The proof can be found in Chapter 27 of [6]. For the non-flat version, the update is similar to the mini-batch SGD except that we add small Gaussian noises to the particle models. In Section 4.2 of the main paper, we provide a comprehensive analysis of the performance concerning In the experiments presented in Tables 1 and 2 in the main paper, we train all models for 300 epochs using SGD, with a learning rate of 0.1 and a cosine schedule. For the baseline of the Deep-Ensemble, SGLD, SGVB and SGVB-LRT methods, we reproduce results following the hyper-parameters and processes as our flat versions. ImageNet: This is a large and challenging dataset with 1000 classes.

Multimodal human action recognition (HAR) leverages complementary sensors for activity classification. Beyond recognition, recent advances in large language models (LLMs) enable detailed descriptions and causal reasoning, motivating new tasks: human action understanding (HAU) and human action reasoning (HARn). However, most LLMs, especially large vision language models (LVLMs), struggle with non-RGB modalities such as depth, IMU, and mmWave due to the lack of large-scale data-caption resources. Existing HAR datasets mainly provide coarse data-label annotations, which are insufficient to capture fine-grained action dynamics needed for HAU and HARn. We consider two ground-truth pair types: (1) data label (discrete category) and (2) data caption (textual description). Naively generating captions from labels often lacks logical and spatiotemporal consistency. We introduce CUHK-X, a large-scale multimodal dataset and benchmark suite for HAR, HAU, and HARn. CUHK-X contains 58,445 samples covering 40 actions performed by 30 participants across two indoor environments. To improve caption consistency, we propose a prompt-based scene creation method that leverages LLMs to generate logically connected activity sequences, followed by human validation. CUHK-X includes three benchmarks with six evaluation tasks. Experiments report average accuracies of 76.52% (HAR), 40.76% (HAU), and 70.25% (HARn). CUHK-X aims to enable the community to apply and develop data-intensive learning methods for robust, multimodal human activity analysis. Project page and code: https://openaiotlab.github.io/CUHK-X/ and https://github.com/openaiotlab/CUHK-X.

Large Language Model (LLM) agents are emerging to transform daily life. However, existing LLM agents primarily follow a reactive paradigm, relying on explicit user instructions to initiate services, which increases both physical and cognitive workload. In this paper, we propose ProAgent, the first end-to-end proactive agent system that harnesses massive sensory contexts and LLM reasoning to deliver proactive assistance. ProAgent first employs a proactive-oriented context extraction approach with on-demand tiered perception to continuously sense the environment and derive hierarchical contexts that incorporate both sensory and persona cues. ProAgent then adopts a context-aware proactive reasoner to map these contexts to user needs and tool calls, providing proactive assistance. We implement ProAgent on Augmented Reality (AR) glasses with an edge server and extensively evaluate it on a real-world testbed, a public dataset, and through a user study. Results show that ProAgent achieves up to 33.4% higher proactive prediction accuracy, 16.8% higher tool-calling F1 score, and notable improvements in user satisfaction over state-of-the-art baselines, marking a significant step toward proactive assistants. A video demonstration of ProAgent is available at https://youtu.be/pRXZuzvrcVs.

The reliable application of deep learning models to software engineering tasks hinges on high-quality training data. Yet, large-scale repositories inevitably introduce noisy or mislabeled examples that degrade both accuracy and robustness. While Noise Label Learning (NLL) has been extensively studied in other fields, there are a few works that investigate NLL in Software Engineering (SE) and Large Language Models (LLMs) for SE tasks. In this work, we propose MANTRA, a Multi-stage Adaptive Noise TReAtment framework that embeds noise diagnosis and mitigation directly into the fine-tuning process of code-Pretrained Language Models (PTM) and code-LLMs. We first investigate the effect of noise at varying levels on convergence and loss trajectories of the models. Then we apply an adaptive dropout strategy guided by per-sample loss dynamics and Gaussian Mixture Model clustering to exclude persistently noisy points while preserving clean data. Applying to code summarization and commit intent classification, our experiments reveal that some LLMs are more sensitive to noise than others. However, with MANTRA, the performance of all models in both tasks is improved. MANTRA enables researchers and practitioners to reduce the impact of errors introduced by the dataset in training, saves time in data cleaning and processing, while maximizing the effect of fine-tuning.

Adversarial training is an effective method to improve the machine learning (ML) model robustness. Most existing studies typically consider the Rectified linear unit (ReLU) activation function and centralized training environments. In this paper, we study the ML model robustness using ten different activation functions through adversarial training in centralized environments and explore the ML model robustness in federal learning environments. In the centralized environment, we first propose an advanced adversarial training approach to improving the ML model robustness by incorporating model architecture change, soft labeling, simplified data augmentation, and varying learning rates. Then, we conduct extensive experiments on ten well-known activation functions in addition to ReLU to better understand how they impact the ML model robustness. Furthermore, we extend the proposed adversarial training approach to the federal learning environment, where both independent and identically distributed (IID) and non-IID data settings are considered. Our proposed centralized adversarial training approach achieves a natural and robust accuracy of 77.08% and 67.96%, respectively on CIFAR-10 against the fast gradient sign attacks. Experiments on ten activation functions reveal ReLU usually performs best. In the federated learning environment, however, the robust accuracy decreases significantly, especially on non-IID data. To address the significant performance drop in the non-IID data case, we introduce data sharing and achieve the natural and robust accuracy of 70.09% and 54.79%, respectively, surpassing the CalFAT algorithm, when 40% data sharing is used. That is, a proper percentage of data sharing can significantly improve the ML model robustness, which is useful to some real-world applications.

Large Language Models (LLMs) are increasingly used for educational support, yet their response quality varies depending on the language of interaction. This paper presents an automated multilingual pipeline for generating, solving, and evaluating math problems aligned with the German K-10 curriculum. We generated 628 math exercises and translated them into English, German, and Arabic. Three commercial LLMs (GPT-4o-mini, Gemini 2.5 Flash, and Qwen-plus) were prompted to produce step-by-step solutions in each language. A held-out panel of LLM judges, including Claude 3.5 Haiku, evaluated solution quality using a comparative framework. Results show a consistent gap, with English solutions consistently rated highest, and Arabic often ranked lower. These findings highlight persistent linguistic bias and the need for more equitable multilingual AI systems in education.

Recent progress in contact-rich robotic manipulation has been striking, yet most deployed systems remain confined to simple, scripted routines. One of the key barriers is the lack of motion planning algorithms that can provide verifiable guarantees for safety, efficiency and reliability. To address this, a family of algorithms called Constant-Time Motion Planning (CTMP) was introduced, which leverages a preprocessing phase to enable collision-free motion queries in a fixed, user-specified time budget (e.g., 10 milliseconds). However, existing CTMP methods do not explicitly incorporate the manipulation behaviors essential for object handling. To bridge this gap, we introduce the \textit{Behavioral Constant-Time Motion Planner} (B-CTMP), an algorithm that extends CTMP to solve a broad class of two-step manipulation tasks: (1) a collision-free motion to a behavior initiation state, followed by (2) execution of a manipulation behavior (such as grasping or insertion) to reach the goal. By precomputing compact data structures, B-CTMP guarantees constant-time query in mere milliseconds while ensuring completeness and successful task execution over a specified set of states. We evaluate B-CTMP on two canonical manipulation tasks in simulation, shelf picking and plug insertion,and demonstrate its effectiveness on a real robot. Our results show that B-CTMP unifies collision-free planning and object manipulation within a single constant-time framework, providing provable guarantees of speed and success for manipulation in semi-structured environments.