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In this paper, we put forward the model of zero-error distributed function compression system of two binary memoryless sources X and Y, where there are two encoders En1 and En2 and one decoder De, connected by two channels (En1, De) and (En2, De) with the capacity constraints C1 and C2, respectively. The encoder En1 can observe X or (X,Y) and the encoder En2 can observe Y or (X,Y) according to the two switches s1 and s2 open or closed (corresponding to taking values 0 or 1). The decoder De is required to compress the binary arithmetic sum f(X,Y)=X+Y with zero error by using the system multiple times. We use (s1s2;C1,C2;f) to denote the model in which it is assumed that C1 \geq C2 by symmetry. The compression capacity for the model is defined as the maximum average number of times that the function f can be compressed with zero error for one use of the system, which measures the efficiency of using the system. We fully characterize the compression capacities for all the four cases of the model (s1s2;C1,C2;f) for s1s2= 00,01,10,11. Here, the characterization of the compression capacity for the case (01;C1,C2;f) with C1>C2 is highly nontrivial, where a novel graph coloring approach is developed. Furthermore, we apply the compression capacity for (01;C1,C2;f) to an open problem in network function computation that whether the best known upper bound of Guang et al. on computing capacity is in general tight.

Instance segmentation is a fundamental skill for many robotic applications. We propose a self-supervised method that uses grasp interactions to collect segmentation supervision for an instance segmentation model. When a robot grasps an item, the mask of that grasped item can be inferred from the images of the scene before and after the grasp. Leveraging this insight, we learn a grasp segmentation model to segment the grasped object from before and after grasp images. Such a model can segment grasped objects from thousands of grasp interactions without costly human annotation. Using the segmented grasped objects, we can "cut" objects from their original scenes and "paste" them into new scenes to generate instance supervision. We show that our grasp segmentation model provides a 5x error reduction when segmenting grasped objects compared with traditional image subtraction approaches. Combined with our "cut-and-paste" generation method, instance segmentation models trained with our method achieve better performance than a model trained with 10x the amount of labeled data. On a real robotic grasping system, our instance segmentation model reduces the rate of grasp errors by over 3x compared to an image subtraction baseline.

We show the convergence of Wasserstein inverse reinforcement learning (WIRL) for multi-objective optimizations with the projective subgradient method by formulating an inverse problem of the optimization problem that is equivalent to WIRL for multi-objective optimizations. In addition, we prove convergence of inverse reinforcement learning (maximum entropy inverse reinforcement learning, guid cost learning) for multi-objective optimization with the projective subgradient method.

Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a mesh-free data-based approximation method for the value function of optimal control problems, which partially mitigates the dimensionality problem. The method is based on a greedy Hermite kernel interpolation scheme and incorporates context-knowledge by its structure. Especially, the value function surrogate is elegantly enforced to be 0 in the target state, non-negative and constructed as a correction of a linearized model. The algorithm is proposed in a matrix-free way, which circumvents the large-matrix-problem for multivariate Hermite interpolation. For finite time horizons, both convergence of the surrogate to the value function as well as for the surrogate vs. the optimal controlled dynamical system are proven. Experiments support the effectiveness of the scheme, using among others a new academic model that has a scalable dimension and an explicitly given value function. It may also be useful for the community to validate other optimal control approaches.

