DARB-Splatting: Generalizing Splatting with Decaying Anisotropic Radial Basis Functions

Splatting-based 3D reconstruction methods have gained popularity with the advent of 3D Gaussian Splatting, efficiently synthesizing high-quality novel views. These methods commonly resort to using exponential family functions, such as the Gaussian function, as reconstruction kernels due to their anisotropic nature, ease of projection, and differentiability in rasterization. However, the field remains restricted to variations within the exponential family, leaving generalized reconstruction kernels largely underexplored, partly due to the lack of easy integrability in 3D to 2D projections. In this light, we show that a class of decaying anisotropic radial basis functions (DARBFs), which are non-negative functions of the Mahalanobis distance, supports splatting by approximating the Gaussian function's closed-form integration advantage. With this fresh perspective, we demonstrate up to 34% faster convergence during training and a 15% reduction in memory consumption across various DARB reconstruction kernels, while maintaining comparable PSNR, SSIM, and LPIPS results. We will make the code available.

Object Agnostic 3D Lifting in Space and Time

We present a spatio-temporal perspective on category-agnostic 3D lifting of 2D keypoints over a temporal sequence. Our approach differs from existing state-of-the-art methods that are either: (i) object agnostic, but can only operate on individual frames, or (ii) can model space-time dependencies, but are only designed to work with a single object category. Our approach is grounded in two core principles. First, when there is a lack of data about an object, general information from similar objects can be leveraged for better performance. Second, while temporal information is important, the most critical information is in immediate temporal proximity. These two principles allow us to outperform current state-of-the-art methods on per-frame and per-sequence metrics for a variety of objects. Lastly, we release a new synthetic dataset containing 3D skeletons and motion sequences of a diverse set animals. Dataset and code will be made publicly available.

Rethinking Softmax: Self-Attention with Polynomial Activations

This paper challenges the conventional belief that softmax attention in transformers is effective primarily because it generates a probability distribution for attention allocation. Instead, we theoretically show that its success lies in its ability to implicitly regularize the Frobenius norm of the attention matrix during training. We then explore alternative activations that regularize the Frobenius norm of the attention matrix, demonstrating that certain polynomial activations can achieve this effect, making them suitable for attention-based architectures. Empirical results indicate these activations perform comparably or better than softmax across various computer vision and language tasks, suggesting new possibilities for attention mechanisms beyond softmax.

Weight Conditioning for Smooth Optimization of Neural Networks

In this article, we introduce a novel normalization technique for neural network weight matrices, which we term weight conditioning. This approach aims to narrow the gap between the smallest and largest singular values of the weight matrices, resulting in better-conditioned matrices. The inspiration for this technique partially derives from numerical linear algebra, where well-conditioned matrices are known to facilitate stronger convergence results for iterative solvers. We provide a theoretical foundation demonstrating that our normalization technique smoothens the loss landscape, thereby enhancing convergence of stochastic gradient descent algorithms. Empirically, we validate our normalization across various neural network architectures, including Convolutional Neural Networks (CNNs), Vision Transformers (ViT), Neural Radiance Fields (NeRF), and 3D shape modeling. Our findings indicate that our normalization method is not only competitive but also outperforms existing weight normalization techniques from the literature.

Invertible Neural Warp for NeRF

This paper tackles the simultaneous optimization of pose and Neural Radiance Fields (NeRF). Departing from the conventional practice of using explicit global representations for camera pose, we propose a novel overparameterized representation that models camera poses as learnable rigid warp functions. We establish that modeling the rigid warps must be tightly coupled with constraints and regularization imposed. Specifically, we highlight the critical importance of enforcing invertibility when learning rigid warp functions via neural network and propose the use of an Invertible Neural Network (INN) coupled with a geometry-informed constraint for this purpose. We present results on synthetic and real-world datasets, and demonstrate that our approach outperforms existing baselines in terms of pose estimation and high-fidelity reconstruction due to enhanced optimization convergence.

Simultaneous Map and Object Reconstruction

In this paper, we present a method for dynamic surface reconstruction of large-scale urban scenes from LiDAR. Depth-based reconstructions tend to focus on small-scale objects or large-scale SLAM reconstructions that treat moving objects as outliers. We take a holistic perspective and optimize a compositional model of a dynamic scene that decomposes the world into rigidly moving objects and the background. To achieve this, we take inspiration from recent novel view synthesis methods and pose the reconstruction problem as a global optimization, minimizing the distance between our predicted surface and the input LiDAR scans. We show how this global optimization can be decomposed into registration and surface reconstruction steps, which are handled well by off-the-shelf methods without any re-training. By careful modeling of continuous-time motion, our reconstructions can compensate for the rolling shutter effects of rotating LiDAR sensors. This allows for the first system (to our knowledge) that properly motion compensates LiDAR scans for rigidly-moving objects, complementing widely-used techniques for motion compensation of static scenes. Beyond pursuing dynamic reconstruction as a goal in and of itself, we also show that such a system can be used to auto-label partially annotated sequences and produce ground truth annotation for hard-to-label problems such as depth completion and scene flow.

Structured Initialization for Attention in Vision Transformers

The training of vision transformer (ViT) networks on small-scale datasets poses a significant challenge. By contrast, convolutional neural networks (CNNs) have an architectural inductive bias enabling them to perform well on such problems. In this paper, we argue that the architectural bias inherent to CNNs can be reinterpreted as an initialization bias within ViT. This insight is significant as it empowers ViTs to perform equally well on small-scale problems while maintaining their flexibility for large-scale applications. Our inspiration for this ``structured'' initialization stems from our empirical observation that random impulse filters can achieve comparable performance to learned filters within CNNs. Our approach achieves state-of-the-art performance for data-efficient ViT learning across numerous benchmarks including CIFAR-10, CIFAR-100, and SVHN.

D'OH: Decoder-Only random Hypernetworks for Implicit Neural Representations

Deep implicit functions have been found to be an effective tool for efficiently encoding all manner of natural signals. Their attractiveness stems from their ability to compactly represent signals with little to no off-line training data. Instead, they leverage the implicit bias of deep networks to decouple hidden redundancies within the signal. In this paper, we explore the hypothesis that additional compression can be achieved by leveraging the redundancies that exist between layers. We propose to use a novel run-time decoder-only hypernetwork - that uses no offline training data - to better model this cross-layer parameter redundancy. Previous applications of hyper-networks with deep implicit functions have applied feed-forward encoder/decoder frameworks that rely on large offline datasets that do not generalize beyond the signals they were trained on. We instead present a strategy for the initialization of run-time deep implicit functions for single-instance signals through a Decoder-Only randomly projected Hypernetwork (D'OH). By directly changing the dimension of a latent code to approximate a target implicit neural architecture, we provide a natural way to vary the memory footprint of neural representations without the costly need for neural architecture search on a space of alternative low-rate structures.

Sine Activated Low-Rank Matrices for Parameter Efficient Learning

Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of parameters, striking a balance between compactness and performance. However, a common challenge has been the compromise between parameter efficiency and the accuracy of the model, where reduced parameters often lead to diminished accuracy compared to their full-rank counterparts. In this work, we propose a novel theoretical framework that integrates a sinusoidal function within the low-rank decomposition process. This approach not only preserves the benefits of the parameter efficiency characteristic of low-rank methods but also increases the decomposition's rank, thereby enhancing model accuracy. Our method proves to be an adaptable enhancement for existing low-rank models, as evidenced by its successful application in Vision Transformers (ViT), Large Language Models (LLMs), Neural Radiance Fields (NeRF), and 3D shape modeling. This demonstrates the wide-ranging potential and efficiency of our proposed technique.

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.