arXiv subjects

Fei Liu

Publications and source records attributed to Fei Liu.

At least 163 records · Page 9Linked to original sources

arXiv2024

Even Order Explicit Symplectic Geometric Algorithms for Solving Quaternions in Guidance Navigation and Control via Diagonal Padé Approximation and Cayley Transform

Quaternion kinematical differential equation (QKDE) plays a key role in navigation, control and guidance systems. Although explicit symplectic geometric algorithms (ESGA) for this problem are available, there is a lack of a unified way for constructing high order symplectic difference schemes with configurable order parameter and the fractional interval sampling problem should be treated carefully. We present even order explicit symplectic geometric algorithms to solve the QKDE with diagonal Padé approximation via a four-step strategy. Firstly, the Padé-Cayley lemma is proved and used to simplify the symplectic Padé approximation for the linear Hamiltonian system with infinitesimal symplectic structure. Secondly, both parallel and alternative iterative methods are proposed to construct the symplectic difference schemes with even order accuracy. Thirdly, the symplecity, orthogonality and invertibility of the single-step transition matrices are proved rigorously. Finally, the explicit symplectic geometric algorithms are designed for both the linear time-invariant and linear time-varying QKDE. The maximum absolute error for solving the QKDE is $\mathcal{O}((t_f-t_0)τ^{2\ell})$ where $τ$ is the time step, $\ell$ is the order parameter and $[t_0,t_f]$ is the time span. The linear time complexity and constant space complexity of computation as well as the simple algorithmic structure show that our algorithms are appropriate for real-time applications in aeronautics, astronautics, robotics and so on. The performance of the proposed algorithms are verified and validated by mathematical analysis and numerical simulation.

eess.SY↗

arXiv2024

On the Myrberg Limit Sets and Bowen-Margulis-Sullivan Measures for Visibility Manifolds without Conjugate Points

In this paper, we clarify the strong relationship between Myrberg type dynamics and the ergodic properties of the geodesic flows on (not necessarily compact) uniform visibility manifolds without conjugate points. We prove that the positivity of the Patterson-Sullivan measure of the Myrberg limit set is equivalent to the conservativity of the geodesic flow with respect to the Bowen-Margulis-Sullivan measure. Moreover we show that the Myrberg limit set is a full Patterson-Sullivan measure subset of the conical limit set. These results extend the classical works of P. Tukia and B. Stratmann from hyperbolic manifolds to the manifolds without conjugate points.

math.DS↗

arXiv2024

Rescue: Ranking LLM Responses with Partial Ordering to Improve Response Generation

Customizing LLMs for a specific task involves separating high-quality responses from lower-quality ones. This skill can be developed using supervised fine-tuning with extensive human preference data. However, obtaining a large volume of expert-annotated data is costly for most tasks. In this paper, we explore a novel method to optimize LLMs using ranking metrics. This method trains the model to prioritize the best responses from a pool of candidates created for a particular task. Rather than a traditional full ordering, we advocate for a partial ordering, as achieving consensus on the perfect order of candidate responses can be challenging. Our partial ordering is more robust, less sensitive to noise, and can be achieved with limited human annotations or through heuristic methods. We test our system's improved response generation ability using benchmark datasets, including textual entailment and multi-document question answering. We conduct ablation studies to understand crucial factors, such as how to gather candidate responses for a specific task, determine their most suitable order, and balance supervised fine-tuning with ranking metrics. Our approach, named Rescue, offers a promising avenue for enhancing the response generation and task accuracy of LLMs.

cs.CL↗

arXiv2024

Smooth Tchebycheff Scalarization for Multi-Objective Optimization

Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. In the past few decades, numerous methods have been proposed to find Pareto solutions that represent optimal trade-offs among the objectives for a given problem. However, these existing methods could have high computational complexity or may not have good theoretical properties for solving a general differentiable multi-objective optimization problem. In this work, by leveraging the smooth optimization technique, we propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization. It has good theoretical properties for finding all Pareto solutions with valid trade-off preferences, while enjoying significantly lower computational complexity compared to other methods. Experimental results on various real-world application problems fully demonstrate the effectiveness of our proposed method.

cs.LG↗

arXiv2024

Harmonizing Material Quantity and Terahertz Wave Interference Shielding Efficiency with Metallic Borophene Nanosheets

