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.

Self-Supervised Multi-Frame Neural Scene Flow

Neural Scene Flow Prior (NSFP) and Fast Neural Scene Flow (FNSF) have shown remarkable adaptability in the context of large out-of-distribution autonomous driving. Despite their success, the underlying reasons for their astonishing generalization capabilities remain unclear. Our research addresses this gap by examining the generalization capabilities of NSFP through the lens of uniform stability, revealing that its performance is inversely proportional to the number of input point clouds. This finding sheds light on NSFP's effectiveness in handling large-scale point cloud scene flow estimation tasks. Motivated by such theoretical insights, we further explore the improvement of scene flow estimation by leveraging historical point clouds across multiple frames, which inherently increases the number of point clouds. Consequently, we propose a simple and effective method for multi-frame point cloud scene flow estimation, along with a theoretical evaluation of its generalization abilities. Our analysis confirms that the proposed method maintains a limited generalization error, suggesting that adding multiple frames to the scene flow optimization process does not detract from its generalizability. Extensive experimental results on large-scale autonomous driving Waymo Open and Argoverse lidar datasets demonstrate that the proposed method achieves state-of-the-art performance.

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.

Convolutional Initialization for Data-Efficient Vision Transformers

Training vision transformer networks on small datasets poses challenges. In contrast, convolutional neural networks (CNNs) can achieve state-of-the-art performance by leveraging their architectural inductive bias. In this paper, we investigate whether this inductive bias can be reinterpreted as an initialization bias within a vision transformer network. Our approach is motivated by the finding that random impulse filters can achieve almost comparable performance to learned filters in CNNs. We introduce a novel initialization strategy for transformer networks that can achieve comparable performance to CNNs on small datasets while preserving its architectural flexibility.

Multi-Body Neural Scene Flow

The test-time optimization of scene flow - using a coordinate network as a neural prior - has gained popularity due to its simplicity, lack of dataset bias, and state-of-the-art performance. We observe, however, that although coordinate networks capture general motions by implicitly regularizing the scene flow predictions to be spatially smooth, the neural prior by itself is unable to identify the underlying multi-body rigid motions present in real-world data. To address this, we show that multi-body rigidity can be achieved without the cumbersome and brittle strategy of constraining the $SE(3)$ parameters of each rigid body as done in previous works. This is achieved by regularizing the scene flow optimization to encourage isometry in flow predictions for rigid bodies. This strategy enables multi-body rigidity in scene flow while maintaining a continuous flow field, hence allowing dense long-term scene flow integration across a sequence of point clouds. We conduct extensive experiments on real-world datasets and demonstrate that our approach outperforms the state-of-the-art in 3D scene flow and long-term point-wise 4D trajectory prediction. The code is available at: \href{https://github.com/kavisha725/MBNSF}{https://github.com/kavisha725/MBNSF}.

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.

Fast Neural Scene Flow

Neural Scene Flow Prior (NSFP) is of significant interest to the vision community due to its inherent robustness to out-of-distribution (OOD) effects and its ability to deal with dense lidar points. The approach utilizes a coordinate neural network to estimate scene flow at runtime, without any training. However, it is up to 100 times slower than current state-of-the-art learning methods. In other applications such as image, video, and radiance function reconstruction innovations in speeding up the runtime performance of coordinate networks have centered upon architectural changes. In this paper, we demonstrate that scene flow is different -- with the dominant computational bottleneck stemming from the loss function itself (i.e., Chamfer distance). Further, we rediscover the distance transform (DT) as an efficient, correspondence-free loss function that dramatically speeds up the runtime optimization. Our fast neural scene flow (FNSF) approach reports for the first time real-time performance comparable to learning methods, without any training or OOD bias on two of the largest open autonomous driving (AV) lidar datasets Waymo Open and Argoverse.

Trading Positional Complexity vs. Deepness in Coordinate Networks

It is well noted that coordinate-based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been mainly studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. In addition, we argue that employing a more complex positional encoding -- that scales exponentially with the number of modes -- requires only a linear (rather than deep) coordinate function to achieve comparable performance. Counter-intuitively, we demonstrate that trading positional embedding complexity for network deepness is orders of magnitude faster than current state-of-the-art; despite the additional embedding complexity. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice.

Neural Scene Flow Prior

Before the deep learning revolution, many perception algorithms were based on runtime optimization in conjunction with a strong prior/regularization penalty. A prime example of this in computer vision is optical and scene flow. Supervised learning has largely displaced the need for explicit regularization. Instead, they rely on large amounts of labeled data to capture prior statistics, which are not always readily available for many problems. Although optimization is employed to learn the neural network, the weights of this network are frozen at runtime. As a result, these learning solutions are domain-specific and do not generalize well to other statistically different scenarios. This paper revisits the scene flow problem that relies predominantly on runtime optimization and strong regularization. A central innovation here is the inclusion of a neural scene flow prior, which uses the architecture of neural networks as a new type of implicit regularizer. Unlike learning-based scene flow methods, optimization occurs at runtime, and our approach needs no offline datasets -- making it ideal for deployment in new environments such as autonomous driving. We show that an architecture based exclusively on multilayer perceptrons (MLPs) can be used as a scene flow prior. Our method attains competitive -- if not better -- results on scene flow benchmarks. Also, our neural prior's implicit and continuous scene flow representation allows us to estimate dense long-term correspondences across a sequence of point clouds. The dense motion information is represented by scene flow fields where points can be propagated through time by integrating motion vectors. We demonstrate such a capability by accumulating a sequence of lidar point clouds.

Deterministic PointNetLK for Generalized Registration

There has been remarkable progress in the application of deep learning to 3D point cloud registration in recent years. Despite their success, these approaches tend to have poor generalization properties when attempting to align unseen point clouds at test time. PointNetLK has proven the exception to this rule by leveraging the intrinsic generalization properties of the Lucas & Kanade (LK) image alignment algorithm to point cloud registration. The approach relies heavily upon the estimation of a gradient through finite differentiation -- a strategy that is inherently ill-conditioned and highly sensitive to the step-size choice. To avoid these problems, we propose a deterministic PointNetLK method that uses analytical gradients. We also develop several strategies to improve large-volume point cloud processing. We compare our approach to canonical PointNetLK and other state-of-the-art methods and demonstrate how our approach provides accurate, reliable registration with high fidelity. Extended experiments on noisy, sparse, and partial point clouds depict the utility of our approach for many real-world scenarios. Further, the decomposition of the Jacobian matrix affords the reuse of feature embeddings for alternate warp functions.