For many statistical experiments, there exists a multitude of optimal designs. If we consider models with uncorrelated observations and adopt the approach of approximate experimental design, the set of all optimal designs typically forms a multivariate polytope. In this paper, we mathematically characterize the polytope of optimal designs. In particular, we show that its vertices correspond to the so-called minimal optimum designs. Consequently, we compute the vertices for several classical multifactor regression models of the first and the second degree. To this end, we use software tools based on rational arithmetic; therefore, the computed list is accurate and complete. The polytope of optimal experimental designs, and its vertices, can be applied in several ways. For instance, it can aid in constructing cost-efficient and efficient exact designs.
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Knowledge graphs play a vital role in numerous artificial intelligence tasks, yet they frequently face the issue of incompleteness. In this study, we explore utilizing Large Language Models (LLM) for knowledge graph completion. We consider triples in knowledge graphs as text sequences and introduce an innovative framework called Knowledge Graph LLM (KG-LLM) to model these triples. Our technique employs entity and relation descriptions of a triple as prompts and utilizes the response for predictions. Experiments on various benchmark knowledge graphs demonstrate that our method attains state-of-the-art performance in tasks such as triple classification and relation prediction. We also find that fine-tuning relatively smaller models (e.g., LLaMA-7B, ChatGLM-6B) outperforms recent ChatGPT and GPT-4.
We consider a statistical problem to estimate variables (effects) that are associated with the edges of a complete bipartite graph $K_{v_1, v_2}=(V_1, V_2 \, ; E)$. Each data is obtained as a sum of selected effects, a subset of $E$. In order to estimate efficiently, we propose a design called Spanning Bipartite Block Design (SBBD). For SBBDs such that the effects are estimable, we proved that the estimators have the same variance (variance balanced). If each block (a subgraph of $K_{v_1, v_2}$) of SBBD is a semi-regular or a regular bipartite graph, we show that the design is A-optimum. We also show a construction of SBBD using an ($r,\lambda$)-design and an ordered design. A BIBD with prime power blocks gives an A-optimum semi-regular or regular SBBD. At last, we mention that this SBBD is able to use for deep learning.
Rigid robots can be precise in repetitive tasks, but struggle in unstructured environments. Nature's versatility in such environments inspires researchers to develop biomimetic robots that incorporate compliant and contracting artificial muscles. Among the recently proposed artificial muscle technologies, electrohydraulic actuators are promising since they offer performance comparable to that of mammalian muscles in terms of speed and power density. However, they require high driving voltages and have safety concerns due to exposed electrodes. These high voltages lead to either bulky or inefficient driving electronics that make untethered, high-degree-of-freedom bio-inspired robots difficult to realize. Here, we present hydraulically amplified low voltage electrostatic (HALVE) actuators that match mammalian skeletal muscles in average power density (50.5 W kg-1) and peak strain rate (971 % s-1) at a driving voltage of just 1100 V. This driving voltage is approx. 5-7 times lower compared to other electrohydraulic actuators using paraelectric dielectrics. Furthermore, HALVE actuators are safe to touch, waterproof, and self-clearing, which makes them easy to implement in wearables and robotics. We characterize, model, and physically validate key performance metrics of the actuator and compare its performance to state-of-the-art electrohydraulic designs. Finally, we demonstrate the utility of our actuators on two muscle-based electrohydraulic robots: an untethered soft robotic swimmer and a robotic gripper. We foresee that HALVE actuators can become a key building block for future highly-biomimetic untethered robots and wearables with many independent artificial muscles such as biomimetic hands, faces, or exoskeletons.
In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed and fixed. In particular, we introduce a latent group structure among individuals to account for the heterogeneous user-specific characteristics. A maximum likelihood approach is proposed to simultaneously cluster individuals in the network and estimate model parameters. A fast EM algorithm is subsequently developed by utilizing the branching representation of the proposed GNHP model. Theoretical properties of the resulting estimators of group memberships and model parameters are investigated under both settings when the number of latent groups $G$ is over-specified or correctly specified. A data-driven criterion that can consistently identify the true $G$ under mild conditions is derived. Extensive simulation studies and an application to a data set collected from Sina Weibo are used to illustrate the effectiveness of the proposed methodology.
Dispatching strategies for gas turbines (GTs) are changing in modern electricity grids. A growing incorporation of intermittent renewable energy requires GTs to operate more but shorter cycles and more frequently on partial loads. Deep reinforcement learning (DRL) has recently emerged as a tool that can cope with this development and dispatch GTs economically. The key advantages of DRL are a model-free optimization and the ability to handle uncertainties, such as those introduced by varying loads or renewable energy production. In this study, three popular DRL algorithms are implemented for an economic GT dispatch problem on a case study in Alberta, Canada. We highlight the benefits of DRL by incorporating an existing thermodynamic software provided by Siemens Energy into the environment model and by simulating uncertainty via varying electricity prices, loads, and ambient conditions. Among the tested algorithms and baseline methods, Deep Q-Networks (DQN) obtained the highest rewards while Proximal Policy Optimization (PPO) was the most sample efficient. We further propose and implement a method to assign GT operation and maintenance cost dynamically based on operating hours and cycles. Compared to existing methods, our approach better approximates the true cost of modern GT dispatch and hence leads to more realistic policies.
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler-Lagrange equations that arise during optimization, and this simplification eliminates the numerical instabilities that plague optimal control in general. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a planar manipulator with two revolute joints. We show in simulation that our approach is able to generate the constrained optimal trajectory in $4.5$ ms while respecting workspace constraints and switching between a `left' and `right' bend in the elbow joint.
Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
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