arXiv subjects

Weijia Wang

Publications and source records attributed to Weijia Wang.

54 records · Page 3Linked to original sources

arXiv2022

Event-Triggered Intermittent Prescribed Performance Control for Spacecraft Attitude Reorientation

This paper focuses on the issue of how to realize spacecraft attitude control with guaranteed performance while conspicuously reducing the actuator acting frequency simultaneously. The prescribed performance control (PPC) scheme is often employed for the control with guaranteed performance. However, conventional PPC controllers are designed from the perspective of continuous system, which contradicts the "discrete" control logic in actual spacecraft control system, and such a problem limited the application value of PPC scheme in actual applications. In order to significantly lower the actuator acting frequency while still maintaining the desired performance, a composite event-trigger mechanism is proposed for this issue, turning off the actuator and eliminating unnecessary control output under appropriate conditions. Further, the proposed composite event-trigger mechanism is combined with a prescribed performance control scheme, constructing a complete controller structure for solving the presented issue. Meanwhile, a special performance function is designed to provide mild transition process. Based on the proposed scheme, a specific backstepping controller is further developed as a validation. Finally, numerical simulation results are presented to validate the effectiveness of the proposed scheme.

eess.SY↗

arXiv2022

Neural Routing in Meta Learning

Meta-learning often referred to as learning-to-learn is a promising notion raised to mimic human learning by exploiting the knowledge of prior tasks but being able to adapt quickly to novel tasks. A plethora of models has emerged in this context and improved the learning efficiency, robustness, etc. The question that arises here is can we emulate other aspects of human learning and incorporate them into the existing meta learning algorithms? Inspired by the widely recognized finding in neuroscience that distinct parts of the brain are highly specialized for different types of tasks, we aim to improve the model performance of the current meta learning algorithms by selectively using only parts of the model conditioned on the input tasks. In this work, we describe an approach that investigates task-dependent dynamic neuron selection in deep convolutional neural networks (CNNs) by leveraging the scaling factor in the batch normalization (BN) layer associated with each convolutional layer. The problem is intriguing because the idea of helping different parts of the model to learn from different types of tasks may help us train better filters in CNNs, and improve the model generalization performance. We find that the proposed approach, neural routing in meta learning (NRML), outperforms one of the well-known existing meta learning baselines on few-shot classification tasks on the most widely used benchmark datasets.

cs.LG↗

arXiv2022

Distribution of Dirichlet $L$-functions

In this article, we study the distribution of values of Dirichlet $L$-functions, the distribution of values of the random models for Dirichlet $L$-functions, and the discrepancy between these two kinds of distributions. For each question, we consider the cases of $\frac12<\RE s<1$ and $\RE s=1$ separately.

math.NT↗

arXiv2022

Efficient Distribution Similarity Identification in Clustered Federated Learning via Principal Angles Between Client Data Subspaces

Clustered federated learning (FL) has been shown to produce promising results by grouping clients into clusters. This is especially effective in scenarios where separate groups of clients have significant differences in the distributions of their local data. Existing clustered FL algorithms are essentially trying to group together clients with similar distributions so that clients in the same cluster can leverage each other's data to better perform federated learning. However, prior clustered FL algorithms attempt to learn these distribution similarities indirectly during training, which can be quite time consuming as many rounds of federated learning may be required until the formation of clusters is stabilized. In this paper, we propose a new approach to federated learning that directly aims to efficiently identify distribution similarities among clients by analyzing the principal angles between the client data subspaces. Each client applies a truncated singular value decomposition (SVD) step on its local data in a single-shot manner to derive a small set of principal vectors, which provides a signature that succinctly captures the main characteristics of the underlying distribution. This small set of principal vectors is provided to the server so that the server can directly identify distribution similarities among the clients to form clusters. This is achieved by comparing the similarities of the principal angles between the client data subspaces spanned by those principal vectors. The approach provides a simple, yet effective clustered FL framework that addresses a broad range of data heterogeneity issues beyond simpler forms of Non-IIDness like label skews. Our clustered FL approach also enables convergence guarantees for non-convex objectives. Our code is available at https://github.com/MMorafah/PACFL.

