Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify breakpoints in piecewise polynomial regression. The algorithm updates the breakpoints to minimize the error by exploring the neighborhood of each breakpoint. It has a fast convergence rate and stability to find optimal breakpoints. Moreover, it can determine the optimal number of breakpoints. The computational results for real and synthetic data show that its accuracy is better than any existing methods. The real-world datasets demonstrate that breakpoints through the proposed algorithm provide valuable data information.

We present Points2Plans, a framework for composable planning with a relational dynamics model that enables robots to solve long-horizon manipulation tasks from partial-view point clouds. Given a language instruction and a point cloud of the scene, our framework initiates a hierarchical planning procedure, whereby a language model generates a high-level plan and a sampling-based planner produces constraint-satisfying continuous parameters for manipulation primitives sequenced according to the high-level plan. Key to our approach is the use of a relational dynamics model as a unifying interface between the continuous and symbolic representations of states and actions, thus facilitating language-driven planning from high-dimensional perceptual input such as point clouds. Whereas previous relational dynamics models require training on datasets of multi-step manipulation scenarios that align with the intended test scenarios, Points2Plans uses only single-step simulated training data while generalizing zero-shot to a variable number of steps during real-world evaluations. We evaluate our approach on tasks involving geometric reasoning, multi-object interactions, and occluded object reasoning in both simulated and real-world settings. Results demonstrate that Points2Plans offers strong generalization to unseen long-horizon tasks in the real world, where it solves over 85% of evaluated tasks while the next best baseline solves only 50%. Qualitative demonstrations of our approach operating on a mobile manipulator platform are made available at sites.google.com/stanford.edu/points2plans.

In a conventional Federated Learning framework, client selection for training typically involves the random sampling of a subset of clients in each iteration. However, this random selection often leads to disparate performance among clients, raising concerns regarding fairness, particularly in applications where equitable outcomes are crucial, such as in medical or financial machine learning tasks. This disparity typically becomes more pronounced with the advent of performance-centric client sampling techniques. This paper introduces two novel methods, namely SUBTRUNC and UNIONFL, designed to address the limitations of random client selection. Both approaches utilize submodular function maximization to achieve more balanced models. By modifying the facility location problem, they aim to mitigate the fairness concerns associated with random selection. SUBTRUNC leverages client loss information to diversify solutions, while UNIONFL relies on historical client selection data to ensure a more equitable performance of the final model. Moreover, these algorithms are accompanied by robust theoretical guarantees regarding convergence under reasonable assumptions. The efficacy of these methods is demonstrated through extensive evaluations across heterogeneous scenarios, revealing significant improvements in fairness as measured by a client dissimilarity metric.

Advancements in chip design and manufacturing have enabled the processing of complex tasks such as deep learning and natural language processing, paving the way for the development of artificial general intelligence (AGI). AI, on the other hand, can be leveraged to innovate and streamline semiconductor technology from planning and implementation to manufacturing. In this paper, we present \textit{Intelligent OPC Engineer Assistant}, an AI/LLM-powered methodology designed to solve the core manufacturing-aware optimization problem known as optical proximity correction (OPC). The methodology involves a reinforcement learning-based OPC recipe search and a customized multi-modal agent system for recipe summarization. Experiments demonstrate that our methodology can efficiently build OPC recipes on various chip designs with specially handled design topologies, a task that typically requires the full-time effort of OPC engineers with years of experience.

Machine Learning (ML), as described by Mitchell et al. (1990), is a multidisciplinary subfield of Artificial Intelligence (AI) focused on developing and implementing algorithms and statistical models that enable computer systems to perform data-driven tasks or make predictions through "leveraging data" and iterative learning processes. This data-driven approach guides the design of ML algorithms, allowing them to grasp the distributions and structures within datasets and unveil correlations that elude traditional mathematical and statistical methods. Professionals in data-related fields, such as data scientists and ML engineers, can engage in autonomous decision-making based on data and benefit from cutting-edge predictions generated by modern ML models. In recent decades, ML has significantly reshaped various industries and gained widespread popularity in academia due to its exceptional predictive capabilities. As summarized by Jordan and Mitchell (2015), ML has made significant contributions in various fields, including robotics, autonomous driving, language processing, and computer vision. The medical and healthcare industry, as suggested by Kononenko (2001) and Qayyum et al. (2020), is increasingly adopting ML for applications such as medical image analysis and clinical treatments. Furthermore, ML models have significantly improved personalization and targeting, marketing strategy, and customer engagement in the marketing sector, as summarized by Ma and Sun (2020). Guerra and Castelli (2021) present the ML innovations in the banking sector, particularly in the analysis of liquidity risks, bank risks, and credit risks. Additionally, there is a growing trend in adopting ML models in the insurance sector and among actuarial researchers and industry practitioners, as evidenced by recent literature.

