While conventional data are represented as discrete vectors, Implicit Neural Representations (INRs) utilize neural networks to represent data points as continuous functions. By incorporating a shared network that maps latent vectors to individual functions, one can model the distribution of functional data, which has proven effective in many applications, such as learning 3D shapes, surface reflectance, and operators. However, the infinite-dimensional nature of these representations makes them prone to overfitting, necessitating sufficient regularization. Naïve regularization methods -- those commonly used with discrete vector representations -- may enforce smoothness to increase robustness but result in a loss of data fidelity due to improper handling of function coordinates. To overcome these challenges, we start by interpreting the mapping from latent variables to INRs as a parametrization of a Riemannian manifold. We then recognize that preserving geometric quantities -- such as distances and angles -- between the latent space and the data manifold is crucial. As a result, we obtain a manifold with minimal intrinsic curvature, leading to robust representations while maintaining high-quality data fitting. Our experiments on various data modalities demonstrate that our method effectively discovers a well-structured latent space, leading to robust data representations even for challenging datasets, such as those that are small or noisy.

Abstract The advancements of the Neural Radiance Field (NeRF) and its variants have demonstrated remarkable capabilities in generating photo‐realistic novel views from a small set of input images. While recent works suggest various techniques and model architectures that enhance speed or reconstruction quality, little attention is paid to exploring the RGB color space of input images. In this paper, we propose a universal color transform module that can maximally harness the captured evidence for the neural networks at hand. The color transform module utilizes an encoder‐decoder framework that maps the RGB color space into a new latent space, enhancing the expressiveness of the input domain. We attach the encoder and the decoder at the input and output of a NeRF model of choice, respectively, and jointly optimize them to maintain the cycle consistency of the proposed transform, in addition to minimizing the reconstruction errors in the feature domain. Our comprehensive experiments demonstrate that the learned color space can significantly improve the quality of reconstructions compared to the conventional RGB representation. Its benefits are particularly pronounced in challenging scenarios characterized by low‐light environments and scenes with low‐textured regions. The proposed color transform pushes the boundaries of limitations in the input domain and offers a promising avenue for advancing the reconstruction capabilities of various neural representations. Source code is available at https://github.com/sangminkim-99/ColorTransformModule .