Discrete Constraints Research Articles

DAH: Discrete Asymmetric Hashing for Efficient Cross-Media Retrieval

Given the merits in high computational efficiency and low storage cost, hashing techniques have been widely studied in cross-media retrieval. Existing methods usually adopt the equal length encoding scheme to represent the multimedia data. However, the strictly equal length scheme maybe not optimal because the dimension of different modalities is often various. Besides, there exists other challenges in designing a cross-media retrieval system, e.g., how to address the discrete constraints, how to avoid using the n*n similarity matrix, and how to effectively exploit the discriminative label information. To conquer the above challenges, we propose a novel method, i.e., discrete asymmetric hashing (DAH). Specifically, DAH exploits a flexible model, which can seamlessly deal with equal or unequal length encoding scenarios. Moreover, DAH constructs a supervised semantic embedding framework by jointly minimizing the distance-distance difference and label reconstructing error, significantly reducing the computational complexity. An asymmetric strategy is employed to establish the connection between hash codes and the latent subspace. Furthermore, the hash codes can be learned discretely by the designed optimization algorithm. In the training stage2, a semantic intersection scheme is proposed to learn more powerful hash functions. Experiments show that our DAH is effective in equal and unequal scenarios.

A Safe and Fast Repulsion Method for GPU-based Cloth Self Collisions

Cloth dynamics and collision handling are the two most challenging topics in cloth simulation. While researchers have substantially improved the performances of cloth dynamics solvers recently, their success in fast collision detection and handling is rather limited. In this article, we focus our research on the safety, efficiency, and realism of the repulsion-based collision handling approach, which has demonstrated its potential in existing GPU-based simulators. Our first discovery is the necessary vertex distance conditions for cloth to enter self intersections, the negations of which can be viewed as vertex distance constraints continuous in time for sufficiently avoiding self collisions. Continuous constraints, however, cannot be enforced with ease. Our solution is to convert continuous constraints into three types of constraints: discrete edge length constraints, discrete vertex distance constraints, and vertex displacement constraints. Based on this solution, we develop a fast and safe collision handling process for enforcing constraints, a novel splitting method for integrating collision handling with dynamics solvers, and static and adaptive remeshing schemes to further improve the runtime performance. In summary, our cloth simulator is efficient, safe, robust, and parallelizable on a GPU. The experiment shows that it runs at least one order of magnitude faster than existing simulators.

Asymmetric Supervised Consistent and Specific Hashing for Cross-Modal Retrieval.

Hashing-based techniques have provided attractive solutions to cross-modal similarity search when addressing vast quantities of multimedia data. However, existing cross-modal hashing (CMH) methods face two critical limitations: 1) there is no previous work that simultaneously exploits the consistent or modality-specific information of multi-modal data; 2) the discriminative capabilities of pairwise similarity is usually neglected due to the computational cost and storage overhead. Moreover, to tackle the discrete constraints, relaxation-based strategy is typically adopted to relax the discrete problem to the continuous one, which severely suffers from large quantization errors and leads to sub-optimal solutions. To overcome the above limitations, in this article, we present a novel supervised CMH method, namely Asymmetric Supervised Consistent and Specific Hashing (ASCSH). Specifically, we explicitly decompose the mapping matrices into the consistent and modality-specific ones to sufficiently exploit the intrinsic correlation between different modalities. Meanwhile, a novel discrete asymmetric framework is proposed to fully explore the supervised information, in which the pairwise similarity and semantic labels are jointly formulated to guide the hash code learning process. Unlike existing asymmetric methods, the discrete asymmetric structure developed is capable of solving the binary constraint problem discretely and efficiently without any relaxation. To validate the effectiveness of the proposed approach, extensive experiments on three widely used datasets are conducted and encouraging results demonstrate the superiority of ASCSH over other state-of-the-art CMH methods.

Planning Jerk-Optimized Trajectory With Discrete Time Constraints for Redundant Robots

We present a method for effectively planning the motion trajectory of robots in manufacturing tasks, the tool-paths of which are usually complex and have a large number of discrete-time constraints as waypoints. Kinematic redundancy also exists in these robotic systems. The jerk of motion is optimized in our trajectory planning method at the meanwhile of fabrication process to improve the quality of fabrication.