Materials with electromagnetic interference (EMI) shielding in the terahertz (THz) regime, while minimizing the quantity used, are highly demanded for future information communication, healthcare and mineral resource exploration applications. Currently, there is often a trade-off between the amount of material used and the absolute EMI shielding effectiveness (EESt) for the EMI shielding materials. Here, we address this trade-off by harnessing the unique properties of two-dimensional (2D) beta12-borophene (beta12-Br) nanosheets. Leveraging beta12-Br's light weight and exceptional electron mobility characteristics, which represent among the highest reported values to date, we simultaneously achieve a THz EMI shield effectiveness (SE) of 70 dB and an EESt of 4.8E5 dB cm^2/g (@0.87 THz) using a beta12-Br polymer composite. This surpasses the values of previously reported THz shielding materials with an EESt less than 3E5 dB cm^2/g and a SE smaller than 60 dB, while only needs 0.1 wt.% of these materials to realize the same SE value. Furthermore, by capitalizing on the composite's superior mechanical properties, with 158% tensile strain at a Young's modulus of 33 MPa, we demonstrate the high-efficiency shielding performances of conformably coated surfaces based on beta12-Br nanosheets, suggesting their great potential in EMI shielding area.

physics.app-ph↗

arXiv2024

Localized Neural Network Modelling of Time Series: A Case Study on US Monetary Policy

In this paper, we investigate a semiparametric regression model under the context of treatment effects via a localized neural network (LNN) approach. Due to a vast number of parameters involved, we reduce the number of effective parameters by (i) exploring the use of identification restrictions; and (ii) adopting a variable selection method based on the group-LASSO technique. Subsequently, we derive the corresponding estimation theory and propose a dependent wild bootstrap procedure to construct valid inferences accounting for the dependence of data. Finally, we validate our theoretical findings through extensive numerical studies. In an empirical study, we revisit the impacts of a tightening monetary policy action on a variety of economic variables, including short-/long-term interest rate, inflation, unemployment rate, industrial price and equity return via the newly proposed framework using a monthly dataset of the US.

econ.EM↗

arXiv2024

Understanding the Importance of Evolutionary Search in Automated Heuristic Design with Large Language Models

Automated heuristic design (AHD) has gained considerable attention for its potential to automate the development of effective heuristics. The recent advent of large language models (LLMs) has paved a new avenue for AHD, with initial efforts focusing on framing AHD as an evolutionary program search (EPS) problem. However, inconsistent benchmark settings, inadequate baselines, and a lack of detailed component analysis have left the necessity of integrating LLMs with search strategies and the true progress achieved by existing LLM-based EPS methods to be inadequately justified. This work seeks to fulfill these research queries by conducting a large-scale benchmark comprising four LLM-based EPS methods and four AHD problems across nine LLMs and five independent runs. Our extensive experiments yield meaningful insights, providing empirical grounding for the importance of evolutionary search in LLM-based AHD approaches, while also contributing to the advancement of future EPS algorithmic development. To foster accessibility and reproducibility, we have fully open-sourced our benchmark and corresponding results.

cs.NE↗

arXiv2024

SportsMetrics: Blending Text and Numerical Data to Understand Information Fusion in LLMs

Large language models hold significant potential for integrating various data types, such as text documents and database records, for advanced analytics. However, blending text and numerical data presents substantial challenges. LLMs need to process and cross-reference entities and numbers, handle data inconsistencies and redundancies, and develop planning capabilities such as building a working memory for managing complex data queries. In this paper, we introduce four novel tasks centered around sports data analytics to evaluate the numerical reasoning and information fusion capabilities of LLMs. These tasks involve providing LLMs with detailed, play-by-play sports game descriptions, then challenging them with adversarial scenarios such as new game rules, longer durations, scrambled narratives, and analyzing key statistics in game summaries. We conduct extensive experiments on NBA and NFL games to assess the performance of LLMs on these tasks. Our benchmark, SportsMetrics, introduces a new mechanism for assessing LLMs' numerical reasoning and fusion skills.

cs.CL↗

arXiv2024

Evolve Cost-aware Acquisition Functions Using Large Language Models

Many real-world optimization scenarios involve expensive evaluation with unknown and heterogeneous costs. Cost-aware Bayesian optimization stands out as a prominent solution in addressing these challenges. To approach the global optimum within a limited budget in a cost-efficient manner, the design of cost-aware acquisition functions (AFs) becomes a crucial step. However, traditional manual design paradigm typically requires extensive domain knowledge and involves a labor-intensive trial-and-error process. This paper introduces EvolCAF, a novel framework that integrates large language models (LLMs) with evolutionary computation (EC) to automatically design cost-aware AFs. Leveraging the crossover and mutation in the algorithmic space, EvolCAF offers a novel design paradigm, significantly reduces the reliance on domain expertise and model training. The designed cost-aware AF maximizes the utilization of available information from historical data, surrogate models and budget details. It introduces novel ideas not previously explored in the existing literature on acquisition function design, allowing for clear interpretations to provide insights into its behavior and decision-making process. In comparison to the well-known EIpu and EI-cool methods designed by human experts, our approach showcases remarkable efficiency and generalization across various tasks, including 12 synthetic problems and 3 real-world hyperparameter tuning test sets.

