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.

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.

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.

Fast Kernel Scene Flow

In contrast to current state-of-the-art methods, such as NSFP [25], which employ deep implicit neural functions for modeling scene flow, we present a novel approach that utilizes classical kernel representations. This representation enables our approach to effectively handle dense lidar points while demonstrating exceptional computational efficiency -- compared to recent deep approaches -- achieved through the solution of a linear system. As a runtime optimization-based method, our model exhibits impressive generalizability across various out-of-distribution scenarios, achieving competitive performance on large-scale lidar datasets. We propose a new positional encoding-based kernel that demonstrates state-of-the-art performance in efficient lidar scene flow estimation on large-scale point clouds. An important highlight of our method is its near real-time performance (~150-170 ms) with dense lidar data (~8k-144k points), enabling a variety of practical applications in robotics and autonomous driving scenarios.

SeMoLi: What Moves Together Belongs Together

We tackle semi-supervised object detection based on motion cues. Recent results suggest that heuristic-based clustering methods in conjunction with object trackers can be used to pseudo-label instances of moving objects and use these as supervisory signals to train 3D object detectors in Lidar data without manual supervision. We re-think this approach and suggest that both, object detection, as well as motion-inspired pseudo-labeling, can be tackled in a data-driven manner. We leverage recent advances in scene flow estimation to obtain point trajectories from which we extract long-term, class-agnostic motion patterns. Revisiting correlation clustering in the context of message passing networks, we learn to group those motion patterns to cluster points to object instances. By estimating the full extent of the objects, we obtain per-scan 3D bounding boxes that we use to supervise a Lidar object detection network. Our method not only outperforms prior heuristic-based approaches (57.5 AP, +14 improvement over prior work), more importantly, we show we can pseudo-label and train object detectors across datasets.