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Kai Wang

Publications and source records attributed to Kai Wang.

At least 649 records · Page 36Linked to original sources
arXiv2021

Controlling wave-particle duality with quantum entanglement

Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave{particle properties of single photons (or single particles in general) show that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with quantum entanglement. By doing so, we experimentally test the complementarity principle in a scenario, in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we send the photon of interest (S) into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon (C), who is entangled with a third photon (A). Therefore, the individual quantum state of photon C is undefined, which implements the undefined settings of the MZI for photon S. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI, and thus the very formulation of the wave-particle properties becomes internally inconsistent.

quant-ph↗
arXiv2021

Roominoes: Generating Novel 3D Floor Plans From Existing 3D Rooms

Realistic 3D indoor scene datasets have enabled significant recent progress in computer vision, scene understanding, autonomous navigation, and 3D reconstruction. But the scale, diversity, and customizability of existing datasets is limited, and it is time-consuming and expensive to scan and annotate more. Fortunately, combinatorics is on our side: there are enough individual rooms in existing 3D scene datasets, if there was but a way to recombine them into new layouts. In this paper, we propose the task of generating novel 3D floor plans from existing 3D rooms. We identify three sub-tasks of this problem: generation of 2D layout, retrieval of compatible 3D rooms, and deformation of 3D rooms to fit the layout. We then discuss different strategies for solving the problem, and design two representative pipelines: one uses available 2D floor plans to guide selection and deformation of 3D rooms; the other learns to retrieve a set of compatible 3D rooms and combine them into novel layouts. We design a set of metrics that evaluate the generated results with respect to each of the three subtasks and show that different methods trade off performance on these subtasks. Finally, we survey downstream tasks that benefit from generated 3D scenes and discuss strategies in selecting the methods most appropriate for the demands of these tasks.

cs.CV↗
arXiv2021

Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games

A growing body of work in game theory extends the traditional Stackelberg game to settings with one leader and multiple followers who play a Nash equilibrium. Standard approaches for computing equilibria in these games reformulate the followers' best response as constraints in the leader's optimization problem. These reformulation approaches can sometimes be effective, but often get trapped in low-quality solutions when followers' objectives are non-linear or non-quadratic. Moreover, these approaches assume a unique equilibrium or a specific equilibrium concept, e.g., optimistic or pessimistic, which is a limiting assumption in many situations. To overcome these limitations, we propose a stochastic gradient descent--based approach, where the leader's strategy is updated by differentiating through the followers' best responses. We frame the leader's optimization as a learning problem against followers' equilibrium, which allows us to decouple the followers' equilibrium constraints from the leader's problem. This approach also addresses cases with multiple equilibria and arbitrary equilibrium selection procedures by back-propagating through a sampled Nash equilibrium. To this end, this paper introduces a novel concept called equilibrium flow to formally characterize the set of equilibrium selection processes where the gradient with respect to a sampled equilibrium is an unbiased estimate of the true gradient. We evaluate our approach experimentally against existing baselines in three Stackelberg problems with multiple followers and find that in each case, our approach is able to achieve higher utility for the leader.

cs.GT↗
arXiv2021

AdnFM: An Attentive DenseNet based Factorization Machine for CTR Prediction

In this paper, we consider the Click-Through-Rate (CTR) prediction problem. Factorization Machines and their variants consider pair-wise feature interactions, but normally we won't do high-order feature interactions using FM due to high time complexity. Given the success of deep neural networks (DNNs) in many fields, researchers have proposed several DNN-based models to learn high-order feature interactions. Multi-layer perceptrons (MLP) have been widely employed to learn reliable mappings from feature embeddings to final logits. In this paper, we aim to explore more about these high-order features interactions. However, high-order feature interaction deserves more attention and further development. Inspired by the great achievements of Densely Connected Convolutional Networks (DenseNet) in computer vision, we propose a novel model called Attentive DenseNet based Factorization Machines (AdnFM). AdnFM can extract more comprehensive deep features by using all the hidden layers from a feed-forward neural network as implicit high-order features, then selects dominant features via an attention mechanism. Also, high-order interactions in the implicit way using DNNs are more cost-efficient than in the explicit way, for example in FM. Extensive experiments on two real-world datasets show that the proposed model can effectively improve the performance of CTR prediction.

