Multilayer-perceptrons (MLP) are known to struggle with learning functions of high-frequencies, and in particular cases with wide frequency bands. We present a spatially adaptive progressive encoding (SAPE) scheme for input signals of MLP networks, which enables them to better fit a wide range of frequencies without sacrificing training stability or requiring any domain specific preprocessing. SAPE gradually unmasks signal components with increasing frequencies as a function of time and space. The progressive exposure of frequencies is monitored by a feedback loop throughout the neural optimization process, allowing changes to propagate at different rates among local spatial portions of the signal space. We demonstrate the advantage of SAPE on a variety of domains and applications, including regression of low dimensional signals and images, representation learning of occupancy networks, and a geometric task of mesh transfer between 3D shapes.

In this paper, we aim to create generalizable and controllable neural signed distance fields (SDFs) that represent clothed humans from monocular depth observations. Recent advances in deep learning, especially neural implicit representations, have enabled human shape reconstruction and controllable avatar generation from different sensor inputs. However, to generate realistic cloth deformations from novel input poses, watertight meshes or dense full-body scans are usually needed as inputs. Furthermore, due to the difficulty of effectively modeling pose-dependent cloth deformations for diverse body shapes and cloth types, existing approaches resort to per-subject/cloth-type optimization from scratch, which is computationally expensive. In contrast, we propose an approach that can quickly generate realistic clothed human avatars, represented as controllable neural SDFs, given only monocular depth images.

The supplementary material is organized as follows. First, we prove Proposition 1 and Theorem 1. We then provide some details on the overall communication complexity of FedRZObl. Lastly, we present some additional numerical experiments. In this section we prove Proposition 1, and some preliminary lemmas.

Neural implicit functions have demonstrated significant importance in various areas such as computer vision, graphics. Their advantages include the ability to represent complex shapes and scenes with high fidelity, smooth interpolation capabilities, and continuous representations. Despite these benefits, the development and analysis of implicit functions have been limited by the lack of comprehensive datasets and the substantial computational resources required for their implementation and evaluation. To address these challenges, we introduce Implicit-Zoo: a large-scale dataset requiring thousands of GPU training days designed to facilitate research and development in this field. Our dataset includes diverse 2D and 3D scenes, such as CIFAR-10, ImageNet-1K, and Cityscapes for 2D image tasks, and the OmniObject3D dataset for 3D vision tasks. We ensure high quality through strict checks, refining or filtering out low-quality data. Using Implicit-Zoo, we showcase two immediate benefits as it enables to: (1) learn token locations for transformer models; (2) Directly regress 3D cameras poses of 2D images with respect to NeRF models. This in turn leads to an \emph{improved performance} in all three task of image classification, semantic segmentation, and 3D pose regression -- thereby unlocking new avenues for research.

The problem of adversarial defenses for image classification, where the goal is to robustify a classifier against adversarial examples, is considered.