In this paper, we point out that differential architecture search (DARTS) makes gradient of architecture parameters biased for network weights and architecture parameters are updated in different datasets alternatively in the bi-level optimization framework. The bias causes the architecture parameters of non-learnable operations to surpass that of learnable operations. Moreover, using softmax as architecture parameters' activation function and inappropriate learning rate would exacerbate the bias. As a result, it's frequently observed that non-learnable operations are dominated in the search phase. To reduce the bias, we propose to use single-level to replace bi-level optimization and non-competitive activation function like sigmoid to replace softmax. As a result, we could search high-performance architectures steadily. Experiments on NAS Benchmark 201 validate our hypothesis and stably find out nearly the optimal architecture. On DARTS space, we search the state-of-the-art architecture with 77.0% top1 accuracy (training setting follows PDARTS and without any additional module) on ImageNet-1K and steadily search architectures up-to 76.5% top1 accuracy (but not select the best from the searched architectures) which is comparable with current reported best result.
Rensselaer Polytechnic Institute(伦斯勒理工学院);IBM Thomas J. Watson Research Center(IBM托马斯·J·沃森研究中心)
Neural architecture search enables automation of architecture design. Despite its success, it is computationally costly and does not provide an insight on how to design a desirable architecture. Here we propose a new way of searching neural network where we search neural architecture by rewiring the corresponding graph and predict the architecture performance by graph properties. Because we do not perform machine learning over the entire graph space and use predicted architecture performance to search architecture, the searching process is remarkably efficient. We find graph based search can g…
Korea University(高丽大学);Hallym University(翰林大学);Kyung Hee University(庆熙大学)
As deep neural networks achieve unprecedented performance in various tasks, neural architecture search (NAS), a research field for designing neural network architectures with automated processes, is actively underway. More recently, differentiable NAS has a great impact by reducing the search cost to the level of training a single network. Besides, the search space that defines candidate architectures to be searched directly affects the performance of the final architecture. In this paper, we propose an adaptation scheme of the search space by introducing a search scope. The effectiveness of p…
Neural architecture search (NAS) is a recent methodology for automating the design of neural network architectures. Differentiable neural architecture search (DARTS) is a promising NAS approach that dramatically increases search efficiency. However, it has been shown to suffer from performance collapse, where the search often leads to detrimental architectures. Many recent works try to address this issue of DARTS by identifying indicators for early stopping, regularising the search objective to reduce the dominance of some operations, or changing the parameterisation of the search problem. In …
University of Alberta(阿尔伯塔大学);Alberta Machine Intelligence Institute (Amii)(阿尔伯塔机器智能研究所(Amii))
Architecture search optimizes the structure of a neural network for some task instead of relying on manual authoring. However, it is slow, as each potential architecture is typically trained from scratch. In this paper we present an approach called Conceptual Expansion Neural Architecture Search (CENAS) that combines a sample-efficient, computational creativity-inspired transfer learning approach with neural architecture search. This approach finds models faster than naive architecture search via transferring existing weights to approximate the parameters of the new model. It outperforms stand…
Google Brain(谷歌大脑);Google Cloud AI(谷歌云人工智能);Baidu Research(百度研究院);Horizon Robotics(地平线机器人);University of Nevada(内华达大学);Landing AI
In this paper, we propose Efficient Progressive Neural Architecture Search (EPNAS), a neural architecture search (NAS) that efficiently handles large search space through a novel progressive search policy with performance prediction based on REINFORCE~\cite{Williams.1992.PG}. EPNAS is designed to search target networks in parallel, which is more scalable on parallel systems such as GPU/TPU clusters. More importantly, EPNAS can be generalized to architecture search with multiple resource constraints, \eg, model size, compute complexity or intensity, which is crucial for deployment in widespread…
Korea University(高丽大学);Hongik University(弘益大学);Hallym University(翰林大学)
In modern deep learning research, finding optimal (or near optimal) neural network models is one of major research directions and it is widely studied in many applications. In this paper, the main research trends of neural architecture search (NAS) are classified as neuro-evolutionary algorithms, reinforcement learning based algorithms, and one-shot architecture search approaches. Furthermore, each research trend is introduced and finally all the major three trends are compared. Lastly, the future research directions of NAS research trends are discussed.
