Until quite recently, the backbone of nearly every state-of-the-art computer vision model has been the 2D convolution. At its core, a 2D convolution simultaneously mixes information across both the spatial and channel dimensions of a representation. Many recent computer vision architectures consist of sequences of isotropic blocks that disentangle the spatial and channel-mixing components. This separation of the operations allows us to more closely juxtapose the effects of spatial and channel mixing in deep learning. In this paper, we take an initial step towards garnering a deeper understanding of the roles of these mixing operations. Through our experiments and analysis, we discover that on both classical (ResNet) and cutting-edge (ConvMixer) models, we can reach nearly the same level of classification performance by and leaving the spatial mixers at their random initializations. Furthermore, we show that models with random, fixed spatial mixing are naturally more robust to adversarial perturbations. Lastly, we show that this phenomenon extends past the classification regime, as such models can also decode pixel-shuffled images.

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.

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.

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. A key component in the transformer architecture is the softmax attention block, enabling transformers to evaluate the importance of individual input elements during output generation. This feature facilitates an efficient method to attend to diverse input elements throughout training, allowing transformers to effectively capture spatial dependencies within sequential data.

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.

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.

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.

Implicit neural representations have emerged as a powerful technique for encoding complex continuous multidimensional signals as neural networks, enabling a wide range of applications in computer vision, robotics, and geometry. While Adam is commonly used for training due to its stochastic proficiency, it entails lengthy training durations. To address this, we explore alternative optimization techniques for accelerated training without sacrificing accuracy. Traditional second-order optimizers like L-BFGS are suboptimal in stochastic settings, making them unsuitable for large-scale data sets. Instead, we propose stochastic training using curvature-aware diagonal preconditioners, showcasing their effectiveness across various signal modalities such as images, shape reconstruction, and Neural Radiance Fields (NeRF).

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.

Recently, neural networks utilizing periodic activation functions have been proven to demonstrate superior performance in vision tasks compared to traditional ReLU-activated networks. However, there is still a limited understanding of the underlying reasons for this improved performance. In this paper, we aim to address this gap by providing a theoretical understanding of periodically activated networks through an analysis of their Neural Tangent Kernel (NTK). We derive bounds on the minimum eigenvalue of their NTK in the finite width setting, using a fairly general network architecture which requires only one wide layer that grows at least linearly with the number of data samples. Our findings indicate that periodically activated networks are \textit{notably more well-behaved}, from the NTK perspective, than ReLU activated networks. Additionally, we give an application to the memorization capacity of such networks and verify our theoretical predictions empirically. Our study offers a deeper understanding of the properties of periodically activated neural networks and their potential in the field of deep learning.