SoPE: Spherical Coordinate-Based Positional Embedding for Enhancing Spatial Perception of 3D LVLMs

3D Large Vision-Language Models (3D LVLMs) built upon Large Language Models (LLMs) have achieved remarkable progress across various multimodal tasks. However, their inherited position-dependent modeling mechanism, Rotary Position Embedding (RoPE), remains suboptimal for 3D multimodal understanding. The vanilla RoPE formulation fails to preserve essential three-dimensional spatial structures when encoding 3D tokens, and its relative distance computation overlooks angular dependencies, hindering the model's ability to capture directional variations in visual representations. To overcome these limitations, we introduce Spherical Coordinate-based Positional Embedding (SoPE). Our method maps point-cloud token indices into a 3D spherical coordinate space, enabling unified modeling of spatial locations and directional angles. This formulation preserves the inherent geometric structure of point-cloud data, enhances spatial awareness, and yields more consistent and expressive geometric representations for multimodal learning. In addition, we introduce a multi-scale frequency mixing strategy to fuse feature information across different frequency domains. Experimental results on multiple 3D scene benchmarks validate the effectiveness of our approach, while real-world deployment experiments further demonstrate its strong generalization capability.

C^2ROPE: Causal Continuous Rotary Positional Encoding for 3D Large Multimodal-Models Reasoning

Recent advances in 3D Large Multimodal Models (LMMs) built on Large Language Models (LLMs) have established the alignment of 3D visual features with LLM representations as the dominant paradigm. However, the inherited Rotary Position Embedding (RoPE) introduces limitations for multimodal processing. Specifically, applying 1D temporal positional indices disrupts the continuity of visual features along the column dimension, resulting in spatial locality loss. Moreover, RoPE follows the prior that temporally closer image tokens are more causally related, leading to long-term decay in attention allocation and causing the model to progressively neglect earlier visual tokens as the sequence length increases. To address these issues, we propose C^2RoPE, an improved RoPE that explicitly models local spatial Continuity and spatial Causal relationships for visual processing. C^2RoPE introduces a spatio-temporal continuous positional embedding mechanism for visual tokens. It first integrates 1D temporal positions with Cartesian-based spatial coordinates to construct a triplet hybrid positional index, and then employs a frequency allocation strategy to encode spatio-temporal positional information across the three index components. Additionally, we introduce Chebyshev Causal Masking, which determines causal dependencies by computing the Chebyshev distance of image tokens in 2D space. Evaluation results across various benchmarks, including 3D scene reasoning and 3D visual question answering, demonstrate C^2RoPE's effectiveness. The code is be available at https://github.com/ErikZ719/C2RoPE.

Navigating Uncertainties in Machine Learning for Structural Dynamics: A Comprehensive Review of Probabilistic and Non-Probabilistic Approaches in Forward and Inverse Problems

In the era of big data, machine learning (ML) has become a powerful tool in various fields, notably impacting structural dynamics. ML algorithms offer advantages by modeling physical phenomena based on data, even in the absence of underlying mechanisms. However, uncertainties such as measurement noise and modeling errors can compromise the reliability of ML predictions, highlighting the need for effective uncertainty awareness to enhance prediction robustness. This paper presents a comprehensive review on navigating uncertainties in ML, categorizing uncertainty-aware approaches into probabilistic methods (including Bayesian and frequentist perspectives) and non-probabilistic methods (such as interval learning and fuzzy learning). Bayesian neural networks, known for their uncertainty quantification and nonlinear mapping capabilities, are emphasized for their superior performance and potential. The review covers various techniques and methodologies for addressing uncertainties in ML, discussing fundamentals and implementation procedures of each method. While providing a concise overview of fundamental concepts, the paper refrains from in-depth critical explanations. Strengths and limitations of each approach are examined, along with their applications in structural dynamic forward problems like response prediction, sensitivity assessment, and reliability analysis, and inverse problems like system identification, model updating, and damage identification. Additionally, the review identifies research gaps and suggests future directions for investigations, aiming to provide comprehensive insights to the research community. By offering an extensive overview of both probabilistic and non-probabilistic approaches, this review aims to assist researchers and practitioners in making informed decisions when utilizing ML techniques to address uncertainties in structural dynamic problems.