cs.LG↗

arXiv2022

Robust Control For Spacecraft Attitude Tracking Under Multiple Physical Limitations with Guaranteed Performance

This paper considers the prescribed performance control (PPC) of spacecraft attitude tracking under multiple physical constraints, focusing on the robust issues. A novel Barrier Lyapunov function is proposed to realize the guaranteed-performance control under angular velocity constraint without singularity. Additionally, an adaptive strategy for the performance function is presented to soften the constraint and quickly re-stabilize the system after severe disturbances occur, providing strong robustness. Further, an auxiliary system is designed to handle the input saturation issue, incorporating the actuator limitation into the system. Based on the proposed structure, a backstepping controller is developed accordingly using a double-layer PPC framework. Numerical simulation results are presented to validate the proposed controller framework's efficiency and robustness.8 pa

eess.SY↗

arXiv2022

Spacecraft Attitude Pointing Control under Pointing Forbidden Constraints with Guaranteed Accuracy

This paper focuses on the attitude pointing control problem under pointing-forbidden constraints and performance constraints. The spacecraft is expected to align its sensor's boresight to a desired direction, while the terminal control accuracy and the attitude adjustment rapidity should also be guaranteed simultaneously. To resolve this problem, a switching controller structure is proposed in this paper based on the reduced-attitude representation, fusing the artificial potential field (APF) methodology and the Prescribed Performance Control (PPC) scheme together. Firstly, a novel artificial potential field is presented, and a particular function is designed for the mollification of the switching process, aiming at providing a smooth transition for the system status. Subsequently, we propose a special performance function, which can freeze the PPC part when necessary. In this way, the intrinsic contradictory between the fast attitude maneuver and forbidden direction avoidance is tackled Further, an asynchronous switching strategy is designed, guarantees the system's stability. Based on these proposed issues, a switching backstepping controller is developed, and a tracking differentiator(TD) is employed to generate a smooth approximation of differential signals. Numerical simulation results are illustrated to show the effectiveness of the proposed scheme.

eess.SY↗

arXiv2022

FLIS: Clustered Federated Learning via Inference Similarity for Non-IID Data Distribution

Classical federated learning approaches yield significant performance degradation in the presence of Non-IID data distributions of participants. When the distribution of each local dataset is highly different from the global one, the local objective of each client will be inconsistent with the global optima which incur a drift in the local updates. This phenomenon highly impacts the performance of clients. This is while the primary incentive for clients to participate in federated learning is to obtain better personalized models. To address the above-mentioned issue, we present a new algorithm, FLIS, which groups the clients population in clusters with jointly trainable data distributions by leveraging the inference similarity of clients' models. This framework captures settings where different groups of users have their own objectives (learning tasks) but by aggregating their data with others in the same cluster (same learning task) to perform more efficient and personalized federated learning. We present experimental results to demonstrate the benefits of FLIS over the state-of-the-art benchmarks on CIFAR-100/10, SVHN, and FMNIST datasets. Our code is available at https://github.com/MMorafah/FLIS.