Benefiting from the search efficiency, differentiable neural architecture search (NAS) has evolved as the most dominant alternative to automatically design competitive deep neural networks (DNNs). We note that DNNs must be executed under strictly hard performance constraints in real-world scenarios, for example, the runtime latency on autonomous vehicles. However, to obtain the architecture that meets the given performance constraint, previous hardware-aware differentiable NAS methods have to repeat a plethora of search runs to manually tune the hyper-parameters by trial and error, and thus th…
Sandia National Laboratories(桑迪亚国家实验室);University of California Santa Barbara(加州大学圣巴巴拉分校)
Early neural network architectures were designed by so-called "grad student descent". Since then, the field of Neural Architecture Search (NAS) has developed with the goal of algorithmically designing architectures tailored for a dataset of interest. Recently, gradient-based NAS approaches have been created to rapidly perform the search. Gradient-based approaches impose more structure on the search, compared to alternative NAS methods, enabling faster search phase optimization. In the real-world, neural architecture performance is measured by more than just high accuracy. There is increasing n…
Graph neural networks (GNNs) have been intensively applied to various graph-based applications. Despite their success, manually designing the well-behaved GNNs requires immense human expertise. And thus it is inefficient to discover the potentially optimal data-specific GNN architecture. This paper proposes DFG-NAS, a new neural architecture search (NAS) method that enables the automatic search of very deep and flexible GNN architectures. Unlike most existing methods that focus on micro-architectures, DFG-NAS highlights another level of design: the search for macro-architectures on how atomic …
Adequate labeled data and expensive compute resources are the prerequisites for the success of neural architecture search(NAS). It is challenging to apply NAS in meta-learning scenarios with limited compute resources and data. In this paper, an across-task neural architecture search (AT-NAS) is proposed to address the problem through combining gradient-based meta-learning with EA-based NAS to learn over the distribution of tasks. The supernet is learned over an entire set of tasks by meta-learning its weights. Architecture encodes of subnets sampled from the supernet are iteratively adapted by…
Existing Neural Architecture Search (NAS) methods either encode neural architectures using discrete encodings that do not scale well, or adopt supervised learning-based methods to jointly learn architecture representations and optimize architecture search on such representations which incurs search bias. Despite the widespread use, architecture representations learned in NAS are still poorly understood. We observe that the structural properties of neural architectures are hard to preserve in the latent space if architecture representation learning and search are coupled, resulting in less effe…
How to discover and evaluate the true strength of models quickly and accurately is one of the key challenges in Neural Architecture Search (NAS). To cope with this problem, we propose an Architecture-Driven Weight Prediction (ADWP) approach for neural architecture search (NAS). In our approach, we first design an architecture-intensive search space and then train a HyperNetwork by inputting stochastic encoding architecture parameters. In the trained HyperNetwork, weights of convolution kernels can be well predicted for neural architectures in the search space. Consequently, the target architec…
Neural Architecture Search (NAS) enabled the discovery of state-of-the-art architectures in many domains. However, the success of NAS depends on the definition of the search space. Current search spaces are defined as a static sequence of decisions and a set of available actions for each decision. Each possible sequence of actions defines an architecture. We propose a more expressive class of search space: directed graphs. In our formalism, each decision is a vertex and each action is an edge. This allows us to model iterative and branching architecture design decisions. We demonstrate in simu…
Recently, differentiable search methods have made major progress in reducing the computational costs of neural architecture search. However, these approaches often report lower accuracy in evaluating the searched architecture or transferring it to another dataset. This is arguably due to the large gap between the architecture depths in search and evaluation scenarios. In this paper, we present an efficient algorithm which allows the depth of searched architectures to grow gradually during the training procedure. This brings two issues, namely, heavier computational overheads and weaker search …
State-of-the-art deep networks are often too large to deploy on mobile devices and embedded systems. Mobile neural architecture search (NAS) methods automate the design of small models but state-of-the-art NAS methods are expensive to run. Differentiable neural architecture search (DNAS) methods reduce the search cost but explore a limited subspace of candidate architectures. In this paper, we introduce Fine-Grained Stochastic Architecture Search (FiGS), a differentiable search method that searches over a much larger set of candidate architectures. FiGS simultaneously selects and modifies oper…
