From Activation to Initialization: Scaling Insights for Optimizing Neural Fields

In the realm of computer vision, Neural Fields have gained prominence as a contemporary tool harnessing neural networks for signal representation. Despite the remarkable progress in adapting these networks to solve a variety of problems, the field still lacks a comprehensive theoretical framework. This article aims to address this gap by delving into the intricate interplay between initialization and activation, providing a foundational basis for the robust optimization of Neural Fields. Our theoretical insights reveal a deep-seated connection among network initialization, architectural choices, and the optimization process, emphasizing the need for a holistic approach when designing cutting-edge Neural Fields.

Backpropagation-free Network for 3D Test-time Adaptation

Real-world systems often encounter new data over time, which leads to experiencing target domain shifts. Existing Test-Time Adaptation (TTA) methods tend to apply computationally heavy and memory-intensive backpropagation-based approaches to handle this. Here, we propose a novel method that uses a backpropagation-free approach for TTA for the specific case of 3D data. Our model uses a two-stream architecture to maintain knowledge about the source domain as well as complementary target-domain-specific information. The backpropagation-free property of our model helps address the well-known forgetting problem and mitigates the error accumulation issue. The proposed method also eliminates the need for the usually noisy process of pseudo-labeling and reliance on costly self-supervised training. Moreover, our method leverages subspace learning, effectively reducing the distribution variance between the two domains. Furthermore, the source-domain-specific and the target-domain-specific streams are aligned using a novel entropy-based adaptive fusion strategy. Extensive experiments on popular benchmarks demonstrate the effectiveness of our method. The code will be available at https://github.com/abie-e/BFTT3D.

ViewFusion: Towards Multi-View Consistency via Interpolated Denoising

Novel-view synthesis through diffusion models has demonstrated remarkable potential for generating diverse and high-quality images. Yet, the independent process of image generation in these prevailing methods leads to challenges in maintaining multiple-view consistency. To address this, we introduce ViewFusion, a novel, training-free algorithm that can be seamlessly integrated into existing pre-trained diffusion models. Our approach adopts an auto-regressive method that implicitly leverages previously generated views as context for the next view generation, ensuring robust multi-view consistency during the novel-view generation process. Through a diffusion process that fuses known-view information via interpolated denoising, our framework successfully extends single-view conditioned models to work in multiple-view conditional settings without any additional fine-tuning. Extensive experimental results demonstrate the effectiveness of ViewFusion in generating consistent and detailed novel views.

A Sampling Theory Perspective on Activations for Implicit Neural Representations

Implicit Neural Representations (INRs) have gained popularity for encoding signals as compact, differentiable entities. While commonly using techniques like Fourier positional encodings or non-traditional activation functions (e.g., Gaussian, sinusoid, or wavelets) to capture high-frequency content, their properties lack exploration within a unified theoretical framework. Addressing this gap, we conduct a comprehensive analysis of these activations from a sampling theory perspective. Our investigation reveals that sinc activations, previously unused in conjunction with INRs, are theoretically optimal for signal encoding. Additionally, we establish a connection between dynamical systems and INRs, leveraging sampling theory to bridge these two paradigms.

LumiNet: The Bright Side of Perceptual Knowledge Distillation

In knowledge distillation research, feature-based methods have dominated due to their ability to effectively tap into extensive teacher models. In contrast, logit-based approaches are considered to be less adept at extracting hidden 'dark knowledge' from teachers. To bridge this gap, we present LumiNet, a novel knowledge-transfer algorithm designed to enhance logit-based distillation. We introduce a perception matrix that aims to recalibrate logits through adjustments based on the model's representation capability. By meticulously analyzing intra-class dynamics, LumiNet reconstructs more granular inter-class relationships, enabling the student model to learn a richer breadth of knowledge. Both teacher and student models are mapped onto this refined matrix, with the student's goal being to minimize representational discrepancies. Rigorous testing on benchmark datasets (CIFAR-100, ImageNet, and MSCOCO) attests to LumiNet's efficacy, revealing its competitive edge over leading feature-based methods. Moreover, in exploring the realm of transfer learning, we assess how effectively the student model, trained using our method, adapts to downstream tasks. Notably, when applied to Tiny ImageNet, the transferred features exhibit remarkable performance, further underscoring LumiNet's versatility and robustness in diverse settings. With LumiNet, we hope to steer the research discourse towards a renewed interest in the latent capabilities of logit-based knowledge distillation.

