We extend the concept of self-consistency for the Fokker-Planck equation (FPE) to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of particles under drift and diffusion, MVE accounts for the additional inter-particle interactions, which are often highly singular in physical systems. Two important examples considered in this paper are the MVE with Coulomb interactions and the vorticity formulation of the 2D Navier-Stokes equation. We show that a generalized self-consistency potential controls the KL-divergence between a hypothesis solution to the ground truth, through entropy dissipation. Built on this result, we propose to solve the MVEs by minimizing this potential function, while utilizing the neural networks for function approximation. We validate the empirical performance of our approach by comparing with state-of-the-art NN-based PDE solvers on several example problems.
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Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會議。
Publisher：IFIP。
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In this work, we solve differential equations using quantum Chebyshev feature maps. We propose a tensor product over a summation of Pauli-Z operators as a change in the measurement observables resulting in improved accuracy and reduced computation time for initial value problems processed by floating boundary handling. This idea has been tested on solving the complex dynamics of a Riccati equation as well as on a system of differential equations. Furthermore, a second-order differential equation is investigated in which we propose adding entangling layers to improve accuracy without increasing the variational parameters. Additionally, a modified self-adaptivity approach of physics-informed neural networks is incorporated to balance the multi-objective loss function. Finally, a new quantum circuit structure is proposed to approximate multivariable functions, tested on solving a 2D Poisson's equation.
We propose a PnP algorithm for a camera constrained to two-dimensional movement (applicable, for instance, to many wheeled robotics platforms). Leveraging this assumption allows performance improvements over 3D PnP algorithms due to the reduction in search space dimensionality. It also reduces the incidence of ambiguous pose estimates (as, in most cases, the spurious solutions fall outside the plane of movement). Our algorithm finds an approximate solution using geometric criteria and refines its prediction iteratively. We compare this algorithm to existing 3D PnP algorithms in the cases of general and coplanar point configurations.
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.
Evolutionary multitasking (EMT) has been attracting much attention over the past years. It aims to handle multiple optimization tasks simultaneously within limited computing resources assisted by inter-task knowledge transfer techniques. Numerous multitask evolutionary algorithms (MTEAs) for solving multitask optimization (MTO) problems have been proposed in the EMT field, but there lacks a comprehensive software platform to help researchers evaluate MTEA performance on benchmark MTO problems as well as explore real-world applications. To address this issue, we introduce the first open-source optimization platform, named MTO-Platform (MToP), for EMT. It incorporates more than 30 MTEAs, more than 150 MTO problem cases with real-world applications, and more than 10 performance metrics. Moreover, for comparing MTEAs with traditional evolutionary algorithms, we modified more than 30 popular single-task evolutionary algorithms to be able to solve MTO problems in MToP. MToP is a user-friendly tool with a graphical user interface that makes it easy to analyze results, export data, and plot schematics. More importantly, MToP is extensible, allowing users to develop new algorithms and define new problems. The source code of MToP is available at //github.com/intLyc/MTO-Platform.
The local convergence of an inexact Newton method is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property which is explored as well. Under suitable conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rate and a semi-local convergence result are obtained for the proposed method. Finally, the theory can be applied to problems of finding a singularity of the sum of two vector fields.
Multi-modal aspect-based sentiment analysis (MABSA) has recently attracted increasing attention. The span-based extraction methods, such as FSUIE, demonstrate strong performance in sentiment analysis due to their joint modeling of input sequences and target labels. However, previous methods still have certain limitations: (i) They ignore the difference in the focus of visual information between different analysis targets (aspect or sentiment). (ii) Combining features from uni-modal encoders directly may not be sufficient to eliminate the modal gap and can cause difficulties in capturing the image-text pairwise relevance. (iii) Existing span-based methods for MABSA ignore the pairwise relevance of target span boundaries. To tackle these limitations, we propose a novel framework called DQPSA for multi-modal sentiment analysis. Specifically, our model contains a Prompt as Dual Query (PDQ) module that uses the prompt as both a visual query and a language query to extract prompt-aware visual information and strengthen the pairwise relevance between visual information and the analysis target. Additionally, we introduce an Energy-based Pairwise Expert (EPE) module that models the boundaries pairing of the analysis target from the perspective of an Energy-based Model. This expert predicts aspect or sentiment span based on pairwise stability. Experiments on three widely used benchmarks demonstrate that DQPSA outperforms previous approaches and achieves a new state-of-the-art performance.
Precise arbitrary trajectory tracking for quadrotors is challenging due to unknown nonlinear dynamics, trajectory infeasibility, and actuation limits. To tackle these challenges, we present Deep Adaptive Trajectory Tracking (DATT), a learning-based approach that can precisely track arbitrary, potentially infeasible trajectories in the presence of large disturbances in the real world. DATT builds on a novel feedforward-feedback-adaptive control structure trained in simulation using reinforcement learning. When deployed on real hardware, DATT is augmented with a disturbance estimator using L1 adaptive control in closed-loop, without any fine-tuning. DATT significantly outperforms competitive adaptive nonlinear and model predictive controllers for both feasible smooth and infeasible trajectories in unsteady wind fields, including challenging scenarios where baselines completely fail. Moreover, DATT can efficiently run online with an inference time less than 3.2 ms, less than 1/4 of the adaptive nonlinear model predictive control baseline
Singularly-perturbed ordinary differential equations often exhibit Stokes' phenomenon, which describes the appearance and disappearance of oscillating exponentially small terms across curves in the complex plane known as Stokes curves. These curves originate at singular points in the leading-order solution to the differential equation. In many important problems, it is impossible to obtain a closed-form expression for these leading-order solutions, and it is therefore challenging to locate these singular points. We present evidence that the analytic leading-order solution of a linear differential equation can be replaced with a rational approximation based on a numerical leading-order solution using the adaptive Antoulas-Anderson (AAA) method. We show that the subsequent exponential asymptotic analysis accurately predicts the exponentially small behaviour present in the solution. We explore the limitations of this approach, and show that for sufficiently small values of the asymptotic parameter, this approach breaks down; however, the range of validity may be extended by increasing the number of poles in the rational approximation. We finish by presenting a related nonlinear problem and discussing the challenges that arise when attempting to apply this method to nonlinear problems.
Due to their inherent capability in semantic alignment of aspects and their context words, attention mechanism and Convolutional Neural Networks (CNNs) are widely applied for aspect-based sentiment classification. However, these models lack a mechanism to account for relevant syntactical constraints and long-range word dependencies, and hence may mistakenly recognize syntactically irrelevant contextual words as clues for judging aspect sentiment. To tackle this problem, we propose to build a Graph Convolutional Network (GCN) over the dependency tree of a sentence to exploit syntactical information and word dependencies. Based on it, a novel aspect-specific sentiment classification framework is raised. Experiments on three benchmarking collections illustrate that our proposed model has comparable effectiveness to a range of state-of-the-art models, and further demonstrate that both syntactical information and long-range word dependencies are properly captured by the graph convolution structure.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
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