arXiv subjects

Dong An

Publications and source records attributed to Dong An.

At least 73 records · Page 4Linked to original sources

arXiv2024

Cross-Modal Conditioned Reconstruction for Language-guided Medical Image Segmentation

Recent developments underscore the potential of textual information in enhancing learning models for a deeper understanding of medical visual semantics. However, language-guided medical image segmentation still faces a challenging issue. Previous works employ implicit and ambiguous architectures to embed textual information. This leads to segmentation results that are inconsistent with the semantics represented by the language, sometimes even diverging significantly. To this end, we propose a novel cross-modal conditioned Reconstruction for Language-guided Medical Image Segmentation (RecLMIS) to explicitly capture cross-modal interactions, which assumes that well-aligned medical visual features and medical notes can effectively reconstruct each other. We introduce conditioned interaction to adaptively predict patches and words of interest. Subsequently, they are utilized as conditioning factors for mutual reconstruction to align with regions described in the medical notes. Extensive experiments demonstrate the superiority of our RecLMIS, surpassing LViT by 3.74% mIoU on the publicly available MosMedData+ dataset and achieving an average increase of 1.89% mIoU for cross-domain tests on our QATA-CoV19 dataset. Simultaneously, we achieve a relative reduction of 20.2% in parameter count and a 55.5% decrease in computational load. The code will be available at https://github.com/ShashankHuang/RecLMIS.

cs.CV↗

arXiv2024

ETPNav: Evolving Topological Planning for Vision-Language Navigation in Continuous Environments

Vision-language navigation is a task that requires an agent to follow instructions to navigate in environments. It becomes increasingly crucial in the field of embodied AI, with potential applications in autonomous navigation, search and rescue, and human-robot interaction. In this paper, we propose to address a more practical yet challenging counterpart setting - vision-language navigation in continuous environments (VLN-CE). To develop a robust VLN-CE agent, we propose a new navigation framework, ETPNav, which focuses on two critical skills: 1) the capability to abstract environments and generate long-range navigation plans, and 2) the ability of obstacle-avoiding control in continuous environments. ETPNav performs online topological mapping of environments by self-organizing predicted waypoints along a traversed path, without prior environmental experience. It privileges the agent to break down the navigation procedure into high-level planning and low-level control. Concurrently, ETPNav utilizes a transformer-based cross-modal planner to generate navigation plans based on topological maps and instructions. The plan is then performed through an obstacle-avoiding controller that leverages a trial-and-error heuristic to prevent navigation from getting stuck in obstacles. Experimental results demonstrate the effectiveness of the proposed method. ETPNav yields more than 10% and 20% improvements over prior state-of-the-art on R2R-CE and RxR-CE datasets, respectively. Our code is available at https://github.com/MarSaKi/ETPNav.

cs.CV↗

arXiv2023

Target-Grounded Graph-Aware Transformer for Aerial Vision-and-Dialog Navigation

This report details the methods of the winning entry of the AVDN Challenge in ICCV CLVL 2023. The competition addresses the Aerial Navigation from Dialog History (ANDH) task, which requires a drone agent to associate dialog history with aerial observations to reach the destination. For better cross-modal grounding abilities of the drone agent, we propose a Target-Grounded Graph-Aware Transformer (TG-GAT) framework. Concretely, TG-GAT first leverages a graph-aware transformer to capture spatiotemporal dependency, which benefits navigation state tracking and robust action planning. In addition,an auxiliary visual grounding task is devised to boost the agent's awareness of referred landmarks. Moreover, a hybrid augmentation strategy based on large language models is utilized to mitigate data scarcity limitations. Our TG-GAT framework won the AVDN Challenge, with 2.2% and 3.0% absolute improvements over the baseline on SPL and SR metrics, respectively. The code is available at https://github.com/yifeisu/TG-GAT.