Existing neural architecture search (NAS) methods often return an architecture with good search performance but generalizes poorly to the test setting. To achieve better generalization, we propose a novel neighborhood-aware NAS formulation to identify flat-minima architectures in the search space, with the assumption that flat minima generalize better than sharp minima. The phrase ``flat-minima architecture'' refers to architectures whose performance is stable under small perturbations in the architecture (e.g., replacing a convolution with a skip connection). Our formulation takes the ``flatn…
Differentiable ARchiTecture Search (DARTS) is one of the most trending Neural Architecture Search (NAS) methods. It drastically reduces search cost by resorting to weight-sharing. However, it also dramatically reduces the search space, thus excluding potential promising architectures. In this article, we propose D-DARTS, a solution that addresses this problem by nesting neural networks at the cell level instead of using weight-sharing to produce more diversified and specialized architectures. Moreover, we introduce a novel algorithm that can derive deeper architectures from a few trained cells…
University of Freiburg(弗莱堡大学);Bosch Center for Artificial Intelligence(博世人工智能中心)
Neural architecture search (NAS) methods rely on a search strategy for deciding which architectures to evaluate next and a performance estimation strategy for assessing their performance (e.g., using full evaluations, multi-fidelity evaluations, or the one-shot model). In this paper, we focus on the search strategy. We introduce the simple yet powerful evolutionary algorithm of differential evolution to the NAS community. Using the simplest performance evaluation strategy of full evaluations, we comprehensively compare this search strategy to regularized evolution and Bayesian optimization and…
The neural architecture search (NAS) algorithm with reinforcement learning can be a powerful and novel framework for the automatic discovering process of neural architectures. However, its application is restricted by noncontinuous and high-dimensional search spaces, which result in difficulty in optimization. To resolve these problems, we proposed NAS in embedding space (NASES), which is a novel framework. Unlike other NAS with reinforcement learning approaches that search over a discrete and high-dimensional architecture space, this approach enables reinforcement learning to search in an emb…
The design of handcrafted neural networks requires a lot of time and resources. Recent techniques in Neural Architecture Search (NAS) have proven to be competitive or better than traditional handcrafted design, although they require domain knowledge and have generally used limited search spaces. In this paper, we propose a novel framework for neural architecture search, utilizing a dictionary of models of base tasks and the similarity between the target task and the atoms of the dictionary; hence, generating an adaptive search space based on the base models of the dictionary. By introducing a …
Harbin Institute of Technology(哈尔滨工业大学);Peng Cheng Laboratory(鹏城实验室)
The search space of neural architecture search (NAS) for convolutional neural network (CNN) is huge. To reduce searching cost, most NAS algorithms use fixed outer network level structure, and search the repeatable cell structure only. Such kind of fixed architecture performs well when enough cells and channels are used. However, when the architecture becomes more lightweight, the performance decreases significantly. To obtain better lightweight architectures, more flexible and diversified neural architectures are in demand, and more efficient methods should be designed for larger search space.…
Tsinghua University(清华大学);The Chinese University of Hong Kong(香港中文大学)
Differentiable architecture search (DARTS) marks a milestone in Neural Architecture Search (NAS), boasting simplicity and small search costs. However, DARTS still suffers from frequent performance collapse, which happens when some operations, such as skip connections, zeroes and poolings, dominate the architecture. In this paper, we are the first to point out that the phenomenon is attributed to bi-level optimization. We propose Single-DARTS which merely uses single-level optimization, updating network weights and architecture parameters simultaneously with the same data batch. Even single-lev…
EPFL(洛桑联邦理工学院);Daskell;Swisscom Digital Lab(瑞士电信数字实验室)
Neural Architecture Search (NAS) aims to facilitate the design of deep networks for new tasks. Existing techniques rely on two stages: searching over the architecture space and validating the best architecture. NAS algorithms are currently compared solely based on their results on the downstream task. While intuitive, this fails to explicitly evaluate the effectiveness of their search strategies. In this paper, we propose to evaluate the NAS search phase. To this end, we compare the quality of the solutions obtained by NAS search policies with that of random architecture selection. We find tha…
Noah’s Ark Lab Huawei Technologies(华为技术有限公司诺亚方舟实验室);Huawei Technologies(华为技术有限公司);The University of Sydney(悉尼大学);Peking University(北京大学)
An effective and efficient architecture performance evaluation scheme is essential for the success of Neural Architecture Search (NAS). To save computational cost, most of existing NAS algorithms often train and evaluate intermediate neural architectures on a small proxy dataset with limited training epochs. But it is difficult to expect an accurate performance estimation of an architecture in such a coarse evaluation way. This paper advocates a new neural architecture evaluation scheme, which aims to determine which architecture would perform better instead of accurately predict the absolute …
