This article addresses the problem of distributed state estimation (DSE) for discrete-time interconnected systems, where the observed system is composed of subsystems interconnected through state-to-state and state-to-output couplings. Inspired by the leader-follower consensus method, we propose a distributed observer that enables each subsystem to estimate the entire state of the interconnected system. Under certain structural assumptions, we derive necessary and sufficient conditions for the stability of the estimation error dynamics. We further present a decentralized design of the proposed observer, where the operation and construction of the observer can be completed by each subsystem using its locally available information, including the system's basic configuration, local measurements, and data exchanged with neighboring subsystems. In addition, we demonstrate that our distributed estimation framework can be applied to solve the distributed estimation problem for linear time-invariant (LTI) systems with fixed composition by employing an observability decomposition method. Finally, we illustrate the effectiveness of our scheme by applying it to vehicle platooning.

Large language models (LLMs) have demonstrated impressive performance in machine translation, but still struggle with unseen lowresource languages, especially those written in underrepresented scripts.To investigate whether LLMs can translate such languages with the help of linguistic resources, we introduce Lotus, a benchmark designed to evaluate translation for Mongolian (in traditional script) and Yi.Our study shows that while linguistic resources can improve translation quality as measured by automatic metrics, LLMs remain limited in their ability to handle these languages effectively.We hope our work provides insights for the low-resource NLP community and fosters further progress in machine translation for underrepresented script low-resource languages.Our code and data are available 1 .

In recent years, the Seq2Seq model has achieved satisfactory results in abstractive summarization tasks with large datasets such as Chinese or English, but this task has not been realized on low-resource Mongolian datasets. At present, the abstractive summarization methods of sota are all based on encoder-decoder architecture and they pay attention to the self-supervision goal in pre-training. Although these models can capture the context information between words in text, they still can’t integrate abstractive summarization tasks with global topic semantics. In addition, the summary generated by the autoregressive model may be inconsistent with the semantics of the source text, which leads to the low quality of the generated summarizations. To solve the above problems, we first create a dataset of Mongolian summarization, and then propose a joint learning model for abstractive summarization on this dataset. The model combines the topic model, the generation model, and the evaluation model for joint training, aiming to ensure that the generated summary not only has global topic information but also more similar to the semantics of the source text. Experiments show that this method can improve the ROUGE score, BLEU value and human evaluation score of the generated summary accordingly.

We investigate the capacity of an adversary to learn the underlying interaction network through repeated best response actions in linear-quadratic games. The adversary strategically perturbs the decisions of a set of action-compromised players and observes the sequential decisions of a set of action-leaked players. The central question pertains to whether such an adversary can fully reconstruct or effectively estimate the underlying interaction structure among the players. To begin with, we establish a series of results that characterize the learnability of the interaction graph from the adversary’s perspective by drawing connections between this network learning problem in games and classical system identification theory. Subsequently, taking into account the inherent stability and sparsity constraints inherent in the network interaction structure, we propose a stable and sparse system identification framework for learning the interaction graph based on complete player action observations. Moreover, we present a stable and sparse subspace identification framework for learning the interaction graph when only partially observed player actions are available. Finally, we demonstrate the efficacy of the proposed learning frameworks through numerical examples.

The Perspective-n-Point (PnP) problem has been widely studied in both computer vision and photogrammetry societies. With the development of feature extraction techniques, a large number of feature points might be available in a single shot. It is promising to devise a consistent estimator, i.e., the estimate can converge to the true camera pose as the number of points increases. To this end, we propose a consistent PnP solver, named CPnP, with bias elimination. Specifically, linear equations are constructed from the original projection model via measurement model modification and variable elimination, based on which a closed-form least-squares solution is obtained. We then analyze and subtract the asymptotic bias of this solution, resulting in a consistent estimate. Additionally, Gauss-Newton (GN) iterations are executed to refine the consistent solution. Our proposed estimator is efficient in terms of computations—it has$O(n)$time complexity. Simulations and real dataset tests show that our proposed estimator is superior to some well-known ones for images with dense visual features, in terms of estimation precision and computing time.

Online optimization has witnessed a massive surge of research attention in recent years. In this paper, we propose online gradient descent and online bandit algorithms over Riemannian manifolds in full information and bandit feedback settings respectively, for both geodesically convex and strongly geodesically convex functions. We establish a series of upper bounds on the regrets for the proposed algorithms over Hadamard manifolds. We also find a universal lower bound for achievable regret on Hadamard manifolds. Our analysis shows how time horizon, dimension, and sectional curvature bounds have impact on the regret bounds. When the manifold permits positive sectional curvature, we prove similar regret bound can be established by handling non-constrictive project maps. In addition, numerical studies on problems defined on symmetric positive definite matrix manifold, hyperbolic spaces, and Grassmann manifolds are provided to validate our theoretical findings, using synthetic and real-world data.