cs.CV↗

arXiv2023

Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation

Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. [1] demonstrated the first efficient quantum algorithm for dissipative quadratic differential equations under the condition $R < 1$, where $R$ measures the ratio of nonlinearity to dissipation using the $\ell_2$ norm. Here we develop an efficient quantum algorithm based on [1] for reaction-diffusion equations, a class of nonlinear partial differential equations (PDEs). To achieve this, we improve upon the Carleman linearization approach introduced in [1] to obtain a faster convergence rate under the condition $R_D < 1$, where $R_D$ measures the ratio of nonlinearity to dissipation using the $\ell_{\infty}$ norm. Since $R_D$ is independent of the number of spatial grid points $n$ while $R$ increases with $n$, the criterion $R_D<1$ is significantly milder than $R<1$ for high-dimensional systems and can stay convergent under grid refinement for approximating PDEs. As applications of our quantum algorithm we consider the Fisher-KPP and Allen-Cahn equations, which have interpretations in classical physics. In particular, we show how to estimate the mean square kinetic energy in the solution by postprocessing the quantum state that encodes it to extract derivative information.

quant-ph↗

arXiv2023

Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation (QSVT). The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

quant-ph↗

arXiv2023

BEVBert: Multimodal Map Pre-training for Language-guided Navigation

Large-scale pre-training has shown promising results on the vision-and-language navigation (VLN) task. However, most existing pre-training methods employ discrete panoramas to learn visual-textual associations. This requires the model to implicitly correlate incomplete, duplicate observations within the panoramas, which may impair an agent's spatial understanding. Thus, we propose a new map-based pre-training paradigm that is spatial-aware for use in VLN. Concretely, we build a local metric map to explicitly aggregate incomplete observations and remove duplicates, while modeling navigation dependency in a global topological map. This hybrid design can balance the demand of VLN for both short-term reasoning and long-term planning. Then, based on the hybrid map, we devise a pre-training framework to learn a multimodal map representation, which enhances spatial-aware cross-modal reasoning thereby facilitating the language-guided navigation goal. Extensive experiments demonstrate the effectiveness of the map-based pre-training route for VLN, and the proposed method achieves state-of-the-art on four VLN benchmarks.

cs.CV↗

arXiv2022

Neighbor Regularized Bayesian Optimization for Hyperparameter Optimization

Bayesian Optimization (BO) is a common solution to search optimal hyperparameters based on sample observations of a machine learning model. Existing BO algorithms could converge slowly even collapse when the potential observation noise misdirects the optimization. In this paper, we propose a novel BO algorithm called Neighbor Regularized Bayesian Optimization (NRBO) to solve the problem. We first propose a neighbor-based regularization to smooth each sample observation, which could reduce the observation noise efficiently without any extra training cost. Since the neighbor regularization highly depends on the sample density of a neighbor area, we further design a density-based acquisition function to adjust the acquisition reward and obtain more stable statistics. In addition, we design a adjustment mechanism to ensure the framework maintains a reasonable regularization strength and density reward conditioned on remaining computation resources. We conduct experiments on the bayesmark benchmark and important computer vision benchmarks such as ImageNet and COCO. Extensive experiments demonstrate the effectiveness of NRBO and it consistently outperforms other state-of-the-art methods.

cs.CV↗

arXiv2022

1st Place Solutions for RxR-Habitat Vision-and-Language Navigation Competition (CVPR 2022)

This report presents the methods of the winning entry of the RxR-Habitat Competition in CVPR 2022. The competition addresses the problem of Vision-and-Language Navigation in Continuous Environments (VLN-CE), which requires an agent to follow step-by-step natural language instructions to reach a target. We present a modular plan-and-control approach for the task. Our model consists of three modules: the candidate waypoints predictor (CWP), the history enhanced planner and the tryout controller. In each decision loop, CWP first predicts a set of candidate waypoints based on depth observations from multiple views. It can reduce the complexity of the action space and facilitate planning. Then, a history-enhanced planner is adopted to select one of the candidate waypoints as the subgoal. The planner additionally encodes historical memory to track the navigation progress, which is especially effective for long-horizon navigation. Finally, we propose a non-parametric heuristic controller named tryout to execute low-level actions to reach the planned subgoal. It is based on the trial-and-error mechanism which can help the agent to avoid obstacles and escape from getting stuck. All three modules work hierarchically until the agent stops. We further take several recent advances of Vision-and-Language Navigation (VLN) to improve the performance such as pretraining based on large-scale synthetic in-domain dataset, environment-level data augmentation and snapshot model ensemble. Our model won the RxR-Habitat Competition 2022, with 48% and 90% relative improvements over existing methods on NDTW and SR metrics respectively.