Recent years have witnessed a surging interest in Neural Architecture Search (NAS). Various algorithms have been proposed to improve the search efficiency and effectiveness of NAS, i.e., to reduce the search cost and improve the generalization performance of the selected architectures, respectively. However, the search efficiency of these algorithms is severely limited by the need for model training during the search process. To overcome this limitation, we propose a novel NAS algorithm called NAS at Initialization (NASI) that exploits the capability of a Neural Tangent Kernel in being able to…
Neural architecture search has shown its great potential in various areas recently. However, existing methods rely heavily on a black-box controller to search architectures, which suffers from the serious problem of lacking interpretability. In this paper, we propose disentangled neural architecture search (DNAS) which disentangles the hidden representation of the controller into semantically meaningful concepts, making the neural architecture search process interpretable. Based on systematical study, we discover the correlation between network architecture and its performance, and propose a d…
School of Computing(计算学院);National University of Singapore(新加坡国立大学)
Neural architecture search (NAS) searches architectures automatically for given tasks, e.g., image classification and language modeling. Improving the search efficiency and effectiveness have attracted increasing attention in recent years. However, few efforts have been devoted to understanding the generated architectures. In this paper, we first reveal that existing NAS algorithms (e.g., DARTS, ENAS) tend to favor architectures with wide and shallow cell structures. These favorable architectures consistently achieve fast convergence and are consequently selected by NAS algorithms. Our empiric…
Recently, Neural Architecture Search (NAS) has successfully identified neural network architectures that exceed human designed ones on large-scale image classification. In this paper, we study NAS for semantic image segmentation. Existing works often focus on searching the repeatable cell structure, while hand-designing the outer network structure that controls the spatial resolution changes. This choice simplifies the search space, but becomes increasingly problematic for dense image prediction which exhibits a lot more network level architectural variations. Therefore, we propose to search t…
Monash University(莫纳什大学);Sun Yat-sen University(中山大学);DarkMatter AI Research(DarkMatter AI研究院);University of Oxford(牛津大学);Alibaba Group(阿里巴巴集团);RMIT University(皇家墨尔本理工大学)
A myriad of recent breakthroughs in hand-crafted neural architectures for visual recognition have highlighted the urgent need to explore hybrid architectures consisting of diversified building blocks. Meanwhile, neural architecture search methods are surging with an expectation to reduce human efforts. However, whether NAS methods can efficiently and effectively handle diversified search spaces with disparate candidates (e.g. CNNs and transformers) is still an open question. In this work, we present Block-wisely Self-supervised Neural Architecture Search (BossNAS), an unsupervised NAS method t…
Weight sharing has become a de facto standard in neural architecture search because it enables the search to be done on commodity hardware. However, recent works have empirically shown a ranking disorder between the performance of stand-alone architectures and that of the corresponding shared-weight networks. This violates the main assumption of weight-sharing NAS algorithms, thus limiting their effectiveness. We tackle this issue by proposing a regularization term that aims to maximize the correlation between the performance rankings of the shared-weight network and that of the standalone arc…
Georgia Institute of Technology(佐治亚理工学院);Google Research(谷歌研究院);Ant Financial(蚂蚁金服)
Neural Architecture Search (NAS) has been quite successful in constructing state-of-the-art models on a variety of tasks. Unfortunately, the computational cost can make it difficult to scale. In this paper, we make the first attempt to study Meta Architecture Search which aims at learning a task-agnostic representation that can be used to speed up the process of architecture search on a large number of tasks. We propose the Bayesian Meta Architecture SEarch (BASE) framework which takes advantage of a Bayesian formulation of the architecture search problem to learn over an entire set of tasks s…
Tianjin University(天津大学);University of Western Ontario(西安大略大学)
Self-attention architectures have emerged as a recent advancement for improving the performance of vision tasks. Manual determination of the architecture for self-attention networks relies on the experience of experts and cannot automatically adapt to various scenarios. Meanwhile, neural architecture search (NAS) has significantly advanced the automatic design of neural architectures. Thus, it is appropriate to consider using NAS methods to discover a better self-attention architecture automatically. However, it is challenging to directly use existing NAS methods to search attention networks b…