Secure Transmission for Intelligent Reflecting Surface-Assisted mmWave and Terahertz Systems

This letter focuses on the secure transmission for an intelligent reflecting surface (IRS)-assisted millimeter-wave (mmWave) and terahertz (THz) system, in which a base station (BS) communicates with its destination via an IRS, in the presence of a passive eavesdropper. To maximize the system secrecy rate, the transmit beamforming at the BS and the reflecting matrix at the IRS are jointly optimized with transmit power and discrete phase-shift constraints. It is first proved that the beamforming design is independent of the phase shift design under the rank-one channel assumption. The formulated non-convex problem is then converted into two subproblems, which are solved alternatively. Specifically, the closed-form solution of transmit beamforming at the BS is derived, and the semidefinite programming (SDP)-based method and element-wise block coordinate descent (BCD)-based method are proposed to design the reflecting matrix. The complexity of our proposed methods is analyzed theoretically. Simulation results reveal that the proposed IRS-assisted secure strategy can significantly boost the secrecy rate performance, regardless of eavesdropper’s locations (near or blocking the confidential beam).

Relaxed Locality Preserving Supervised Discrete Hashing

Supervised discrete hashing (SDH) has widely attracted attention because it can directly obtain hash codes rather than relaxing the discrete constraint, which reduces information loss during the quantization process. However, SDH and its extensions tend to ignore the underlying geometry structure of data, while in many cases, data is lying on a low-dimensional manifold. Therefore, based on SDH, we propose a novel manifold learning-based supervised discrete hashing method in this paper to further improve the performance. Our goal is to learn compact hash codes by discovering latent information and using the local structure of data. To this end, we utilize the anchor graph to capture local neighborhood relationship embedding in data for manifold learning. Besides, since the previous methods use a strict binary label matrix for classification, we jointly optimize a relaxed label matrix to increase the discriminative ability of the proposed model. As such, the learned hash codes are more suitable for classification. Compared with SDH and other popular hashing methods, the experimental results on four large-scale datasets show that the proposed hashing method has better performance.

A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver

We develop a conservative configuration- and velocity-space (i.e., phase-space) moving-grid strategy for the Vlasov–Fokker–Planck (VFP) equation in a planar geometry. The velocity-space grid is normalized and shifted in terms of the thermal speed and the bulk-fluid velocity, respectively. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The resulting inertial terms in the transformed VFP equations are discretized to ensure the discrete conservation of mass, momentum, and energy. To satisfy the discrete conservation theorems in the presence of phase-space mesh motion, we employ the method of discrete nonlinear constraints – explored in previous studies – but the underlying symmetries are determined in a much more efficient manner than before. The conservative grid-adaptivity strategy provides an efficient scheme that resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity. The problems test independent components of the algorithms, as well as the integrated capability on settings relevant to inertial confinement fusion.

Two effects in nucleon-induced nonelastic cross sections based on the intranuclear cascade model

Proton- and neutron-induced nonelastic cross sections for $^{12}\mathrm{C}, ^{27}\mathrm{Al}, ^{56}\mathrm{Fe}$, and $^{208}\mathrm{Pb}$ are investigated in the low-energy region from 100 MeV down to nearly 0 MeV based on a framework of the extended intranuclear cascade (INC) model. It is shown that the present INC model can reproduce the experimental data both for the proton- and for the neutron-induced nonelastic cross sections of a wide range of targets in a systematic way and that the crucial point is to include the suppressed transition probability of the excited particles due to the discrete level constraint. On the basis of the reliability of the INC calculation, we analyze two effects of the discrete level constraint and Coulomb repulsion separately for the proton and for the neutron injection cases, and we elucidate the domain of the target mass and the incident energy where two effects play important roles.

