Exploring the Meaningfulness of Nearest Neighbor Search in High-Dimensional Space

Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these vector can exceed several thousands easily. Despite the nearest neighbor search (NNS) over these dense high dimensional vectors have been widely used for retrieval augmented generation (RAG) and many other applications, the effectiveness of NNS in such a high-dimensional space remains uncertain, given the possible challenge caused by the "curse of dimensionality." To address above question, in this paper, we conduct extensive NNS studies with different distance functions, such as $L_1$ distance, $L_2$ distance and angular-distance, across diverse embedding datasets, of varied types, dimensionality and modality. Our aim is to investigate factors influencing the meaningfulness of NNS. Our experiments reveal that high-dimensional text embeddings exhibit increased resilience as dimensionality rises to higher levels when compared to random vectors. This resilience suggests that text embeddings are less affected to the "curse of dimensionality," resulting in more meaningful NNS outcomes for practical use. Additionally, the choice of distance function has minimal impact on the relevance of NNS. Our study shows the effectiveness of the embedding-based data representation method and can offer opportunity for further optimization of dense vector-related applications.

SGW-based Multi-Task Learning in Vision Tasks

Multi-task-learning(MTL) is a multi-target optimization task. Neural networks try to realize each target using a shared interpretative space within MTL. However, as the scale of datasets expands and the complexity of tasks increases, knowledge sharing becomes increasingly challenging. In this paper, we first re-examine previous cross-attention MTL methods from the perspective of noise. We theoretically analyze this issue and identify it as a flaw in the cross-attention mechanism. To address this issue, we propose an information bottleneck knowledge extraction module (KEM). This module aims to reduce inter-task interference by constraining the flow of information, thereby reducing computational complexity. Furthermore, we have employed neural collapse to stabilize the knowledge-selection process. That is, before input to KEM, we projected the features into ETF space. This mapping makes our method more robust. We implemented and conducted comparative experiments with this method on multiple datasets. The results demonstrate that our approach significantly outperforms existing methods in multi-task learning.

Scalable Geometric Fracture Assembly via Co-creation Space among Assemblers

Geometric fracture assembly presents a challenging practical task in archaeology and 3D computer vision. Previous methods have focused solely on assembling fragments based on semantic information, which has limited the quantity of objects that can be effectively assembled. Therefore, there is a need to develop a scalable framework for geometric fracture assembly without relying on semantic information. To improve the effectiveness of assembling geometric fractures without semantic information, we propose a co-creation space comprising several assemblers capable of gradually and unambiguously assembling fractures. Additionally, we introduce a novel loss function, i.e., the geometric-based collision loss, to address collision issues during the fracture assembly process and enhance the results. Our framework exhibits better performance on both PartNet and Breaking Bad datasets compared to existing state-of-the-art frameworks. Extensive experiments and quantitative comparisons demonstrate the effectiveness of our proposed framework, which features linear computational complexity, enhanced abstraction, and improved generalization. Our code is publicly available at https://github.com/Ruiyuan-Zhang/CCS.

Score-PA: Score-based 3D Part Assembly

Autonomous 3D part assembly is a challenging task in the areas of robotics and 3D computer vision. This task aims to assemble individual components into a complete shape without relying on predefined instructions. In this paper, we formulate this task from a novel generative perspective, introducing the Score-based 3D Part Assembly framework (Score-PA) for 3D part assembly. Knowing that score-based methods are typically time-consuming during the inference stage. To address this issue, we introduce a novel algorithm called the Fast Predictor-Corrector Sampler (FPC) that accelerates the sampling process within the framework. We employ various metrics to assess assembly quality and diversity, and our evaluation results demonstrate that our algorithm outperforms existing state-of-the-art approaches. We release our code at https://github.com/J-F-Cheng/Score-PA_Score-based-3D-Part-Assembly.