cs.NE↗

arXiv2024

Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model

Heuristics are widely used for dealing with complex search and optimization problems. However, manual design of heuristics can be often very labour extensive and requires rich working experience and knowledge. This paper proposes Evolution of Heuristic (EoH), a novel evolutionary paradigm that leverages both Large Language Models (LLMs) and Evolutionary Computation (EC) methods for Automatic Heuristic Design (AHD). EoH represents the ideas of heuristics in natural language, termed thoughts. They are then translated into executable codes by LLMs. The evolution of both thoughts and codes in an evolutionary search framework makes it very effective and efficient for generating high-performance heuristics. Experiments on three widely studied combinatorial optimization benchmark problems demonstrate that EoH outperforms commonly used handcrafted heuristics and other recent AHD methods including FunSearch. Particularly, the heuristic produced by EoH with a low computational budget (in terms of the number of queries to LLMs) significantly outperforms widely-used human hand-crafted baseline algorithms for the online bin packing problem.

cs.NE↗

arXiv2024

Real-to-Sim Deformable Object Manipulation: Optimizing Physics Models with Residual Mappings for Robotic Surgery

Accurate deformable object manipulation (DOM) is essential for achieving autonomy in robotic surgery, where soft tissues are being displaced, stretched, and dissected. Many DOM methods can be powered by simulation, which ensures realistic deformation by adhering to the governing physical constraints and allowing for model prediction and control. However, real soft objects in robotic surgery, such as membranes and soft tissues, have complex, anisotropic physical parameters that a simulation with simple initialization from cameras may not fully capture. To use the simulation techniques in real surgical tasks, the "real-to-sim" gap needs to be properly compensated. In this work, we propose an online, adaptive parameter tuning approach for simulation optimization that (1) bridges the real-to-sim gap between a physics simulation and observations obtained 3D perceptions through estimating a residual mapping and (2) optimizes its stiffness parameters online. Our method ensures a small residual gap between the simulation and observation and improves the simulation's predictive capabilities. The effectiveness of the proposed mechanism is evaluated in the manipulation of both a thin-shell and volumetric tissue, representative of most tissue scenarios. This work contributes to the advancement of simulation-based deformable tissue manipulation and holds potential for improving surgical autonomy.

cs.RO↗

arXiv2024

L-AutoDA: Leveraging Large Language Models for Automated Decision-based Adversarial Attacks

In the rapidly evolving field of machine learning, adversarial attacks present a significant challenge to model robustness and security. Decision-based attacks, which only require feedback on the decision of a model rather than detailed probabilities or scores, are particularly insidious and difficult to defend against. This work introduces L-AutoDA (Large Language Model-based Automated Decision-based Adversarial Attacks), a novel approach leveraging the generative capabilities of Large Language Models (LLMs) to automate the design of these attacks. By iteratively interacting with LLMs in an evolutionary framework, L-AutoDA automatically designs competitive attack algorithms efficiently without much human effort. We demonstrate the efficacy of L-AutoDA on CIFAR-10 dataset, showing significant improvements over baseline methods in both success rate and computational efficiency. Our findings underscore the potential of language models as tools for adversarial attack generation and highlight new avenues for the development of robust AI systems.

cs.CR↗

arXiv2024

Prompt Learning for Generalized Vehicle Routing

Neural combinatorial optimization (NCO) is a promising learning-based approach to solving various vehicle routing problems without much manual algorithm design. However, the current NCO methods mainly focus on the in-distribution performance, while the real-world problem instances usually come from different distributions. A costly fine-tuning approach or generalized model retraining from scratch could be needed to tackle the out-of-distribution instances. Unlike the existing methods, this work investigates an efficient prompt learning approach in NCO for cross-distribution adaptation. To be concrete, we propose a novel prompt learning method to facilitate fast zero-shot adaptation of a pre-trained model to solve routing problem instances from different distributions. The proposed model learns a set of prompts among various distributions and then selects the best-matched one to prompt a pre-trained attention model for each problem instance. Extensive experiments show that the proposed prompt learning approach facilitates the fast adaptation of pre-trained routing models. It also outperforms existing generalized models on both in-distribution prediction and zero-shot generalization to a diverse set of new tasks. Our code implementation is available online https://github.com/FeiLiu36/PromptVRP.