Discretely-constrained deep network for weakly supervised segmentation

An efficient strategy for weakly-supervised segmentation is to impose constraints or regularization priors on target regions. Recent efforts have focused on incorporating such constraints in the training of convolutional neural networks (CNN), however this has so far been done within a continuous optimization framework. Yet, various segmentation constraints and regularization priors can be modeled and optimized more efficiently in a discrete formulation. This paper proposes a method, based on the alternating direction method of multipliers (ADMM) algorithm, to train a CNN with discrete constraints and regularization priors. This method is applied to the segmentation of medical images with weak annotations, where both size constraints and boundary length regularization are enforced. Experiments on two benchmark datasets for medical image segmentation show our method to provide significant improvements compared to existing approaches in terms of segmentation accuracy, constraint satisfaction and convergence speed.

Accelerating a continuous-time analog SAT solver using GPUs

Recently, a continuous-time, deterministic analog solver based on ordinary differential equations (CTDS) was introduced, to solve Boolean satisfiability (SAT), a family of discrete constraint satisfaction problems. Since SAT is NP-complete, efficient algorithms would benefit solving a large number of decision type problems, both within industry and the sciences. Here we present a graphics processing units (GPU) based implementation of the CTDS and its variants and show that one can achieve significantly improved performance within a wide range of SAT problems. We present and discuss three versions of our GPU implementation and compare their performance to CPU implementations, showing an improvement factor of up to two orders of magnitude. We illustrate the performance of our GPU-based solver on random SAT problems and a notoriously difficult graph coloring problem, the Ramsey number problem R(3,3,3,3), and compare it with the state-of-the-art SAT solver MiniSAT’s performances on CPUs.

Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations

The entropy-conservative/stable, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernández et al. (2019) is extended from the compressible Euler equations to the compressible Navier–Stokes equations. A simple and flexible coupling procedure with planar interpolation operators between adjoining nonconforming elements is used. Curvilinear volume metric terms are numerically approximated via a minimization procedure and satisfy the discrete geometric conservation law conditions. Distinct curvilinear surface metrics are used on the adjoining interfaces to construct the interface coupling terms, thereby localizing the discrete geometric conservation law constraints to each individual element. The resulting scheme is entropy conservative/stable, element-wise conservative, and freestream preserving. Viscous interface dissipation operators that retain the entropy stability of the base scheme are developed. The accuracy and stability of the resulting numerical scheme are shown to be comparable to those of the original conforming scheme in Carpenter et al. (2014) and Parsani et al. (2016), i.e., this scheme achieves ∼p+1/2 convergence on geometrically high-order distorted element grids; this is demonstrated in the context of the viscous shock problem, the Taylor–Green vortex problem at a Reynolds number of Re=1,600, and a subsonic turbulent flow past a sphere at Re=2,000.

Security Enhancement via Antenna Selection in MIMOME Channels With Discrete Inputs

Transmit antenna selection (TAS) is an emerging technology in physical layer security. To provide new insights into the achievable secrecy performance of TAS in practical communication systems, this paper investigates the average secrecy rate (ASR) and secrecy outage probability (SOP) under practical modulation schemes in TAS aided multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) wiretap channels over Rayleigh fading. Particularly, this research concentrates more on the square $M$ -ary quadrature amplitude modulation ( $M$ -QAM). Furthermore, in the considered MIMOME channel, a single antenna is selected to transmit the secret message, and selection combining (SC) or maximal-ratio combining (MRC) is utilized at the legitimate receiver and the eavesdropper. Based on this system model, novel expressions for the ASR and SOP are formulated to characterize the secrecy performance of the finite-alphabet driven MIMOME channel. Besides exact analysis, an asymptotic analysis is performed using the considered performance metrics in high signal-to-noise ratio (SNR) regime. Theoretical analyses suggest that the asymptotic ASR and SOP converge to finite constants in high SNR regime due to the discrete constellation constraint, and we find that the asymptotic behaviour of discrete inputs differs from that of Gaussian inputs. Furthermore, we derive concise expressions to characterize the rate of convergence (ROC) of the ASR and SOP, respectively. To unveil more system design insights, we discuss the relationship between the ROC and several important system parameters such as the antenna number and the modulation order.