Robust Point Cloud Processing through Positional Embedding

End-to-end trained per-point embeddings are an essential ingredient of any state-of-the-art 3D point cloud processing such as detection or alignment. Methods like PointNet, or the more recent point cloud transformer -- and its variants -- all employ learned per-point embeddings. Despite impressive performance, such approaches are sensitive to out-of-distribution (OOD) noise and outliers. In this paper, we explore the role of an analytical per-point embedding based on the criterion of bandwidth. The concept of bandwidth enables us to draw connections with an alternate per-point embedding -- positional embedding, particularly random Fourier features. We present compelling robust results across downstream tasks such as point cloud classification and registration with several categories of OOD noise.

Curvature-Aware Training for Coordinate Networks

Coordinate networks are widely used in computer vision due to their ability to represent signals as compressed, continuous entities. However, training these networks with first-order optimizers can be slow, hindering their use in real-time applications. Recent works have opted for shallow voxel-based representations to achieve faster training, but this sacrifices memory efficiency. This work proposes a solution that leverages second-order optimization methods to significantly reduce training times for coordinate networks while maintaining their compressibility. Experiments demonstrate the effectiveness of this approach on various signal modalities, such as audio, images, videos, shape reconstruction, and neural radiance fields.

BLiRF-RF: Bandlimited Radiance Fields for Dynamic Scene Modeling

Reasoning the 3D structure of a non-rigid dynamic scene from a single moving camera is an under-constrained problem. Inspired by the remarkable progress of neural radiance fields (NeRFs) in photo-realistic novel view synthesis of static scenes, extensions have been proposed for dynamic settings. These methods heavily rely on neural priors in order to regularize the problem. In this work, we take a step back and reinvestigate how current implementations may entail deleterious effects, including limited expressiveness, entanglement of light and density fields, and sub-optimal motion localization. As a remedy, we advocate for a bridge between classic non-rigid-structure-from-motion (\nrsfm) and NeRF, enabling the well-studied priors of the former to constrain the latter. To this end, we propose a framework that factorizes time and space by formulating a scene as a composition of bandlimited, high-dimensional signals. We demonstrate compelling results across complex dynamic scenes that involve changes in lighting, texture and long-range dynamics.

On the effectiveness of neural priors in modeling dynamical systems

Modelling dynamical systems is an integral component for understanding the natural world. To this end, neural networks are becoming an increasingly popular candidate owing to their ability to learn complex functions from large amounts of data. Despite this recent progress, there has not been an adequate discussion on the architectural regularization that neural networks offer when learning such systems, hindering their efficient usage. In this paper, we initiate a discussion in this direction using coordinate networks as a test bed. We interpret dynamical systems and coordinate networks from a signal processing lens, and show that simple coordinate networks with few layers can be used to solve multiple problems in modelling dynamical systems, without any explicit regularizers.

BaLi-RF: Bandlimited Radiance Fields for Dynamic Scene Modeling

Reasoning the 3D structure of a non-rigid dynamic scene from a single moving camera is an under-constrained problem. Inspired by the remarkable progress of neural radiance fields (NeRFs) in photo-realistic novel view synthesis of static scenes, extensions have been proposed for dynamic settings. These methods heavily rely on neural priors in order to regularize the problem. In this work, we take a step back and reinvestigate how current implementations may entail deleterious effects, including limited expressiveness, entanglement of light and density fields, and sub-optimal motion localization. As a remedy, we advocate for a bridge between classic non-rigid-structure-from-motion (\nrsfm) and NeRF, enabling the well-studied priors of the former to constrain the latter. To this end, we propose a framework that factorizes time and space by formulating a scene as a composition of bandlimited, high-dimensional signals. We demonstrate compelling results across complex dynamic scenes that involve changes in lighting, texture and long-range dynamics.