cs.AI↗
arXiv2021

Eigenvalue topology of non-Hermitian band structures in two and three dimensions

In the band theory for non-Hermitian systems, the energy eigenvalues, which are complex, can exhibit non-trivial topology which is not present in Hermitian systems. In one dimension, it was recently noted theoretically and demonstrated experimentally that the eigenvalue topology is classified by the braid group. The classification of eigenvalue topology in higher dimensions, however, remained an open question. Here, we give a complete description of eigenvalue topology in two and three dimensional systems, including the gapped and gapless cases. We reduce the topological classification problem to a purely computational problem in algebraic topology. In two dimensions, the Brillouin zone torus is punctured by exceptional points, and each nontrivial loop in the punctured torus acquires a braid group invariant. These braids satisfy the constraint that the composite of the braids around the exceptional points is equal to the commutator of the braids on the fundamental cycles of the torus. In three dimensions, there are exceptional knots and links, and the classification depends on how they are embedded in the Brillouin zone three-torus. When the exceptional link is contained in a contractible ball, the classification can be expressed in terms of the knot group of the link. Our results provide a comprehensive understanding of non-Hermitian eigenvalue topology in higher dimensional systems, and should be important for the further explorations of topologically robust open quantum and classical systems.

physics.optics↗
arXiv2021

Incremental Meta-Learning via Episodic Replay Distillation for Few-Shot Image Recognition

Most meta-learning approaches assume the existence of a very large set of labeled data available for episodic meta-learning of base knowledge. This contrasts with the more realistic continual learning paradigm in which data arrives incrementally in the form of tasks containing disjoint classes. In this paper we consider this problem of Incremental Meta-Learning (IML) in which classes are presented incrementally in discrete tasks. We propose an approach to IML, which we call Episodic Replay Distillation (ERD), that mixes classes from the current task with class exemplars from previous tasks when sampling episodes for meta-learning. These episodes are then used for knowledge distillation to minimize catastrophic forgetting. Experiments on four datasets demonstrate that ERD surpasses the state-of-the-art. In particular, on the more challenging one-shot, long task sequence incremental meta-learning scenarios, we reduce the gap between IML and the joint-training upper bound from 3.5% / 10.1% / 13.4% with the current state-of-the-art to 2.6% / 2.9% / 5.0% with our method on Tiered-ImageNet / Mini-ImageNet / CIFAR100, respectively.

cs.CV↗
arXiv2021

Atomistic aspects of load transfer and fracture in CNT-reinforced aluminium

This paper describes atomistic simulations of deformation and fracture of Al reinforced with carbon nanotubes (CNTs). We use density functional theory (DFT) to understand the energetics of Al-graphene interfaces and gain reference data for the parameterization of Al-C empirical potentials. We then investigate the load transfer between CNTs and Al and its effect on composite strengthening. To this end, we perform uniaxial tensile simulations of an Al crystal reinforced with CNTs of various volume fractions. We also study the interaction of the embedded CNTs with a crack. We show that the interaction between CNTs and Al is weak such that, under tensile loading, CNTs can easily slide inside the Al matrix and get pulled out from the cracked surface. This effect is almost independent of CNT length and volume fraction. Little load transfer and consequently no crack bridging are observed during the simulation of pristine CNTs threading the crack surfaces. CNTs that are geometrically fixated inside Al, on the other hand, can increase the fracture stress and enhance plastic dissipation in the matrix. CNTs located in front of a growing crack blunt the crack and induce plastic deformation of the Al matrix. Depending on the CNT orientation, these processes can either increase or decrease the failure stress of the composite.

cond-mat.mtrl-sci↗
arXiv2021

Hyperbolic Geometry is Not Necessary: Lightweight Euclidean-Based Models for Low-Dimensional Knowledge Graph Embeddings

Recent knowledge graph embedding (KGE) models based on hyperbolic geometry have shown great potential in a low-dimensional embedding space. However, the necessity of hyperbolic space in KGE is still questionable, because the calculation based on hyperbolic geometry is much more complicated than Euclidean operations. In this paper, based on the state-of-the-art hyperbolic-based model RotH, we develop two lightweight Euclidean-based models, called RotL and Rot2L. The RotL model simplifies the hyperbolic operations while keeping the flexible normalization effect. Utilizing a novel two-layer stacked transformation and based on RotL, the Rot2L model obtains an improved representation capability, yet costs fewer parameters and calculations than RotH. The experiments on link prediction show that Rot2L achieves the state-of-the-art performance on two widely-used datasets in low-dimensional knowledge graph embeddings. Furthermore, RotL achieves similar performance as RotH but only requires half of the training time.

cs.AI↗
arXiv2021

HCV: Hierarchy-Consistency Verification for Incremental Implicitly-Refined Classification

Human beings learn and accumulate hierarchical knowledge over their lifetime. This knowledge is associated with previous concepts for consolidation and hierarchical construction. However, current incremental learning methods lack the ability to build a concept hierarchy by associating new concepts to old ones. A more realistic setting tackling this problem is referred to as Incremental Implicitly-Refined Classification (IIRC), which simulates the recognition process from coarse-grained categories to fine-grained categories. To overcome forgetting in this benchmark, we propose Hierarchy-Consistency Verification (HCV) as an enhancement to existing continual learning methods. Our method incrementally discovers the hierarchical relations between classes. We then show how this knowledge can be exploited during both training and inference. Experiments on three setups of varying difficulty demonstrate that our HCV module improves performance of existing continual learning methods under this IIRC setting by a large margin. Code is available in https://github.com/wangkai930418/HCV_IIRC.