cs.LG↗

arXiv2024

JIGGLE: An Active Sensing Framework for Boundary Parameters Estimation in Deformable Surgical Environments

Surgical automation can improve the accessibility and consistency of life saving procedures. Most surgeries require separating layers of tissue to access the surgical site, and suturing to reattach incisions. These tasks involve deformable manipulation to safely identify and alter tissue attachment (boundary) topology. Due to poor visual acuity and frequent occlusions, surgeons tend to carefully manipulate the tissue in ways that enable inference of the tissue's attachment points without causing unsafe tearing. In a similar fashion, we propose JIGGLE, a framework for estimation and interactive sensing of unknown boundary parameters in deformable surgical environments. This framework has two key components: (1) a probabilistic estimation to identify the current attachment points, achieved by integrating a differentiable soft-body simulator with an extended Kalman filter (EKF), and (2) an optimization-based active control pipeline that generates actions to maximize information gain of the tissue attachments, while simultaneously minimizing safety costs. The robustness of our estimation approach is demonstrated through experiments with real animal tissue, where we infer sutured attachment points using stereo endoscope observations. We also demonstrate the capabilities of our method in handling complex topological changes such as cutting and suturing.

cs.RO↗

arXiv2024

Joint Near Field Uplink Communication and Localization Using Message Passing-Based Sparse Bayesian Learning

This work deals with the problem of uplink communication and localization in an integrated sensing and communication system, where users are in the near field (NF) of antenna aperture due to the use of high carrier frequency and large antenna arrays at base stations. We formulate joint NF signal detection and localization as a problem of recovering signals with a sparse pattern. To solve the problem, we develop a message passing based sparse Bayesian learning (SBL) algorithm, where multiple unitary approximate message passing (UAMP)-based sparse signal estimators work jointly to recover the sparse signals with low complexity. Simulation results demonstrate the effectiveness of the proposed method.

cs.IT↗

arXiv2024

Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a learning-based model to solve VRPs without manual algorithm design has gained substantial attention. However, current NCO methods typically require building one model for each routing problem, which significantly hinders their practical application for real-world industry problems with diverse attributes. In this work, we make the first attempt to tackle the crucial challenge of cross-problem generalization. In particular, we formulate VRPs as different combinations of a set of shared underlying attributes and solve them simultaneously via a single model through attribute composition. In this way, our proposed model can successfully solve VRPs with unseen attribute combinations in a zero-shot generalization manner. Extensive experiments are conducted on eleven VRP variants, benchmark datasets, and industry logistic scenarios. The results show that the unified model demonstrates superior performance in the eleven VRPs, reducing the average gap to around 5% from over 20% in the existing approach and achieving a significant performance boost on benchmark datasets as well as a real-world logistics application. The source code is included in https://github.com/FeiLiu36/MTNCO.

cs.LG↗

arXiv2024

Large Language Model for Multi-objective Evolutionary Optimization

Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the search operators need a carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and the learned operators might not generalize well on new problems. To tackle the above challenges, this work investigates a novel approach that leverages the powerful large language model (LLM) to design MOEA operators. With proper prompt engineering, we successfully let a general LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D) in a zero-shot manner. In addition, by learning from the LLM behavior, we further design an explicit white-box operator with randomness and propose a new version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on different test benchmarks show that our proposed method can achieve competitive performance with widely used MOEAs. It is also promising to see the operator only learned from a few instances can have robust generalization performance on unseen problems with quite different patterns and settings. The results reveal the potential benefits of using pre-trained LLMs in the design of MOEAs.To foster reproducibility and accessibility, the source code is https://github.com/FeiLiu36/LLM4MOEA.

cs.NE↗

arXiv2024

Robust Surgical Tool Tracking with Pixel-based Probabilities for Projected Geometric Primitives

Controlling robotic manipulators via visual feedback requires a known coordinate frame transformation between the robot and the camera. Uncertainties in mechanical systems as well as camera calibration create errors in this coordinate frame transformation. These errors result in poor localization of robotic manipulators and create a significant challenge for applications that rely on precise interactions between manipulators and the environment. In this work, we estimate the camera-to-base transform and joint angle measurement errors for surgical robotic tools using an image based insertion-shaft detection algorithm and probabilistic models. We apply our proposed approach in both a structured environment as well as an unstructured environment and measure to demonstrate the efficacy of our methods.

cs.RO↗