As an emerging technology, digital twin (DT) can provide real-time status and dynamic topology mapping for Internet of Things (IoT) devices. However, DT and its implementation within industrial IoT networks necessitates substantial, distributed data support, which often leads to ``data silos'' and raises privacy concerns. To address these issues, we develop a dynamic resource scheduling algorithm tailored for the asynchronous federated learning (FL)-based lightweight DT empowered IoT network. Specifically, our approach aims to minimize a multi-objective function that encompasses both energy consumption and latency by optimizing IoT device selection and transmit power control, subject to FL model performance constraints. We utilize the Lyapunov method to decouple the formulated problem into a series of one-slot optimization problems and develop a two-stage optimization algorithm to achieve the optimal transmission power control and IoT device scheduling strategies. In the first stage, we derive closed-form solutions for optimal transmit power on the IoT device side. In the second stage, since partial state information is unknown, e.g., the transmitting power and computational frequency of IoT device, the edge server employs a multi-armed bandit (MAB) framework to model the IoT device selection problem and utilizes an efficient online algorithm, namely the client utility-based upper confidence bound (CU-UCB), to address it. Numerical results validate our algorithm's superiority over benchmark schemes, and simulations demonstrate that our algorithm achieves faster training speeds on the Fashion-MNIST and CIFAR-10 datasets within the same training duration.

Critical points of an invariant function may or may not be symmetric. We prove, however, that if a symmetric critical point exists, those adjacent to it are generically symmetry breaking. This mathematical mechanism is shown to carry important implications for our ability to efficiently minimize invariant nonconvex functions, in particular those associated with neural networks.

Real-time dynamic path planning in complex traffic environments presents challenges, such as varying traffic volumes and signal wait times. Traditional static routing algorithms like Dijkstra and A* compute shortest paths but often fail under dynamic conditions. Recent Reinforcement Learning (RL) approaches offer improvements but tend to focus on local optima, risking dead-ends or boundary issues. This paper proposes a novel approach based on causal inference for real-time dynamic path planning, balancing global and local optimality. We first use the static Dijkstra algorithm to compute a globally optimal baseline path. A distributed control strategy then guides vehicles along this path. At intersections, DynamicRouteGPT performs real-time decision-making for local path selection, considering real-time traffic, driving preferences, and unexpected events. DynamicRouteGPT integrates Markov chains, Bayesian inference, and large-scale pretrained language models like Llama3 8B to provide an efficient path planning solution. It dynamically adjusts to traffic scenarios and driver preferences and requires no pre-training, offering broad applicability across road networks. A key innovation is the construction of causal graphs for counterfactual reasoning, optimizing path decisions. Experimental results show that our method achieves state-of-the-art performance in real-time dynamic path planning for multiple vehicles while providing explainable path selections, offering a novel and efficient solution for complex traffic environments.

Despite the widespread adoption of multi-task training in deep learning, little is understood about how multi-task learning (MTL) affects generalization. Prior work has conjectured that the negative effects of MTL are due to optimization challenges that arise during training, and many optimization methods have been proposed to improve multi-task performance. However, recent work has shown that these methods fail to consistently improve multi-task generalization. In this work, we seek to improve our understanding of these failures by empirically studying how MTL impacts the optimization of tasks, and whether this impact can explain the effects of MTL on generalization. We show that MTL results in a generalization gap--a gap in generalization at comparable training loss--between single-task and multi-task trajectories early into training. However, we find that factors of the optimization trajectory previously proposed to explain generalization gaps in single-task settings cannot explain the generalization gaps between single-task and multi-task models. Moreover, we show that the amount of gradient conflict between tasks is correlated with negative effects to task optimization, but is not predictive of generalization. Our work sheds light on the underlying causes for failures in MTL and, importantly, raises questions about the role of general purpose multi-task optimization algorithms.

The Metaverse, a burgeoning collective virtual space merging augmented reality and persistent virtual worlds, necessitates advanced artificial intelligence (AI) and communication technologies to support immersive and interactive experiences. Federated learning (FL) has emerged as a promising technique for collaboratively training AI models while preserving data privacy. However, FL faces challenges such as high communication overhead and substantial computational demands, particularly for neural network (NN) models. To address these issues, we propose an integrated federated split learning and hyperdimensional computing (FSL-HDC) framework for emerging foundation models. This novel approach reduces communication costs, computation load, and privacy risks, making it particularly suitable for resource-constrained edge devices in the Metaverse, ensuring real-time responsive interactions. Additionally, we introduce an optimization algorithm that concurrently optimizes transmission power and bandwidth to minimize the maximum transmission time among all users to the server. The simulation results based on the MNIST dataset indicate that FSL-HDC achieves an accuracy rate of approximately 87.5%, which is slightly lower than that of FL-HDC. However, FSL-HDC exhibits a significantly faster convergence speed, approximately 3.733x that of FSL-NN, and demonstrates robustness to non-IID data distributions. Moreover, our proposed optimization algorithm can reduce the maximum transmission time by up to 64% compared with the baseline.