Enhanced Discrete Multi-Modal Hashing: More Constraints Yet Less Time to Learn

Due to the exponential growth of multimedia data, multi-modal hashing as a promising technique to make cross-view retrieval scalable is attracting more and more attention. However, most of the existing multi-modal hashing methods either divide the learning process unnaturally into two separate stages or treat the discrete optimization problem simplistically as a continuous one, which leads to suboptimal results. Recently, a few discrete multi-modal hashing methods that try to address such issues have emerged, but they still ignore several important discrete constraints (such as the balance and decorrelation of hash bits). In this paper, we overcome those limitations by proposing a novel method named “Enhanced Discrete Multi-modal Hashing (EDMH)” which learns binary codes and hashing functions simultaneously from the pairwise similarity matrix of data, under the aforementioned discrete constraints. Although the model of EDMH looks a lot more complex than the other models for multi-modal hashing, we are actually able to develop a fast iterative learning algorithm for it, since the subproblems of its optimization all have closed-form solutions after introducing a couple of auxiliary variables. Our experimental results on three real-world datasets have revealed the usefulness of those previously ignored discrete constraints and demonstrated that EDMH not only performs much better than state-of-the-art competitors according to several retrieval metrics but also runs much faster than most of them.

Joint D2D Assignment, Bandwidth and Power Allocation in Cognitive UAV-Enabled Networks

This paper considers a cognitive communication network, which consists of a flying base station deployed by an unmanned aerial vehicle (UAV) to serve its multiple downlink ground terminals (GTs), and multiple underlaid device-to-device (D2D) users. To support the GTs’ throughput while guaranteeing the quality-of-service for the D2D users, the paper proposes the joint design of D2D assignment, bandwidth, and power allocation. This design task poses a computationally challenging mixed-binary optimization problem, for which a new computational method for its solution is developed. Multiple binary (discrete) constraints for the D2D assignment are equivalently expressed by continuous constraints to leverage systematic processes of continuous optimization. As a result, this problem of mixed-binary optimization is reformulated by an exactly penalized continuous optimization problem, for which an alternating descent algorithm is proposed. Each round of the algorithm invokes two simple convex optimization problems of low computational complexity. The theoretical convergence of the algorithm can be easily proved and the provided numerical results demonstrate its rapid convergence to an optimal solution. Such a cognitive network is even more desirable as it outperforms a non-cognitive network, which uses a partial bandwidth for D2D users only.

Integrating Relation Constraints with Neural Relation Extractors

Recent years have seen rapid progress in identifying predefined relationship between entity pairs using neural networks (NNs). However, such models often make predictions for each entity pair individually, thus often fail to solve the inconsistency among different predictions, which can be characterized by discrete relation constraints. These constraints are often defined over combinations of entity-relation-entity triples, since there often lack of explicitly well-defined type and cardinality requirements for the relations. In this paper, we propose a unified framework to integrate relation constraints with NNs by introducing a new loss term, Constraint Loss. Particularly, we develop two efficient methods to capture how well the local predictions from multiple instance pairs satisfy the relation constraints. Experiments on both English and Chinese datasets show that our approach can help NNs learn from discrete relation constraints to reduce inconsistency among local predictions, and outperform popular neural relation extraction (NRE) models even enhanced with extra post-processing. Our source code and datasets will be released at https://github.com/PKUYeYuan/Constraint-Loss-AAAI-2020.

Efficient Neural Architecture Search via Proximal Iterations

Neural architecture search (NAS) attracts much research attention because of its ability to identify better architectures than handcrafted ones. Recently, differentiable search methods become the state-of-the-arts on NAS, which can obtain high-performance architectures in several days. However, they still suffer from huge computation costs and inferior performance due to the construction of the supernet. In this paper, we propose an efficient NAS method based on proximal iterations (denoted as NASP). Different from previous works, NASP reformulates the search process as an optimization problem with a discrete constraint on architectures and a regularizer on model complexity. As the new objective is hard to solve, we further propose an efficient algorithm inspired by proximal iterations for optimization. In this way, NASP is not only much faster than existing differentiable search methods, but also can find better architectures and balance the model complexity. Finally, extensive experiments on various tasks demonstrate that NASP can obtain high-performance architectures with more than 10 times speedup over the state-of-the-arts.