University of California San Diego(加州大学圣地亚哥分校);Rutgers University(罗格斯大学)
Neural architecture search, which aims to automatically search for architectures (e.g., convolution, max pooling) of neural networks that maximize validation performance, has achieved remarkable progress recently. In many application scenarios, several parties would like to collaboratively search for a shared neural architecture by leveraging data from all parties. However, due to privacy concerns, no party wants its data to be seen by other parties. To address this problem, we propose federated neural architecture search (FNAS), where different parties collectively search for a differentiable…
Johns Hopkins University(约翰霍普金斯大学);Facebook AI Research(Facebook人工智能研究院)
Existing neural network architectures in computer vision -- whether designed by humans or by machines -- were typically found using both images and their associated labels. In this paper, we ask the question: can we find high-quality neural architectures using only images, but no human-annotated labels? To answer this question, we first define a new setup called Unsupervised Neural Architecture Search (UnNAS). We then conduct two sets of experiments. In sample-based experiments, we train a large number (500) of diverse architectures with either supervised or unsupervised objectives, and find t…
Paradigm Inc(第四范式公司);Center for Data Science, Peking University(北京大学数据科学中心);School of Mathematical Sciences, Peking University(北京大学数学科学学院);Beijing Institute of Big Data Research (BIBDR)(北京大数据研究院)
Neural architecture search (NAS) recently attracts much research attention because of its ability to identify better architectures than handcrafted ones. However, many NAS methods, which optimize the search process in a discrete search space, need many GPU days for convergence. Recently, DARTS, which constructs a differentiable search space and then optimizes it by gradient descent, can obtain high-performance architecture and reduces the search time to several days. However, DARTS is still slow as it updates an ensemble of all operations and keeps only one after convergence. Besides, DARTS ca…
In neural architecture search, the structure of the neural network to best model a given dataset is determined by an automated search process. Efficient Neural Architecture Search (ENAS), proposed by Pham et al. (2018), has recently received considerable attention due to its ability to find excellent architectures within a comparably short search time. In this work, which is motivated by the quest to further improve the learning speed of architecture search, we evaluate the learning progress of the controller which generates the architectures in ENAS. We measure the progress by comparing the a…
This survey focuses on categorizing and evaluating the methods of supernet optimization in the field of Neural Architecture Search (NAS). Supernet optimization involves training a single, over-parameterized network that encompasses the search space of all possible network architectures. The survey analyses supernet optimization methods based on their approaches to spatial and temporal optimization. Spatial optimization relates to optimizing the architecture and parameters of the supernet and its subnets, while temporal optimization deals with improving the efficiency of selecting architectures…
Automating the research for the best neural network model is a task that has gained more and more relevance in the last few years. In this context, Neural Architecture Search (NAS) represents the most effective technique whose results rival the state of the art hand-crafted architectures. However, this approach requires a lot of computational capabilities as well as research time, which makes prohibitive its usage in many real-world scenarios. With its sequential model-based optimization strategy, Progressive Neural Architecture Search (PNAS) represents a possible step forward to face this res…
Southern University of Science and Technology(南方科技大学)
Recent advances in adversarial attacks show the vulnerability of deep neural networks searched by Neural Architecture Search (NAS). Although NAS methods can find network architectures with the state-of-the-art performance, the adversarial robustness and resource constraint are often ignored in NAS. To solve this problem, we propose an Effective, Efficient, and Robust Neural Architecture Search (E2RNAS) method to search a neural network architecture by taking the performance, robustness, and resource constraint into consideration. The objective function of the proposed E2RNAS method is formulat…
Microsoft Research(微软研究院);University of Cambridge(剑桥大学)
In neural architecture search (NAS), the space of neural network architectures is automatically explored to maximize predictive accuracy for a given task. Despite the success of recent approaches, most existing methods cannot be directly applied to large scale problems because of their prohibitive computational complexity or high memory usage. In this work, we propose a Probabilistic approach to neural ARchitecture SEarCh (PARSEC) that drastically reduces memory requirements while maintaining state-of-the-art computational complexity, making it possible to directly search over more complex arc…