cs.CV↗

arXiv2022

Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. Our method can be used for efficient Hamiltonian simulation in the interaction picture. In particular, we demonstrate that for the simulation of the Schrödinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate, of which the proof rests on a careful application of pseudo-differential calculus. Numerical results verify the effectiveness and the superconvergence property of our method.

quant-ph↗

arXiv2022

Quantum linear system solver based on time-optimal adiabatic quantum computing and quantum approximate optimization algorithm

We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with $\mathcal{O}(κ~\text{poly}(\log(κ/ε)))$ runtime, where $κ$ is the condition number, and $ε$ is the target accuracy. This is near optimal with respect to both $κ$ and $ε$. Our method is applicable to general non-Hermitian matrices, and the cost as well as the number of qubits can be reduced when restricted to Hermitian matrices, and further to Hermitian positive definite matrices. The success of the time-optimal AQC implies that the quantum approximate optimization algorithm (QAOA) with an optimal control protocol can also achieve the same complexity in terms of the runtime. Numerical results indicate that QAOA can yield the lowest runtime compared to the time-optimal AQC, vanilla AQC, and the recently proposed randomization method.

quant-ph↗

arXiv2021

Optimal scaling quantum linear systems solver via discrete adiabatic theorem

Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition number $κ$ of the linear system, without requiring a complicated variable-time amplitude amplification procedure. However, the most efficient of those procedures is still asymptotically sub-optimal by a factor of $\log(κ)$. Here, we prove a rigorous form of the adiabatic theorem that bounds the error in terms of the spectral gap for intrinsically discrete time evolutions. We use this discrete adiabatic theorem to develop a quantum algorithm for solving linear systems that is asymptotically optimal, in the sense that the complexity is strictly linear in $κ$, matching a known lower bound on the complexity. Our $\mathcal{O}(κ\log(1/ε))$ complexity is also optimal in terms of the combined scaling in $κ$ and the precision $ε$. Compared to existing suboptimal methods, our algorithm is simpler and easier to implement. Moreover, we determine the constant factors in the algorithm, which would be suitable for determining the complexity in terms of gate counts for specific applications.

quant-ph↗

arXiv2021

Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block-encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the planewave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed particle manifold and note that this approach may be valuable for simulation more broadly. Besides solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. We introduce two efficient approaches for such a task, based on the contour integral formulation and the inverse transform respectively.

quant-ph↗

arXiv2021

Neighbor-view Enhanced Model for Vision and Language Navigation

Vision and Language Navigation (VLN) requires an agent to navigate to a target location by following natural language instructions. Most of existing works represent a navigation candidate by the feature of the corresponding single view where the candidate lies in. However, an instruction may mention landmarks out of the single view as references, which might lead to failures of textual-visual matching of existing methods. In this work, we propose a multi-module Neighbor-View Enhanced Model (NvEM) to adaptively incorporate visual contexts from neighbor views for better textual-visual matching. Specifically, our NvEM utilizes a subject module and a reference module to collect contexts from neighbor views. The subject module fuses neighbor views at a global level, and the reference module fuses neighbor objects at a local level. Subjects and references are adaptively determined via attention me'chanisms. Our model also includes an action module to utilize the strong orientation guidance (e.g., "turn left") in instructions. Each module predicts navigation action separately and their weighted sum is used for predicting the final action. Extensive experimental results demonstrate the effectiveness of the proposed method on the R2R and R4R benchmarks against several state-of-the-art navigators, and NvEM even beats some pre-training ones. Our code is available at https://github.com/MarSaKi/NvEM.

cs.CV↗

arXiv2021

Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance

Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic speed-up for multilevel Monte Carlo methods in a general setting. As applications, we apply it to compute expectation values determined by classical solutions of SDEs, with improved dependence on precision. We demonstrate the use of this algorithm in a variety of applications arising in mathematical finance, such as the Black-Scholes and Local Volatility models, and Greeks. We also provide a quantum algorithm based on sublinear binomial sampling for the binomial option pricing model with the same improvement.