cs.CV↗
arXiv2021

Takagi topological insulator with odd $\mathcal P\mathcal T$ pairs of corner states

We present a novel class of topological insulators, termed the Takagi topological insulators (TTIs), which is protected by the sublattice symmetry and spacetime inversion ($\mathcal P\mathcal T$) symmetry. The required symmetries for the TTIs can be realized on any bipartite lattice where the inversion exchanges sublattices. The protecting symmetries lead to the classifying space of Hamiltonians being unitary symmetric matrices, and therefore Takagi's factorization can be performed. Particularly, the global Takagi's factorization can (cannot) be done on a $3$D ($2$D) sphere. In 3D, there is a $\mathbb{Z}_2$ topological invariant corresponding to the parity of the winding number of Takagi's unitary-matrix factor over the entire Brillouin zone, where the $\mathbb Z_2$ nature comes from the $O(N)$ gauge degrees of freedom in Takagi's factorization. In 2D, the obstruction for a global Takagi's factorization is characterized by another $\mathbb{Z}_2$ topological invariant, equivalent to the second Stiefel-Whitney number. For the third-order topological phases, the $3$D TTIs feature a parity condition for corner zero-modes, i.e., there always exist odd $\mathcal P\mathcal T$ pairs of corners with zero-modes. Moreover, for any $\mathcal P\mathcal T$ invariant sample geometry, all configurations of corner zero-modes satisfying the parity condition can exist with the same nontrivial bulk topological invariant. Actually, without closing the bulk gap, the boundary phase diagram have a cellular structure, where each topological boundary phase associated with a particular (cross-order) boundary-mode pattern corresponds to a contractible cell with certain dimension in the parameter space.

cond-mat.mes-hall↗
arXiv2021

Feudal Reinforcement Learning by Reading Manuals

Reading to act is a prevalent but challenging task which requires the ability to reason from a concise instruction. However, previous works face the semantic mismatch between the low-level actions and the high-level language descriptions and require the human-designed curriculum to work properly. In this paper, we present a Feudal Reinforcement Learning (FRL) model consisting of a manager agent and a worker agent. The manager agent is a multi-hop plan generator dealing with high-level abstract information and generating a series of sub-goals in a backward manner. The worker agent deals with the low-level perceptions and actions to achieve the sub-goals one by one. In comparison, our FRL model effectively alleviate the mismatching between text-level inference and low-level perceptions and actions; and is general to various forms of environments, instructions and manuals; and our multi-hop plan generator can significantly boost for challenging tasks where multi-step reasoning form the texts is critical to resolve the instructed goals. We showcase our approach achieves competitive performance on two challenging tasks, Read to Fight Monsters (RTFM) and Messenger, without human-designed curriculum learning.

cs.AI↗
arXiv2021

The Low-Energy Spectral Index of Gamma-Ray Burst Prompt Emission from Internal Shocks

The prompt emission of most gamma-ray bursts (GRBs) typically exhibits a non-thermal Band component. The synchrotron radiation in the popular internal shock model is generally put forward to explain such a non-thermal component. However, the low-energy photon index $α\sim -1.5$ predicted by the synchrotron radiation is inconsistent with the observed value $α\sim -1$. Here, we investigate the evolution of a magnetic field during propagation of internal shocks within an ultrarelativistic outflow, and revisit the fast cooling of shock-accelerated electrons via synchrotron radiation for this evolutional magnetic field. We find that the magnetic field is first nearly constant and then decays as $B'\propto t^{-1}$, which leads to a reasonable range of the low-energy photon index, $-3/2 < α< -2/3$. In addition, if a rising electron injection rate during a GRB is introduced, we find that $α$ reaches $-2/3$ more easily. We thus fit the prompt emission spectra of GRB 080916c and GRB~080825c.

astro-ph.HE↗
arXiv2021

Prevalence of Extra Power-Law Spectral Components in Short Gamma-Ray Bursts

Prompt extra power-law (PL) spectral component is discovered in some bright gamma-ray bursts (GRBs), which usually dominates the spectral energy distribution below tens of keV or above about 10 MeV. However, its origin is still unclear. In this paper, we present a systematic analysis 13 Fermi short GRBs as of August 2020, with the contemporaneous keV-MeV and GeV detections at the prompt emission phase. We find that the extra PL component is a ubiquitous spectral feature for short GRBs, showing up in all 13 analyzed GRBs. The PL indices are mostly harder than -2.0, which may be well reproduced by considering the electromagnetic cascade induced by ultra-relativistic protons or electrons accelerated in the prompt emission phase. The average flux of these extra PL components positively correlates with that of the main spectral components, which implies they may share the same physical origin.