We consider a distributed online convex optimization problem when streaming data are distributed among computing agents over a connected communication network. Since the data are high-dimensional or the network is large-scale, communication load can be a bottleneck for the efficiency of distributed algorithms. To tackle this bottleneck, we apply the state-of-art data compression scheme to the fundamental GD-based distributed online algorithms. Three algorithms with difference-compressed communication are proposed for full information feedback (DC-DOGD), one-point bandit feedback (DC-DOBD), and two-point bandit feedback (DC-DO2BD), respectively. We obtain regret bounds explicitly in terms of time horizon, compression ratio, decision dimension, agent number, and network parameters. Our algorithms are proved to be no-regret and match the same regret bounds, w.r.t. time horizon, with their uncompressed versions for both convex and strongly convex losses. Numerical experiments are given to validate the theoretical findings and illustrate that the proposed algorithms can effectively reduce the total transmitted bits for distributed online training compared with the uncompressed baseline.

Grasping objects in cluttered scenarios is a challenging task in robotics. Performing pre-grasp actions such as pushing and shifting to scatter objects is a way to reduce clutter. Based on deep reinforcement learning, we propose a Fast-Learning Grasping (FLG) framework, that can integrate pre-grasping actions along with grasping to pick up objects from cluttered scenarios with reduced real-world training time. We associate rewards for performing moving actions with the change of environmental clutter and utilize a hybrid triggering method, leading to data-efficient learning and synergy. Then we use the output of an extended fully convolutional network as the value function of each pixel point of the workspace and establish an accurate estimation of the grasp probability for each action. We also introduce a mask function as prior knowledge to enable the agents to focus on the accurate pose adjustment to improve the effectiveness of collecting training data and, hence, to learn efficiently. We carry out pre-training of the FLG over simulated environment, and then the learnt model is transferred to the real world with minimal fine-tuning for further learning during actions. Experimental results demonstrate a 94% grasp success rate and the ability to generalize to novel objects. Compared to state-of-the-art approaches in the literature, the proposed FLG framework can achieve similar or higher grasp success rate with lesser amount of training in the real world. Supplementary video is available at https://youtu.be/KTGj1fGU6ho.

We consider online optimization over Riemannian manifolds, where a learner attempts to minimize a sequence of time-varying loss functions defined on Riemannian manifolds. Though many Euclidean online convex optimization algorithms have been proven useful in a wide range of areas, less attention has been paid to their Riemannian counterparts. In this paper, we study Riemannian online gradient descent (R-OGD) on Hadamard manifolds for both geodesically convex and strongly geodesically convex loss functions, and Riemannian bandit algorithm (R-BAN) on Hadamard homogeneous manifolds for geodesically convex functions. We establish upper bounds on the regrets of the problem with respect to time horizon, manifold curvature, and manifold dimension. We also find a universal lower bound for the achievable regret by constructing an online convex optimization problem on Hadamard manifolds. All the obtained regret bounds match the corresponding results are provided in Euclidean spaces. Finally, some numerical experiments validate our theoretical results.

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the network-wide data. It then updates its predictor for the next round according to the received local feedback and information received from neighboring nodes. The predictions made at a given node are assessed through the notion of regret, defined as the difference between their cumulative network-wide square errors and those of the best off-line network-wide linear predictor. Various scenarios are investigated, depending on the nature of the local feedback (full information or bandit feedback), on the set of available predictors (the decision set), and the way data is generated (by an oblivious or adaptive adversary). We propose simple and natural distributed regression algorithms, involving, at each node and in each round, a local gradient descent step and a communication and averaging step where nodes aim at aligning their predictors to those of their neighbors. We establish regret upper bounds typically in O(T3/4) when the decision set is unbounded and in O(√T) in case of bounded decision set.

