducing Few-shot Implicit Function Generation and the EquiGen framework. EquiGen leverages permutation-based weight-space equivariance through a three-stage pipeline: an equivariant encoder trained with contrastive learning, an equivariance-guided diffusion model, and controlled subspace perturbations for diversity during few-shot adaptation. Across 2D INR image datasets and 3D ShapeNet INRs, EquiGen delivers higher quality and greater diversity than strong baselines, demonstrating the value of exploiting weight-space symmetries for data-efficient INR generation. This work enables practical, data-efficient exploration of INR weight spaces with potential downstream benefits for 3D shape generation and flexible implicit representations.

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.
Paper Structure (18 sections, 7 equations, 8 figures, 4 tables)

This paper contains 18 sections, 7 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Implicit Neural Representation
  4. Equivariant Architectures
  5. Neural Network Weight Generation
  6. Preliminaries
  7. Problem Definition
  8. Equivariance and Equivariant architecture
  9. Methodology
  10. Overview
  11. Equivariant Encoder Pre-training
  12. Equivariance Guided Diffusion
  13. Few-shot Fine-tuning
  14. Experiments
  15. Experimental Setup
  16. ...and 3 more sections

Figures (8)

  • Figure 1: Illustration of the Few-shot Implicit Function Generation setting with 3D INR data examples. The goal is to generate diverse INR weights from limited target samples. Source samples (top) show previously observed INRs of diverse shape categories. In practice, only limited target samples (bottom left) are available for training. The framework aims to learn a generator that can produce diverse generated samples (right) despite the limited training data. This setting addresses the practical scenario where only a few examples of new shapes are available for training.
  • Figure 2: Overview of our EquiGen framework. The method consists of three stages: (1) Equivariant Encoder Pre-training through contrastive learning with smooth and INR-based augmentations, (2) Distribution Modeling via a diffusion process conditioned on learned equivariant features, and (3) Few-shot Adaptation using equivariant subspace disturbance for diverse weight generation. Our framework leverages the inherent equivariance of neural network weights to address both generalization and mode collapse challenges.
  • Figure 3: Equivariant architecture $E_\phi$ aims to map weights from the same equivariance group to similar representations, creating a structured latent space that captures the inherent symmetries of neural networks. By leveraging this equivariant subspace, we can implement a controlled disturbance strategy that sample diverse equivariant features while maintaining class consistency.
  • Figure 4: To optimize the equivariant feature extraction, we seek permutations that minimize the weight matrix's total variation. This smoothing operation reduces abrupt discontinuities in the weight space, facilitates more effective learning of inherent equivariant properties by starting from an optimized point. The smoother weight manifold (bottom) enables better equivariant feature capture compared to the original space (up).
  • Figure 5: Visualizations of generated ShapeNet-INRs from the few-shot airplane example. The outputs exhibit diverse shape variations while preserving the airplane category characteristics.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Definition 1: Few-shot INR Generation