In this paper, we present a unified algorithm for stochastic optimization that makes use of a "momentum" term; in other words, the stochastic gradient depends not only on the current true gradient of the objective function, but also on the true gradient at the previous iteration. Our formulation includes the Stochastic Heavy Ball (SHB) and the Stochastic Nesterov Accelerated Gradient (SNAG) algorithms as special cases. In addition, in our formulation, the momentum term is allowed to vary as a function of time (i.e., the iteration counter). The assumptions on the stochastic gradient are the most general in the literature, in that it can be biased, and have a conditional variance that grows in an unbounded fashion as a function of time. This last feature is crucial in order to make the theory applicable to "zero-order" methods, where the gradient is estimated using just two function evaluations. We present a set of sufficient conditions for the convergence of the unified algorithm. These conditions are natural generalizations of the familiar Robbins-Monro and Kiefer-Wolfowitz-Blum conditions for standard stochastic gradient descent. We also analyze another method from the literature for the SHB algorithm with a time-varying momentum parameter, and show that it is impracticable.

Safety, reliability, and user trust are crucial in human-robot interaction (HRI) where the robots must address hazards in real-time. This study presents hazard driven low-level control strategies implemented in robot-assisted dressing (RAD) scenarios where hazards like garment snags and user discomfort in real-time can affect task performance and user safety. The proposed control mechanisms include: (1) Garment Snagging Control Strategy, which detects excessive forces and either seeks user intervention via a chatbot or autonomously adjusts its trajectory, and (2) User Discomfort/Pain Mitigation Strategy, which dynamically reduces velocity based on user feedback and aborts the task if necessary. We used physical dressing trials in order to evaluate these control strategies. Results confirm that integrating force monitoring with user feedback improves safety and task continuity. The findings emphasise the need for hybrid approaches that balance autonomous intervention, user involvement, and controlled task termination, supported by bi-directional interaction and real-time user-driven adaptability, paving the way for more responsive and personalised HRI systems.

The advancement of Multi-modal Pre-training highlights the necessity for a robust Multi-Modal Knowledge Graph (MMKG) representation learning framework. This framework is crucial for integrating structured knowledge into multi-modal Large Language Models (LLMs) at scale, aiming to alleviate issues like knowledge misconceptions and multi-modal hallucinations. In this work, to evaluate models' ability to accurately embed entities within MMKGs, we focus on two widely researched tasks: Multi-modal Knowledge Graph Completion (MKGC) and Multi-modal Entity Alignment (MMEA). Building on this foundation, we propose a novel SNAG method that utilizes a Transformer-based architecture equipped with modality-level noise masking for the robust integration of multi-modal entity features in KGs. By incorporating specific training objectives for both MKGC and MMEA, our approach achieves SOTA performance across a total of ten datasets (three for MKGC and seven for MEMA), demonstrating its robustness and versatility. Besides, SNAG can not only function as a standalone model but also enhance other existing methods, providing stable performance improvements. Our code and data are available at: https://github.com/zjukg/SNAG.

Fox News Flash top headlines are here. Check out what's clicking on Foxnews.com. A total overhaul of bus routes for Louisville's school district turned into a logistical meltdown on the first day of classes because the new plan created too steep a learning curve for the system, district officials said Friday, forcing administrators to cancel two days of classes and leaving parents and state legislators fuming. It took just one disastrous day for Jefferson County Public Schools leaders to completely reexamine the transportation plan for Kentucky's largest district, which serves 96,000 students. Some kids arrived home hours late on Wednesday, and classes were canceled Thursday and Friday.

Purchases you make through the links below may earn us and our publishing partners a commission. "Breath of the Wild" fans, rejoice: The Blood Moon rises once again. The next game in Nintendo's "The Legend of Zelda" franchise, "The Legend of Zelda: Tears of the Kingdom" arrives tomorrow. Make smart choices without hours of googling. In "Tears of the Kingdom," players will return to Hyrule and follow up on Link's story in the wake of "Breath of the Wild."

Adam-type algorithms have become a preferred choice for optimisation in the deep learning setting, however, despite success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type algorithms (called UAdam). This is equipped with a general form of the second-order moment, which makes it possible to include Adam and its variants as special cases, such as NAdam, AMSGrad, AdaBound, AdaFom, and Adan. This is supported by a rigorous convergence analysis of UAdam in the non-convex stochastic setting, showing that UAdam converges to the neighborhood of stationary points with the rate of $\mathcal{O}(1/T)$. Furthermore, the size of neighborhood decreases as $\beta$ increases. Importantly, our analysis only requires the first-order momentum factor to be close enough to 1, without any restrictions on the second-order momentum factor. Theoretical results also show that vanilla Adam can converge by selecting appropriate hyperparameters, which provides a theoretical guarantee for the analysis, applications, and further developments of the whole class of Adam-type algorithms.

We prove that various stochastic gradient descent methods, including the stochastic gradient descent (SGD), stochastic heavy-ball (SHB), and stochastic Nesterov's accelerated gradient (SNAG) methods, almost surely avoid any strict saddle manifold. To the best of our knowledge, this is the first time such results are obtained for SHB and SNAG methods. Moreover, our analysis expands upon previous studies on SGD by removing the need for bounded gradients of the objective function and uniformly bounded noise. Instead, we introduce a more practical local boundedness assumption for the noisy gradient, which is naturally satisfied in empirical risk minimization problems typically seen in training of neural networks. Keywords: Stochastic gradient descent, stochastic heavy-ball, stochastic Nesterov's accelerated gradient, almost sure saddle avoidance

A few bright spots remain in the autonomous vehicle industry even amid macroeconomic headwinds that have nearly shut off the spigot of venture capital and led to further consolidation. Helm.ai, a startup developing software designed for advanced driver assistance systems, autonomous driving and robotics, is one of them. The Menlo Park, California-based startup recently raised $31 million in a Series C round led by Freeman Group, just one year after it snagged $26 million in venture funding. This latest round, which included ACVC Partners, Amplo and strategic investors Honda Motor Co., Goodyear Ventures and Sungwoo Hitech, has pushed Helm.ai's valuation to $431 million. Brandon Freeman, founder of the Freeman Group, is joining the Helm.ai board of directors as part of this financing.

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NASA's Perseverance Mars rover has run into another snag on its mission to find evidence of ancient microbial life.