cs.LG↗

arXiv2022

Singularity-Avoidance Prescribed Performance Attitude Tracking of Spacecraft

The attitude tracking problem with preassigned performance requirements has earned tremendous interest in recent years, and the Prescribed Performance Control (PPC) scheme is often adopted to tackle this problem. Nevertheless, traditional PPC schemes have inherent problems, which the solution still lacks, such as the singularity problem when the state constraint is violated and the potential over-control problem when the state trajectory approaches the constraint boundary. This paper proposes a Singularity-Avoidance Prescribed Performance Control scheme (SAPPC) to deal with these problems. A novel shear mapping-based error transformation is proposed to provide a globally non-singular error transformation procedure, while a time-varying constraint boundary is employed to exert appropriate constraint strength at different control stages, alleviating the potential instability caused by the over-control problem. Besides, a novel piece-wise reference performance function (RPF) is constructed to provide a relevant reference trajectory for the state responding signals, allowing precise control of the system's responding behavior. Based on the proposed SAPPC scheme, a backstepping controller is developed, with the predefined-time stability technique and the dynamic surface control technique employed to enhance the controller's robustness and performance. Finally, theoretical analysis and numerical simulation results are presented to validate the proposed control scheme's effectiveness and robustness.

eess.SY↗

arXiv2022

Meromorphic quasi-modular forms and their $L$-functions

We investigate the meromorphic quasi-modular forms and their $L$-functions. We study the space of meromorphic quasi-modular forms. Then we define their $L$-functions by using the technique of regularized integral. Moreover, we give an explicit formula for the $L$-functions. As an application, we obtain some vanishing results of special $L$-values of meromorphic quasi-modular forms.

math.NT↗

arXiv2021

Learning Accurate and Interpretable Decision Rule Sets from Neural Networks

This paper proposes a new paradigm for learning a set of independent logical rules in disjunctive normal form as an interpretable model for classification. We consider the problem of learning an interpretable decision rule set as training a neural network in a specific, yet very simple two-layer architecture. Each neuron in the first layer directly maps to an interpretable if-then rule after training, and the output neuron in the second layer directly maps to a disjunction of the first-layer rules to form the decision rule set. Our representation of neurons in this first rules layer enables us to encode both the positive and the negative association of features in a decision rule. State-of-the-art neural net training approaches can be leveraged for learning highly accurate classification models. Moreover, we propose a sparsity-based regularization approach to balance between classification accuracy and the simplicity of the derived rules. Our experimental results show that our method can generate more accurate decision rule sets than other state-of-the-art rule-learning algorithms with better accuracy-simplicity trade-offs. Further, when compared with uninterpretable black-box machine learning approaches such as random forests and full-precision deep neural networks, our approach can easily find interpretable decision rule sets that have comparable predictive performance.

cs.LG↗

arXiv2021

Reduced expression of minimal infinite reduced words of affine Weyl groups

For an infinite Coxeter system, one can extend the weak right order to the set of infinite reduced words. This is called limit weak order. In [Transformation Groups 18(1), 2013, 179-231], Lam and Pylyavskyy showed that for affine Weyl groups of type $\widetilde{A}_n$ minimal infinite reduced words under the limit weak order are precisely those infinite Coxeter elements and asked the question of characterization, in terms of infinite reduced words, of the minimal elements of the limit weak order for other affine types. In this paper, we answer this question by characterizing the minimal infinite reduced words for other irreducible affine Weyl groups by one of their reduced expressions.

math.GR↗

arXiv2020

Unsupervised Meta-Learning through Latent-Space Interpolation in Generative Models

Unsupervised meta-learning approaches rely on synthetic meta-tasks that are created using techniques such as random selection, clustering and/or augmentation. Unfortunately, clustering and augmentation are domain-dependent, and thus they require either manual tweaking or expensive learning. In this work, we describe an approach that generates meta-tasks using generative models. A critical component is a novel approach of sampling from the latent space that generates objects grouped into synthetic classes forming the training and validation data of a meta-task. We find that the proposed approach, LAtent Space Interpolation Unsupervised Meta-learning (LASIUM), outperforms or is competitive with current unsupervised learning baselines on few-shot classification tasks on the most widely used benchmark datasets. In addition, the approach promises to be applicable without manual tweaking over a wider range of domains than previous approaches.

cs.LG↗

arXiv2020

How initial distribution affects symmetry breaking induced by panic in ants: experiment and flee-pheromone model

