The uniqueness of an optimal solution to a combinatorial optimization problem attracts many fields of researchers' attention because it has a wide range of applications, it is related to important classes in computational complexity, and an instance with only one solution is often critical for algorithm designs in theory. However, as the authors know, there is no major benchmark set consisting of only instances with unique solutions, and no algorithm generating instances with unique solutions is known; a systematic approach to getting a problem instance guaranteed having a unique solution would be helpful. A possible approach is as follows: Given a problem instance, we specify a small part of a solution in advance so that only one optimal solution meets the specification. This paper formulates such a ``pre-assignment'' approach for the vertex cover problem as a typical combinatorial optimization problem and discusses its computational complexity. First, we show that the problem is $\Sigma^P_2$-complete in general, while the problem becomes NP-complete when an input graph is bipartite. We then present an $O(2.1996^n)$-time algorithm for general graphs and an $O(1.9181^n)$-time algorithm for bipartite graphs, where $n$ is the number of vertices. The latter is based on an FPT algorithm with $O^*(3.6791^{\tau})$ time for vertex cover number $\tau$. Furthermore, we show that the problem for trees can be solved in $O(1.4143^n)$ time.
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Multi-instance registration is a challenging problem in computer vision and robotics, where multiple instances of an object need to be registered in a standard coordinate system. In this work, we propose the first iterative framework called instance-by-instance (IBI) for multi-instance 3D registration (MI-3DReg). It successively registers all instances in a given scenario, starting from the easiest and progressing to more challenging ones. Throughout the iterative process, outliers are eliminated continuously, leading to an increasing inlier rate for the remaining and more challenging instances. Under the IBI framework, we further propose a sparse-to-dense-correspondence-based multi-instance registration method (IBI-S2DC) to achieve robust MI-3DReg. Experiments on the synthetic and real datasets have demonstrated the effectiveness of IBI and suggested the new state-of-the-art performance of IBI-S2DC, e.g., our MHF1 is 12.02%/12.35% higher than the existing state-of-the-art method ECC on the synthetic/real datasets.
An obstacle toward construction robotization is the lack of methods to plan robot operations within the entire construction planning process. Despite the strength in modeling construction site conditions, 4D BIM technologies cannot perform construction robot task planning considering the contexts of given work environments. To address this limitation, this study presents a framework that integrates 4D BIM and robot task planning, presents an information flow for the integration, and performs high-level robot task planning and detailed simulation. The framework uniquely incorporates a construction robot knowledge base that derives robot-related modeling requirements to augment a 4D BIM model. Then, the 4D BIM model is converted into a robot simulation world where a robot performs a sequence of actions retrieving construction-related information. A case study focusing on the interior wall frame installation demonstrates the potential of systematic integration in achieving context-aware robot task planning and simulation in construction environments.
We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upwinding Petrov-Galerkin discretization based on bubble modification of the test space and connect the method with the general upwinding approach used in finite difference discretization. We write the finite difference and the finite element systems such that the two corresponding linear systems have the same stiffness matrices, and compare the right hand side load vectors for the two methods. This new approach allows for improving well known upwinding finite difference methods and for obtaining new error estimates. We prove that the exponential bubble Petrov-Galerkin discretization can recover the interpolant of the exact solution. As a consequence, we estimate the closeness of the related finite difference solutions to the interpolant. The ideas we present in this work, can lead to building efficient new discretization methods for multidimensional convection dominated problems.
Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in Load forecasting. Transformer models have the potential to improve Load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer based Neural Network model integrated with different metaheuristic algorithms by their performance in Load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in Load forecasting accuracy and provide optimal hyperparameters for each model.
The efficacy of self-supervised speech models has been validated, yet the optimal utilization of their representations remains challenging across diverse tasks. In this study, we delve into Acoustic Word Embeddings (AWEs), a fixed-length feature derived from continuous representations, to explore their advantages in specific tasks. AWEs have previously shown utility in capturing acoustic discriminability. In light of this, we propose measuring layer-wise similarity between AWEs and word embeddings, aiming to further investigate the inherent context within AWEs. Moreover, we evaluate the contribution of AWEs, in comparison to other types of speech features, in the context of Speech Emotion Recognition (SER). Through a comparative experiment and a layer-wise accuracy analysis on two distinct corpora, IEMOCAP and ESD, we explore differences between AWEs and raw self-supervised representations, as well as the proper utilization of AWEs alone and in combination with word embeddings. Our findings underscore the acoustic context conveyed by AWEs and showcase the highly competitive SER accuracies by appropriately employing AWEs.
Many methods for estimating conditional average treatment effects (CATEs) can be expressed as weighted pseudo-outcome regressions (PORs). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. For example, we point out that R-Learning implicitly performs a POR with inverse-variance weights (IVWs). In the CATE setting, IVWs mitigate the instability associated with inverse-propensity weights, and lead to convenient simplifications of bias terms. We demonstrate the superior performance of IVWs in simulations, and derive convergence rates for IVWs that are, to our knowledge, the fastest yet shown without assuming knowledge of the covariate distribution.
Despite the success of the Adam optimizer in practice, the theoretical understanding of its algorithmic components still remains limited. In particular, most existing analyses of Adam show the convergence rate that can be simply achieved by non-adative algorithms like SGD. In this work, we provide a different perspective based on online learning that underscores the importance of Adam's algorithmic components. Inspired by Cutkosky et al. (2023), we consider the framework called online learning of updates, where we choose the updates of an optimizer based on an online learner. With this framework, the design of a good optimizer is reduced to the design of a good online learner. Our main observation is that Adam corresponds to a principled online learning framework called Follow-the-Regularized-Leader (FTRL). Building on this observation, we study the benefits of its algorithmic components from the online learning perspective.
Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the convergence of such regularisation, particularly within the context of critical points as opposed to global minima. In this paper, we present a generalised formulation of convergent regularisation in terms of critical points, and show that this is achieved by a class of weakly convex regularisers. We prove convergence of the primal-dual hybrid gradient method for the associated variational problem, and, given a Kurdyka-Lojasiewicz condition, an $\mathcal{O}(\log{k}/k)$ ergodic convergence rate. Finally, applying this theory to learned regularisation, we prove universal approximation for input weakly convex neural networks (IWCNN), and show empirically that IWCNNs can lead to improved performance of learned adversarial regularisers for computed tomography (CT) reconstruction.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
We propose a novel attention gate (AG) model for medical imaging that automatically learns to focus on target structures of varying shapes and sizes. Models trained with AGs implicitly learn to suppress irrelevant regions in an input image while highlighting salient features useful for a specific task. This enables us to eliminate the necessity of using explicit external tissue/organ localisation modules of cascaded convolutional neural networks (CNNs). AGs can be easily integrated into standard CNN architectures such as the U-Net model with minimal computational overhead while increasing the model sensitivity and prediction accuracy. The proposed Attention U-Net architecture is evaluated on two large CT abdominal datasets for multi-class image segmentation. Experimental results show that AGs consistently improve the prediction performance of U-Net across different datasets and training sizes while preserving computational efficiency. The code for the proposed architecture is publicly available.
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