Recent advances in Neural Architecture Search (NAS) have produced state-of-the-art architectures on several tasks. NAS shifts the efforts of human experts from developing novel architectures directly to designing architecture search spaces and methods to explore them efficiently. The search space definition captures prior knowledge about the properties of the architectures and it is crucial for the complexity and the performance of the search algorithm. However, different search space definitions require restarting the learning process from scratch. We propose a novel agent based on the Transf…
The fundamental problem in Neural Architecture Search (NAS) is to efficiently find high-performing architectures from a given search space. We propose a simple but powerful method which we call FEAR, for ranking architectures in any search space. FEAR leverages the viewpoint that neural networks are powerful non-linear feature extractors. First, we train different architectures in the search space to the same training or validation error. Then, we compare the usefulness of the features extracted by each architecture. We do so with a quick training keeping most of the architecture frozen. This …
One-shot Neural Architecture Search (NAS) aims to minimize the computational expense of discovering state-of-the-art models. However, in the past year attention has been drawn to the comparable performance of naive random search across the same search spaces used by leading NAS algorithms. To address this, we explore the effects of drastically relaxing the NAS search space, and we present Bonsai-Net, an efficient one-shot NAS method to explore our relaxed search space. Bonsai-Net is built around a modified differential pruner and can consistently discover state-of-the-art architectures that ar…
The dramatic success of deep neural networks across multiple application areas often relies on experts painstakingly designing a network architecture specific to each task. To simplify this process and make it more accessible, an emerging research effort seeks to automate the design of neural network architectures, using e.g. evolutionary algorithms or reinforcement learning or simple search in a constrained space of neural modules. Considering the typical size of the search space (e.g. $10^{10}$ candidates for a $10$-layer network) and the cost of evaluating a single candidate, current archit…
Neural architecture search (NAS) has been an active direction of automatic machine learning (Auto-ML), aiming to explore efficient network structures. The searched architecture is evaluated by training on datasets with fixed data augmentation policies. However, recent works on auto-augmentation show that the suited augmentation policies can vary over different structures. Therefore, this work considers the possible coupling between neural architectures and data augmentation and proposes an effective algorithm jointly searching for them. Specifically, 1) for the NAS task, we adopt a single-path…
Neural network architectures found by sophistic search algorithms achieve strikingly good test performance, surpassing most human-crafted network models by significant margins. Although computationally efficient, their design is often very complex, impairing execution speed. Additionally, finding models outside of the search space is not possible by design. While our space is still limited, we implement undiscoverable expert knowledge into the economic search algorithm Efficient Neural Architecture Search (ENAS), guided by the design principles and architecture of ShuffleNet V2. While maintain…
King Abdullah University of Science and Technology (KAUST)(阿卜杜拉国王科技大学(KAUST));Intel Labs(英特尔研究院)
Architecture design has become a crucial component of successful deep learning. Recent progress in automatic neural architecture search (NAS) shows a lot of promise. However, discovered architectures often fail to generalize in the final evaluation. Architectures with a higher validation accuracy during the search phase may perform worse in the evaluation. Aiming to alleviate this common issue, we introduce sequential greedy architecture search (SGAS), an efficient method for neural architecture search. By dividing the search procedure into sub-problems, SGAS chooses and prunes candidate opera…
Most applications demand high-performance deep neural architectures costing limited resources. Neural architecture searching is a way of automatically exploring optimal deep neural networks in a given huge search space. However, all sub-networks are usually evaluated using the same criterion; that is, early stopping on a small proportion of the training dataset, which is an inaccurate and highly complex approach. In contrast to conventional methods, here we present a divide-and-conquer (DC) approach to effectively and efficiently search deep neural architectures. Given an arbitrary search spac…
Neural Architecture Search (NAS) has proved effective in offering outperforming alternatives to handcrafted neural networks. In this paper we analyse the benefits of NAS for image classification tasks under strict computational constraints. Our aim is to automate the design of highly efficient deep neural networks, capable of offering fast and accurate predictions and that could be deployed on a low-memory, low-power system-on-chip. The task thus becomes a three-party trade-off between accuracy, computational complexity, and memory requirements. To address this concern, we propose Multi-Scale …
Transferrable Surrogates in Expressive Neural Architecture Search Spaces
University of Edinburgh(爱丁堡大学);Charles University, Faculty of Mathematics and Physics(查理大学数学与物理系);The Czech Academy of Sciences, Institute of Computer Science(捷克科学院计算机科学研究所);University of Siegen(锡根大学)