Collective escaping is a ubiquitous phenomenon in animal groups. Symmetry breaking caused by panic escape exhibits a shared feature across species that one exit is used more than the other when agents escaping from a closed space with two symmetrically located exists. Intuitively, one exit will be used more by more individuals close to it, namely there is an asymmetric distribution initially. We used ant groups to investigate how initial distribution of colonies would influence symmetry breaking in collective escaping. Surprisingly, there was no positive correlation between symmetry breaking and the asymmetrically initial distribution, which was quite counter-intuitive. In the experiments, a flee stage was observed and accordingly a flee-pheromone model was introduced to depict this special behavior in the early stage of escaping. Simulation results fitted well with the experiment. Furthermore, the flee stage duration was calibrated quantitatively and the model reproduced the observation demonstrated by our previous work. This paper explicitly distinguished two stages in ant panic escaping for the first time, thus enhancing the understanding in escaping behavior of ant colonies.

q-bio.QM↗

arXiv2020

Local Finiteness of the Twisted Bruhat Orders on Affine Weyl Groups

In this paper, we investigate various properties of strong and weak twisted Bruhat orders on a Coxeter group. In particular, we prove that any twisted strong Bruhat order on an affine Weyl group is locally finite, strengthening a result of Dyer in J. Algebra, 163, 861--879 (1994). We also show that for a non-finite and non-cofinite biclosed set $B$ in the positive system of an affine root system with rank greater than 2, the set of elements having a fixed $B$-twisted length is infinite. This implies that the twisted strong and weak Bruhat orders have an infinite antichain in those cases. Finally, we show that twisted weak Bruhat order can be applied to the study of the tope poset of an infinite oriented matroid arising from an affine root system.

math.RT↗

arXiv2019

A characterization of simplicial oriented geometries as groupoids with root systems

This paper shows that simplicial oriented geometries can be characterized as groupoids with root systems having certain favorable properties, as conjectured by the first author. The proof first translates Handa's characterization of oriented matroids, as acycloids which remain acycloids under iterated elementary contractions, into the language of groupoids with root systems, then establishes favorable lattice theoretic properties of a generalization of a construction which Brink and Howlett used in their study of normalizers of parabolic subgroups of Coxeter groups and uses Björner-Edelman-Ziegler's lattice theoretic characterization of simplicial oriented geometries amongst oriented geometries.

math.GR↗

arXiv2019

Infinite Reduced Words, Lattice Property And Braid Graph of Affine Weyl Groups

In this paper, we establish a bijection between the infinite reduced words of an affine Weyl group and certain biclosed sets of its positive system and determine all finitely generated biclosed sets in the positive system of an affine Weyl group. Using these results, we show first that the biclosed sets in the standard positive system of rank 3 affine Weyl groups when ordered by inclusion form a complete algebraic ortholattice and secondly that the (generalized) braid graphs of those Coxeter groups are connected, which can be thought of as an infinite version of Tit's solution to the word problem.

math.RT↗

arXiv2018

Twisted Weak Orders of Coxeter Groups

In this paper, we initiate the study of the twisted weak order associated to a twisted Bruhat order for a Coxeter group and explore the relationship between the lattice property of such order and the infinite reduced words. We show that for a 2 closure biclosed set $B$ in $Φ^+$, the $B$-twisted weak order is a non-complete meet semilattice if $B$ is the inversion set of an infinite reduced word and that the converse also holds in the case of affine Weyl groups.

math.RT↗

arXiv2017

Oriented Matroid Structures From Realized Root Systems

This paper investigates the question of uniqueness of the reduced oriented matroid structure arising from root systems of a Coxeter group in real vector spaces. We settle the question for finite Coxeter groups, irreducible affine Weyl groups and all rank three Coxeter groups. In these cases, the oriented matroid structure is unique unless $W$ is of type $\widetilde{A}_n, n\geq 3$, in which case there are three possibilities.

math.RT↗