quant-ph↗

arXiv2021

Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory

Direct simulation of the von Neumann dynamics for a general (pure or mixed) quantum state can often be expensive. One prominent example is the real-time time-dependent density functional theory (rt-TDDFT), a widely used framework for the first principle description of many-electron dynamics in chemical and materials systems. Practical rt-TDDFT calculations often avoid the direct simulation of the von Neumann equation, and solve instead a set of Schrödinger equations, of which the dynamics is equivalent to that of the von Neumann equation. However, the time step size employed by the Schrödinger dynamics is often much smaller. In order to improve the time step size and the overall efficiency of the simulation, we generalize a recent work of the parallel transport (PT) dynamics for simulating pure states [An, Lin, Multiscale Model. Simul. 18, 612, 2020] to general quantum states. The PT dynamics provides the optimal gauge choice, and can employ a time step size comparable to that of the von Neumann dynamics. Going beyond the linear and near adiabatic regime in previous studies, we find that the error of the PT dynamics can be bounded by certain commutators between Hamiltonians, density matrices, and their derived quantities. Such a commutator structure is not present in the Schrödinger dynamics. We demonstrate that the parallel transport-implicit midpoint (PT-IM) method is a suitable method for simulating the PT dynamics, especially when the spectral radius of the Hamiltonian is large. The commutator structure of the error bound, and numerical results for model rt-TDDFT calculations in both linear and nonlinear regimes, confirm the advantage of the PT dynamics.

math.NA↗

arXiv2021

Time-dependent unbounded Hamiltonian simulation with vector norm scaling

The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable discretization, the norm of the Hamiltonian can be very large, which significantly increases the simulation cost. However, the operator norm measures the worst-case error of the quantum simulation, while practical simulation concerns the error with respect to a given initial vector at hand. We demonstrate that under suitable assumptions of the Hamiltonian and the initial vector, if the error is measured in terms of the vector norm, the computational cost may not increase at all as the norm of the Hamiltonian increases using Trotter type methods. In this sense, our result outperforms all previous error bounds in the quantum simulation literature. Our result extends that of [Jahnke, Lubich, BIT Numer. Math. 2000] to the time-dependent setting. We also clarify the existence and the importance of commutator scalings of Trotter and generalized Trotter methods for time-dependent Hamiltonian simulations.

quant-ph↗

arXiv2020

Towards sharp error analysis of extended Lagrangian molecular dynamics

The extended Lagrangian molecular dynamics (XLMD) method provides a useful framework for reducing the computational cost of a class of molecular dynamics simulations with constrained latent variables. The XLMD method relaxes the constraints by introducing a fictitious mass $\varepsilon$ for the latent variables, solving a set of singularly perturbed ordinary differential equations. While favorable numerical performance of XLMD has been demonstrated in several different contexts in the past decade, mathematical analysis of the method remains scarce. We propose the first error analysis of the XLMD method in the context of a classical polarizable force field model. While the dynamics with respect to the atomic degrees of freedom are general and nonlinear, the key mathematical simplification of the polarizable force field model is that the constraints on the latent variables are given by a linear system of equations. We prove that when the initial value of the latent variables is compatible in a sense that we define, XLMD converges as the fictitious mass $\varepsilon$ is made small with $\mathcal{O}(\varepsilon)$ error for the atomic degrees of freedom and with $\mathcal{O}(\sqrt{\varepsilon})$ error for the latent variables, when the dimension of the latent variable $d'$ is 1. Furthermore, when the initial value of the latent variables is improved to be optimally compatible in a certain sense, we prove that the convergence rate can be improved to $\mathcal{O}(\varepsilon)$ for the latent variables as well. Numerical results verify that both estimates are sharp not only for $d' =1$, but also for arbitrary $d'$. In the setting of general $d'$, we do obtain convergence, but with the non-sharp rate of $\mathcal{O}(\sqrt{\varepsilon})$ for both the atomic and latent variables.

math.NA↗

arXiv2020

Stochastic Constrained Extended System Dynamics for Solving Charge Equilibration Models

We present a new stochastic extended Lagrangian solution to charge equilibration that eliminates self-consistent field (SCF) calculations, eliminating the computational bottleneck in solving the many-body solution with standard SCF solvers. By formulating both charges and chemical potential as latent variables, and introducing a holonomic constraint that satisfies charge conservation, the SC-XLMD method accurately reproduces structural, thermodynamic, and dynamics properties using ReaxFF, and shows excellent weak- and strong-scaling performance in the LAMMPS molecular simulation package.

physics.comp-ph↗