Modified K-means Algorithm with Local Optimality Guarantees

The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its local optimality guarantees. In this paper, we first present conditions under which the K-means algorithm converges to a locally optimal solution. Based on this, we propose simple modifications to the K-means algorithm which ensure local optimality in both the continuous and discrete sense, with the same computational complexity as the original K-means algorithm. As the dissimilarity measure, we consider a general Bregman divergence, which is an extension of the squared Euclidean distance often used in the K-means algorithm. Numerical experiments confirm that the K-means algorithm does not always find a locally optimal solution in practice, while our proposed methods provide improved locally optimal solutions with reduced clustering loss. Our code is available at https://github.com/lmingyi/LO-K-means.

TAMO:Fine-Grained Root Cause Analysis via Tool-Assisted LLM Agent with Multi-Modality Observation Data

With the development of distributed systems, microservices and cloud native technologies have become central to modern enterprise software development. Despite bringing significant advantages, these technologies also increase system complexity and operational challenges. Traditional root cause analysis (RCA) struggles to achieve automated fault response, heavily relying on manual intervention. In recent years, large language models (LLMs) have made breakthroughs in contextual inference and domain knowledge integration, providing new solutions for Artificial Intelligence for Operations (AIOps). However, Existing LLM-based approaches face three key challenges: text input constraints, dynamic service dependency hallucinations, and context window limitations. To address these issues, we propose a tool-assisted LLM agent with multi-modality observation data, namely TAMO, for fine-grained RCA. It unifies multi-modal observational data into time-aligned representations to extract consistent features and employs specialized root cause localization and fault classification tools for perceiving the contextual environment. This approach overcomes the limitations of LLM in handling real-time changing service dependencies and raw observational data and guides LLM to generate repair strategies aligned with system contexts by structuring key information into a prompt. Experimental results show that TAMO performs well in root cause analysis when dealing with public datasets characterized by heterogeneity and common fault types, demonstrating its effectiveness.

Unity is Power: Semi-Asynchronous Collaborative Training of Large-Scale Models with Structured Pruning in Resource-Limited Clients

In this work, we study to release the potential of massive heterogeneous weak computing power to collaboratively train large-scale models on dispersed datasets. In order to improve both efficiency and accuracy in resource-adaptive collaborative learning, we take the first step to consider the \textit{unstructured pruning}, \textit{varying submodel architectures}, \textit{knowledge loss}, and \textit{straggler} challenges simultaneously. We propose a novel semi-asynchronous collaborative training framework, namely ${Co\text{-}S}^2{P}$, with data distribution-aware structured pruning and cross-block knowledge transfer mechanism to address the above concerns. Furthermore, we provide theoretical proof that ${Co\text{-}S}^2{P}$ can achieve asymptotic optimal convergence rate of $O(1/\sqrt{N^*EQ})$. Finally, we conduct extensive experiments on a real-world hardware testbed, in which 16 heterogeneous Jetson devices can be united to train large-scale models with parameters up to 0.11 billion. The experimental results demonstrate that $Co\text{-}S^2P$ improves accuracy by up to 8.8\% and resource utilization by up to 1.2$\times$ compared to state-of-the-art methods, while reducing memory consumption by approximately 22\% and training time by about 24\% on all resource-limited devices.

Thing2Reality: Transforming 2D Content into Conditioned Multiviews and 3D Gaussian Objects for XR Communication

During remote communication, participants often share both digital and physical content, such as product designs, digital assets, and environments, to enhance mutual understanding. Recent advances in augmented communication have facilitated users to swiftly create and share digital 2D copies of physical objects from video feeds into a shared space. However, conventional 2D representations of digital objects restricts users' ability to spatially reference items in a shared immersive environment. To address this, we propose Thing2Reality, an Extended Reality (XR) communication platform that enhances spontaneous discussions of both digital and physical items during remote sessions. With Thing2Reality, users can quickly materialize ideas or physical objects in immersive environments and share them as conditioned multiview renderings or 3D Gaussians. Thing2Reality enables users to interact with remote objects or discuss concepts in a collaborative manner. Our user study revealed that the ability to interact with and manipulate 3D representations of objects significantly enhances the efficiency of discussions, with the potential to augment discussion of 2D artifacts.