Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

A.1 Coordinate Systems and Transformation To achieve spatial synchronization between different sensors, vehicle-vehicle-UAV collaboration requires using sensor parameter information to perform coordinate system transformations. The relationships between the coordinate systems are illustrated in Fig. S 1. Figure 1: Relationship between coordinate systems. The pixel coordinate system refers to a two-dimensional coordinate system defined on the image plane, typically represented as (u,v), with units in pixels. In this system, the origin is located at the top-left corner of the image, the u-axis points to the right along the horizontal direction, and the v-axis points downward along the vertical direction. This coordinate system is used to describe the position of points on the two-dimensional image captured by the camera.

By sharing information across multiple agents, collaborative perception helps autonomous vehicles mitigate occlusions and improve overall perception accuracy. While most previous work focus on vehicle-to-vehicle and vehicle-to-infrastructure collaboration, with limited attention to aerial perspectives provided by UAVs, which uniquely offer dynamic, top-down views to alleviate occlusions and monitor large-scale interactive environments. A major reason for this is the lack of highquality datasets for aerial-ground collaborative scenarios. To bridge this gap, we present AGC-Drive, the first large-scale real-world dataset for Aerial-Ground Cooperative 3D perception. The data collection platform consists of two vehicles, each equipped with five cameras and one LiDAR sensor, and one UAV carrying a forward-facing camera and a LiDAR sensor, enabling comprehensive multi-view and multi-agent perception.

Collaborative visual perception methods have gained widespread attention in the autonomous driving community in recent years due to their ability to address sensor limitation problems. However, the absence of explicit depth information often makes it difficult for camera-based perception systems, e.g., 3D object detection, to generate accurate predictions. To alleviate the ambiguity in depth estimation, we propose RayFusion, a ray-based fusion method for collaborative visual perception. Using ray occupancy information from collaborators, RayFusion reduces redundancy and false positive predictions along camera rays, enhancing the detection performance of purely camera-based collaborative perception systems. Comprehensive experiments show that our method consistently outperforms existing stateof-the-art models, substantially advancing the performance of collaborative visual perception.

Dense 3D scene reconstruction from an ordered sequence or unordered image collections is a critical step when bringing research in computer vision into practical scenarios. Following the paradigm introduced by DUSt3R, which unifies an image pair densely into a shared coordinate system, subsequent methods maintain an implicit memory to achieve dense 3D reconstruction from more images. However, such implicit memory is limited in capacity and may suffer from information loss of earlier frames. We propose Point3R, an online framework targeting dense streaming 3D reconstruction. To be specific, we maintain an explicit spatial pointer memory directly associated with the 3D structure of the current scene. Each pointer in this memory is assigned a specific 3D position and aggregates scene information nearby in the global coordinate system into a changing spatial feature. Information extracted from the latest frame interacts explicitly with this pointer memory, enabling dense integration of the current observation into the global coordinate system. We design a 3D hierarchical position embedding to promote this interaction and design a simple yet effective fusion mechanism to ensure that our pointer memory is uniform and efficient. Our method achieves competitive or state-of-the-art performance on various tasks with low training costs.

Dense 3D scene reconstruction from an ordered sequence or unordered image collections is a critical step when bringing research in computer vision into practical scenarios. Following the paradigm introduced by DUSt3R, which unifies an image pair densely into a shared coordinate system, subsequent methods maintain an implicit memory to achieve dense 3D reconstruction from more images. However, such implicit memory is limited in capacity and may suffer from information loss of earlier frames. We propose Point3R, an online framework targeting dense streaming 3D reconstruction. To be specific, we maintain an explicit spatial pointer memory directly associated with the 3D structure of the current scene. Each pointer in this memory is assigned a specific 3D position and aggregates scene information nearby in the global coordinate system into a changing spatial feature. Information extracted from the latest frame interacts explicitly with this pointer memory, enabling dense integration of the current observation into the global coordinate system. We design a 3D hierarchical position embedding to promote this interaction and design a simple yet effective fusion mechanism to ensure that our pointer memory is uniform and efficient. Our method achieves competitive or state-of-the-art performance on various tasks with low training costs.

Accurate modeling of aerodynamic loads is essential for understanding and predicting the responses of complex structural systems. However, these models often rely on simplifications of the true physical forces, introducing assumptions that can limit their accuracy. Validating such models becomes particularly challenging in the presence of noisy or incomplete data. To address this, we introduce a probabilistic physics-informed machine learning approach designed to reconstruct the underlying aerodynamic loads from noisy measurements of structural dynamic responses. The model avoids overfitting, eliminates the need for regularization schemes, and allows for the use of heterogeneous and multi-fidelity data during the training process. The efficacy of the approach is demonstrated through the reconstruction of aerodynamic loads on the Great Belt East Bridge, simulated under a linear unsteady assumption. Results show a strong agreement between true and predicted loads, particularly related to root mean squared errors, magnitude, phase angle and peak values of the signals. The method for load reconstructing holds broad applicability, such as modeling validation, future load estimation, and structural damage prognosis.

The Adam optimization algorithm has proven remarkably effective for optimization problems across machine learning and even traditional tasks in geometry processing. At the same time, the development of equivariant methods, which preserve their output under the action of rotation or some other transformation, has proven to be important for geometry problems across these domains. In this work, we observe that Adam -- when treated as a function that maps initial conditions to optimized results -- is not rotation equivariant for vector-valued parameters due to per-coordinate moment updates. This leads to significant artifacts and biases in practice. We propose to resolve this deficiency with VectorAdam, a simple modification which makes Adam rotation-equivariant by accounting for the vector structure of optimization variables. We demonstrate this approach on problems in machine learning and traditional geometric optimization, showing that equivariant VectorAdam resolves the artifacts and biases of traditional Adam when applied to vector-valued data, with equivalent or even improved rates of convergence.