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arXiv 2501.01601cs.CVcs.AI
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基于等变性的少样本隐式函数生成

Few-shot Implicit Function Generation via Equivariance

Shanghai Jiao Tong University(上海交通大学);National University of Singapore(新加坡国立大学)

Suizhi Huang, Xingyi Yang, Hongtao Lu, Xinchao Wang

AI总结:

本文提出EquiGen框架,利用权重置换形成的等变群和等变潜在空间,在少样本条件下生成多样化且功能一致的隐式神经表示权重。

摘要:

隐式神经表示(INRs)已成为表示连续信号的强大框架。然而,由于训练数据有限,生成多样化的INR权重仍然具有挑战性。我们引入了少样本隐式函数生成这一新问题设置,旨在仅从少量示例中生成多样化且功能一致的INR权重。这一任务具有挑战性,因为即使对于同一信号,最优的INR也可能因其初始化不同而存在显著差异。为解决这一问题,我们提出了EquiGen框架,该框架能够从有限数据中生成新的INR。其核心思想是,功能相似的网络可以通过权重置换相互转换,从而形成一个等变群。通过将这些权重投影到等变潜在空间中,我们能够在这些群内实现多样化生成,即使只有少量示例。EquiGen通过以下方式实现这一目标:一个经由对比学习和平滑增强训练的等变编码器、一个等变性引导的扩散过程,以及在等变子空间中的受控扰动。在2D图像和3D形状INR数据集上的实验表明,我们的方法在少样本场景下能够有效生成多样化的INR权重,同时保持其功能属性。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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