Incorporating Discrete Constraints Into Random Walk-Based Graph Matching

Graph matching is a fundamental problem in theoretical computer science and artificial intelligence, and lays the foundation for many computer vision and machine learning tasks. Approximate algorithms are necessary for graph matching due to its NP-complete nature. Inspired by the usage in network-related tasks, random walk is generalized to graph matching as a type of approximate algorithm. However, it may be inappropriate for the previous random walk-based graph matching algorithms to utilize continuous techniques without considering the discrete property. In this paper, we propose a novel random walk-based graph matching algorithm by incorporating both continuous and discrete constraints in the optimization process. Specifically, after interpreting graph matching by random walk, the continuous constraints are directly embedded in the random walk constraint in each iteration. Further, both the assignment matrix (vector) and the pairwise similarity measure between graphs are iteratively updated according the discrete constraints, which automatically leads the continuous solution to the discrete domain. Comparisons on both synthetic and real-world data demonstrate the effectiveness of the proposed algorithm.

Hybrid High-Order Methods for the Elliptic Obstacle Problem

Hybrid High-Order methods are introduced and analyzed for the elliptic obstacle problem in two and three space dimensions. The methods are formulated in terms of face unknowns which are polynomials of degree $$k=0$$ or $$k=1$$ and in terms of cell unknowns which are polynomials of degree $$l=0$$. The discrete obstacle constraints are enforced on the cell unknowns. Higher polynomial degrees are not considered owing to the modest regularity of the exact solution. A priori error estimates of optimal order, that is, up to the expected regularity of the exact solution, are shown. Specifically, for $$k=1$$, the method employs a local quadratic reconstruction operator and achieves an energy-error estimate of order $$h^{\frac{3}{2}-\epsilon }$$, $$\epsilon >0$$. To our knowledge, this result fills a gap in the literature for the quadratic approximation of the three-dimensional obstacle problem. Numerical experiments in two and three space dimensions illustrate the theoretical results.

Supervised discrete hashing through similarity learning

Supervised hashing has achieved better accuracy than unsupervised hashing in many practical applications owing to its use of semantic label information. However, the mutual relationship between semantic labels is always ignored when leveraging label information. In addition, the major challenge in learning hash is of handling the discrete constraints imposed on the hash codes, which typically transform the hash optimization into NP-hard problems. To address these issues, a form of supervised discrete hashing through learning mutual similarities is proposed. Different from the existing supervised hashing methods that learn hash codes from least-squares classification by regressing the hash codes to their corresponding labels, we leverage the mutual relation between different semantic labels to learn more stable hash codes. In addition, the proposed method can simultaneously learn the discrete hash codes for training samples and the projections between the original features and their corresponding hash codes for the out-of-sample cases. Experiments have beeen performed on two public datasets. The experimental results demonstrate the superiority of the proposed method.

Combinatorial Optimization of AC Optimal Power Flow With Discrete Demands in Radial Networks

The ac optimal power flow (OPF) problem is one of the most fundamental problems in power systems engineering. For the past few decades, researchers have been relying on unproven heuristics to tackle OPF. The hardness of OPF stems from two issues: 1) nonconvexity and 2) combinatorial constraints (e.g., discrete power extraction constraints). The recent advances in providing sufficient conditions on the exactness of convex relaxation of OPF can address the issue of nonconvexity. To complete the understanding of OPF, this article presents a polynomial-time approximation algorithm to solve the convex-relaxed OPF with discrete demands as combinatorial constraints, which has a provably small parameterized approximation ratio (also known as polynomial-time approximation scheme (PTAS) algorithm). Together with the sufficient conditions on the exactness of the convex relaxation, we provide an efficient approximation algorithm to solve OPF with discrete demands, when the underlying network is radial with a fixed size and one feeder. The running time of the PTAS is O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4m</sup> / <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ϵ</sup> T), where T is the time required to solve a convex relaxation of the problem, and m and ϵ are fixed constants. Based on prior hardness results of OPF, our PTAS is among the best achievable in theory. Simulations show that our algorithm can produce close-to-optimal solutions in practice.