The work studies how node-to-node communications over an Erd\H{o}s-R\'enyi random network influence distributed online convex optimization, which is vital in solving large-scale machine learning in antagonistic or changing environments. At per step, each node (computing unit) makes a local decision, experiences a loss evaluated with a convex function, and communicates the decision with other nodes over a network. The node-to-node communications are described by the Erd\H{o}s-R\'enyi rule, where independently each link takes place with a probability $p$ over a prescribed connected graph. The objective is to minimize the system-wide loss accumulated over a finite time horizon. We consider standard distributed gradient descents with full gradients, one-point bandits and two-points bandits for convex and strongly convex losses, respectively. We establish how the regret bounds scale with respect to time horizon $T$, network size $N$, decision dimension $d$, and an algebraic network connectivity. The regret bounds scaling with respect to $T$ match those obtained by state-of-the-art algorithms and fundamental limits in the corresponding centralized online optimization problems, e.g., $\mathcal{O}(\sqrt{T}) $ and $\mathcal{O}(\ln(T)) $ regrets are established for convex and strongly convex losses with full gradient feedback and two-points information, respectively. For classical Erd\H{o}s-R\'enyi networks over all-to-all possible node communications, the regret scalings with respect to the probability $p$ are analytically established, based on which the tradeoff between the communication overhead and computation accuracy is clearly demonstrated. Numerical studies have validated the theoretical findings.

This paper proposes and investigates a framework for clique gossip protocols. As complete subnetworks, the existence of cliques is ubiquitous in various social, computer, and engineering networks. By clique gossiping, nodes interact with each other along a sequence of cliques. Clique-gossip protocols are defined as arbitrary linear node interactions where node states are vectors evolving as linear dynamical systems. Such protocols become clique-gossip averaging algorithms when node states are scalars under averaging rules. We generalize the classical notion of line graph to capture the essential node interaction structure induced by both the underlying network and the specific clique sequence. We prove a fundamental eigenvalue invariance principle for periodic clique-gossip protocols, which implies that any permutation of the clique sequence leads to the same spectrum for the overall state transition when the generalized line graph contains no cycle. We also prove that for a network with n nodes, cliques with smaller sizes determined by factors of n can always be constructed leading to finite-time convergent clique-gossip averaging algorithms, provided n is not a prime number. Particularly, such finite-time convergence can be achieved with cliques of equal size m if and only if n is divisible by m and they have exactly the same prime factors. A proven fastest finite-time convergent clique-gossip algorithm is constructed for clique-gossiping using size-m cliques. Additionally, the acceleration effects of clique-gossiping are illustrated via numerical examples.

In this paper, we investigate probabilistic stability of Kalman filtering over fading channels modeled by *-mixing random processes, where channel fading is allowed to generate non-stationary packet dropouts with temporal and/or spatial correlations. Upper/lower almost sure (a.s.) stabilities and absolutely upper/lower a.s. stabilities are defined for characterizing the sample-path behaviors of the Kalman filtering. We prove that both upper and lower a.s. stabilities follow a zero-one law, i.e., these stabilities must happen with a probability either zero or one, and when the filtering system is one-step observable, the absolutely upper and lower a.s. stabilities can also be interpreted using a zero-one law. We establish general stability conditions for (absolute) upper and lower a.s. stabilities. In particular, with one-step observability, we show the equivalence between absolutely a.s. stabilities and a.s. ones, and necessary and sufficient conditions in terms of packet arrival rate are derived; for the so-called non-degenerate systems, we also manage to give a necessary and sufficient condition for upper a.s. stability.

This paper proposes and investigates a Boolean gossip model as a simplified but non-trivial probabilistic Boolean network. With positive node interactions, in view of standard theories from Markov chains, we prove that the node states asymptotically converge to an agreement at a binary random variable, whose distribution is characterized for large-scale networks by mean-field approximation. Using combinatorial analysis, we also successfully count the number of communication classes of the positive Boolean network explicitly in terms of the topology of the underlying interaction graph, where remarkably minor variation in local structures can drastically change the number of network communication classes. With general Boolean interaction rules, emergence of absorbing network Boolean dynamics is shown to be determined by the network structure with necessary and sufficient conditions established regarding when the Boolean gossip process defines absorbing Markov chains. Particularly, it is shown that for the majority of the Boolean interaction rules, except for nine out of the total 216- 1 possible nonempty sets of binary Boolean functions, whether the induced chain is absorbing has nothing to do with the topology of the underlying interaction graph, as long as connectivity is assumed. These results illustrate the possibilities of relating dynamical properties of Boolean networks to graphical properties of the underlying interactions.

