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This letter presents a continuous probabilistic modeling methodology for spatial point cloud data using finite Gaussian Mixture Models (GMMs) where the number of components are adapted based on the scene complexity. Few hierarchical and…

Previous studies have demonstrated the effectiveness of point-based neural models on the point cloud analysis task. However, there remains a crucial issue on producing the efficient input embedding for raw point coordinates. Moreover,…

In recent years, parametric representations of point clouds have been widely applied in tasks such as memory-efficient mapping and multi-robot collaboration. Highly adaptive models, like spline surfaces or quadrics, are computationally…

Foundation models for point cloud data have recently grown in capability, often leveraging extensive representation learning from language or vision. In this work, we take a more controlled approach by introducing a lightweight…

Self-attention in Transformers is typically implemented as $\mathrm{softmax}(QK^\top/\sqrt{d})V$, where $Q=XW_Q$, $K=XW_K$, and $V=XW_V$ are learned linear projections of the input $X$. We ask whether these learned projections are…

Language and vision-language models have shown impressive performance across a wide range of tasks, but their internal mechanisms remain only partly understood. In this work, we study how individual attention heads in text-generative models…

Transformer plays an increasingly important role in various computer vision areas and remarkable achievements have also been made in point cloud analysis. Since they mainly focus on point-wise transformer, an adaptive channel encoding…

Transformer-based models have demonstrated considerable potential for source code modeling tasks in software engineering. However, they are limited by their dependence solely on automatic self-attention weight learning mechanisms. Previous…

As 3D point clouds become the prevailing shape representation in computer vision, generating high-quality point clouds remains a challenging problem. Flow-based models have shown strong potential due to exact likelihood estimation and…

While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this…

Point clouds produced by 3D sensors are often sparse and noisy, posing challenges for tasks requiring dense and high-fidelity 3D representations. Prior work has explored both implicit feature-based upsampling and distance-function learning…

General point clouds have been increasingly investigated for different tasks, and recently Transformer-based networks are proposed for point cloud analysis. However, there are barely related works for medical point clouds, which are…

Transformer networks have achieved remarkable success across diverse domains, leveraging a variety of architectural innovations, including residual connections. However, traditional residual connections, which simply sum the outputs of…

Recent years have witnessed the increasing application of place recognition in various environments, such as city roads, large buildings, and a mix of indoor and outdoor places. This task, however, still remains challenging due to the…

Self-attention modules have demonstrated remarkable capabilities in capturing long-range relationships and improving the performance of point cloud tasks. However, point cloud objects are typically characterized by complex, disordered, and…

Pairwise dot product-based attention allows Transformers to exchange information between tokens in an input-dependent way, and is key to their success across diverse applications in language and vision. However, a typical Transformer model…

Transformer-based architectures have become the prevailing backbone of large language models. However, the quadratic time and memory complexity of self-attention remains a fundamental obstacle to efficient long-context modeling. To address…

The modeling of high-dimensional spatio-temporal processes presents a fundamental dichotomy between the probabilistic rigor of classical geostatistics and the flexible, high-capacity representations of deep learning. While Gaussian…

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…

Notwithstanding the prominent performance achieved in various applications, point cloud recognition models have often suffered from natural corruptions and adversarial perturbations. In this paper, we delve into boosting the general…