astro-ph.HE↗
arXiv2021

Deformations and homotopy theory of Rota-Baxter algebras of any weight

This paper studies formal deformations and homotopy theory of Rota-Baxter algebras of any weight. We define an $L_\infty$-algebra, which controls simultaneous deformations of associative products and Rota-Baxter operators. As a consequence, we develop a cohomology theory of Rota-Baxter algebras of any weight and justify it by interpreting lower degree cohomology groups as formal deformations and abelian extensions. The notion of homotopy Rota-Baxter algebras is introduced and it is shown that the operad governing homotopy Rota-Baxter algebras is a minimal model of the operad of Rota-Baxter algebras.

math.RA↗
arXiv2021

Eden: A Unified Environment Framework for Booming Reinforcement Learning Algorithms

With AlphaGo defeats top human players, reinforcement learning(RL) algorithms have gradually become the code-base of building stronger artificial intelligence(AI). The RL algorithm design firstly needs to adapt to the specific environment, so the designed environment guides the rapid and profound development of RL algorithms. However, the existing environments, which can be divided into real world games and customized toy environments, have obvious shortcomings. For real world games, it is designed for human entertainment, and too much difficult for most of RL researchers. For customized toy environments, there is no widely accepted unified evaluation standard for all RL algorithms. Therefore, we introduce the first virtual user-friendly environment framework for RL. In this framework, the environment can be easily configured to realize all kinds of RL tasks in the mainstream research. Then all the mainstream state-of-the-art(SOTA) RL algorithms can be conveniently evaluated and compared. Therefore, our contributions mainly includes the following aspects: 1.single configured environment for all classification of SOTA RL algorithms; 2.combined environment of more than one classification RL algorithms; 3.the evaluation standard for all kinds of RL algorithms. With all these efforts, a possibility for breeding an AI with capability of general competency in a variety of tasks is provided, and maybe it will open up a new chapter for AI.

cs.LG↗
arXiv2021

Multi-UAV Cooperative Trajectory for Servicing Dynamic Demands and Charging Battery

Unmanned Aerial Vehicle (UAV) technology is a promising solution for providing high-quality mobile services to ground users, where a UAV with limited service coverage travels among multiple geographical user locations (e.g., hotspots) for servicing their demands locally. How to dynamically determine a UAV swarm's cooperative path planning to best meet many users' spatio-temporally distributed demands is an important question but is unaddressed in the literature. To our best knowledge, this paper is the first to design and analyze cooperative path planning algorithms of a large UAV swarm for optimally servicing many spatial locations, where ground users' demands are released dynamically in the long time horizon. Regarding a single UAV's path planning design, we manage to substantially simplify the traditional dynamic program and propose an optimal algorithm of low computation complexity, which is only polynomial with respect to both the numbers of spatial locations and user demands. After coordinating a large number $K$ of UAVs, this simplified dynamic optimization problem becomes intractable and we alternatively present a fast iterative cooperation algorithm with provable approximation ratio $1-(1-\frac{1}{K})^{K}$ in the worst case, which is proved to obviously outperform the traditional approach of partitioning UAVs to serve different location clusters separately. To relax UAVs' battery capacity limit for sustainable service provisioning, we further allow UAVs to travel to charging stations in the mean time and thus jointly design UAVs' path planning over users' locations and charging stations. Despite of the problem difficulty, for the optimal solution, we successfully transform the problem to an integer linear program by creating novel directed acyclic graph of the UAV-state transition diagram, and propose an iterative algorithm with constant approximation ratio.

cs.NI↗
arXiv2021

Interpretable Visual Reasoning via Induced Symbolic Space

We study the problem of concept induction in visual reasoning, i.e., identifying concepts and their hierarchical relationships from question-answer pairs associated with images; and achieve an interpretable model via working on the induced symbolic concept space. To this end, we first design a new framework named object-centric compositional attention model (OCCAM) to perform the visual reasoning task with object-level visual features. Then, we come up with a method to induce concepts of objects and relations using clues from the attention patterns between objects' visual features and question words. Finally, we achieve a higher level of interpretability by imposing OCCAM on the objects represented in the induced symbolic concept space. Our model design makes this an easy adaption via first predicting the concepts of objects and relations and then projecting the predicted concepts back to the visual feature space so the compositional reasoning module can process normally. Experiments on the CLEVR and GQA datasets demonstrate: 1) our OCCAM achieves a new state of the art without human-annotated functional programs; 2) our induced concepts are both accurate and sufficient as OCCAM achieves an on-par performance on objects represented either in visual features or in the induced symbolic concept space.

cs.CV↗