Gossip algorithms are widely used in modern distributed systems, with applications ranging from sensor networks and peer-to-peer networks to mobile vehicle networks and social networks. A tremendous research effort has been devoted to analyzing and improving the asymptotic rate of convergence for gossip algorithms. In this work we study finite-time convergence of deterministic gossiping. We show that there exists a symmetric gossip algorithm that converges in finite time if and only if the number of network nodes is a power of two, while there always exists an asymmetric gossip algorithm with finite-time convergence, independent of the number of nodes. For n=2mnodes, we prove that a fastest convergence can be reached in nm=nlog2 n node updates via symmetric gossiping. On the other hand, under asymmetric gossip among n=2m+r nodes with , it takes at least mn+2r node updates for achieving finite-time convergence. It is also shown that the existence of finite-time convergent gossiping often imposes strong structural requirements on the underlying interaction graph. Finally, we apply our results to gossip algorithms in quantum networks, where the goal is to control the state of a quantum system via pairwise interactions. We show that finite-time convergence is never possible for such systems.

Distributed consensus computation over random graph processes is considered. The random graph process is defined as a sequence of random variables which take values from the set of all possible digraphs over the node set. At each time step, every node updates its state based on a Bernoulli trial, independent in time and among different nodes: either averaging among the neighbor set generated by the random graph, or sticking with its current state. The connectivity-independence and arc-independence are introduced to capture the fundamental influence of the random graphs on the consensus convergence. Necessary and/or sufficient conditions are presented on the success probabilities of the Bernoulli trials for the network to reach a global almost sure consensus, with some sharp threshold established revealing a consensus zero-one law. Convergence rates are established by the lower and upper bounds of the ϵ-computation time. We also generalize the concepts of connectivity/arc independence to their analogues from the *-mixing point of view, so that our results apply to a very wide class of graphical models, including the majority of random graph models in the literature, e.g., Erdos-Rényi, gossiping, and Markovian random graphs. We show that under *-mixing, our convergence analysis continues to hold and the corresponding almost sure consensus conditions are established. Finally, we further investigate almost sure finite-time convergence of random gossiping algorithms, and prove that the Bernoulli trials play a key role in ensuring finite-time convergence. These results add to the understanding of the interplay between random graphs, random computations, and convergence probability for distributed information processing.

This paper investigates the role persistent relations play for a social network to reach a global belief agreement under discrete-time or continuous-time evolution. Each directed arc in the underlying communication graph is assumed to be associated with a time-dependent weight function, which describes the strength of the information flow from one node to another. An arc is said to be persistent if its weight function has infinite L1or l1norm for continuous or discrete belief evolutions, respectively. The graph that consists of all persistent arcs is called the persistent graph of the underlying network. Three necessary and sufficient conditions on agreement or ε-agreement are established. We prove that the persistent graph fully determines the convergence to a common opinion in a social network. It is shown how the convergence rate explicitly depends on the diameter of the persistent graph. For a social networking service like Facebook, our results indicate how permanent friendships need to be and what network topology they should form for the network to be an efficient platform for opinion diffusion.

The dynamics of an agreement protocol interacting with a disagreement process over a common random network is considered. The model can represent the spreading of true and false information over a communication network, the propagation of faults in a large-scale control system, or the development of trust and mistrust in a society. At each time instance and with a given probability, a pair of network nodes interact. At random each of the nodes then updates its state towards the state of the other node (attraction), away from the other node (repulsion), or sticks to its current state (neglect). Agreement convergence and disagreement divergence results are obtained for various strengths of the updates for both symmetric and asymmetric update rules. Impossibility theorems show that a specific level of attraction is required for almost sure asymptotic agreement and a specific level of repulsion is required for almost sure asymptotic disagreement. A series of sufficient and/or necessary conditions are then established for agreement convergence or disagreement divergence. In particular, under symmetric updates, a critical convergence measure in the attraction and repulsion update strength is found, in the sense that the asymptotic property of the network state evolution transits from agreement convergence to disagreement divergence when this measure goes from negative to positive. The result can be interpreted as a tight bound on how much bad action needs to be injected in a dynamic network in order to consistently steer its overall behavior away from consensus.

One of the most important problems for the study of singular distributed parameter systems is the well-posedness. Not only is it very important for the study of stability of singular distributed parameter systems, but also it is the theoretic basis for the study of the related problem of optimal control. In this paper, the concepts and the properties of generalized operator semigroup(GOS) and generalized integral semigroup(GIS) are given in Hilbert space, the solving problem of the non-homogeneous singular distributed parameter system is discussed by the concepts and the properties of GOS and GIS in Hilbert space, and some important results of the two classes of singular distributed parameter systems are given.