Current few-shot action recognition involves two primary sources of information for classification:(1) intra-video information, determined by frame content within a single video clip, and (2) inter-video information, measured by relationships (e.g., feature similarity) among videos. However, existing methods inadequately exploit these two information sources. In terms of intra-video information, current sampling operations for input videos may omit critical action information, reducing the utilization efficiency of video data. For the inter-video information, the action misalignment among videos makes it challenging to calculate precise relationships. Moreover, how to jointly consider both inter- and intra-video information remains under-explored for few-shot action recognition. To this end, we propose a novel framework, Video Information Maximization (VIM), for few-shot video action recognition. VIM is equipped with an adaptive spatial-temporal video sampler and a spatiotemporal action alignment model to maximize intra- and inter-video information, respectively. The video sampler adaptively selects important frames and amplifies critical spatial regions for each input video based on the task at hand. This preserves and emphasizes informative parts of video clips while eliminating interference at the data level. The alignment model performs temporal and spatial action alignment sequentially at the feature level, leading to more precise measurements of inter-video similarity. Finally, These goals are facilitated by incorporating additional loss terms based on mutual information measurement. Consequently, VIM acts to maximize the distinctiveness of video information from limited video data. Extensive experimental results on public datasets for few-shot action recognition demonstrate the effectiveness and benefits of our framework.

Principled accountability in the aftermath of harms is essential to the trustworthy design and governance of algorithmic decision making. Legal philosophy offers a paramount method for assessing culpability: putting the agent 'on the stand' to subject their actions and intentions to cross-examination. We show that under minimal assumptions automated reasoning can rigorously interrogate algorithmic behaviors as in the adversarial process of legal fact finding. We model accountability processes, such as trials or review boards, as Counterfactual-Guided Logic Exploration and Abstraction Refinement (CLEAR) loops. We use an SMT-based oracle to discharge queries about agent behavior in factual and counterfactual scenarios, as adaptively formulated by a human investigator. For a decision algorithm $\mathcal{A}$, we use symbolic execution to represent its logic as a statement $\Pi$ in the decidable theory $\texttt{QF_FPBV}$. We implement our framework in a tool called $\textsf{soid}$ with an accompanying GUI, and demonstrate its utility on an illustrative car crash scenario.

Previous group activity recognition approaches were limited to reasoning using human relations or finding important subgroups and tended to ignore indispensable group composition and human-object interactions. This absence makes a partial interpretation of the scene and increases the interference of irrelevant actions on the results. Therefore, we propose our DynamicFormer with Dynamic composition Module (DcM) and Dynamic interaction Module (DiM) to model relations and locations of persons and discriminate the contribution of participants, respectively. Our findings on group composition and human-object interaction inspire our core idea. Group composition tells us the location of people and their relations inside the group, while interaction reflects the relation between humans and objects outside the group. We utilize spatial and temporal encoders in DcM to model our dynamic composition and build DiM to explore interaction with a novel GCN, which has a transformer inside to consider the temporal neighbors of human/object. Also, a Multi-level Dynamic Integration is employed to integrate features from different levels. We conduct extensive experiments on two public datasets and show that our method achieves state-of-the-art.

Several task and motion planning algorithms have been proposed recently to design paths for mobile robot teams with collaborative high-level missions specified using formal languages, such as Linear Temporal Logic (LTL). However, the designed paths often lack reactivity to failures of robot capabilities (e.g., sensing, mobility, or manipulation) that can occur due to unanticipated events (e.g., human intervention or system malfunctioning) which in turn may compromise mission performance. To address this novel challenge, in this paper, we propose a new resilient mission planning algorithm for teams of heterogeneous robots with collaborative LTL missions. The robots are heterogeneous with respect to their capabilities while the mission requires applications of these skills at certain areas in the environment in a temporal/logical order. The proposed method designs paths that can adapt to unexpected failures of robot capabilities. This is accomplished by re-allocating sub-tasks to the robots based on their currently functioning skills while minimally disrupting the existing team motion plans. We provide experiments and theoretical guarantees demonstrating the efficiency and resiliency of the proposed algorithm.

Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from observing its inputs and outputs. Despite the huge effort made to study this property and to introduce analytical criteria able to check whether a dynamic system satisfies this property or not, there is no general analytical criterion to automatically check the state observability when the dynamics are also driven by unknown inputs. Here, we introduce the general analytical solution of this fundamental problem, often called the unknown input observability problem. This paper provides the general analytical solution of this problem, namely, it provides the systematic procedure, based on automatic computation (differentiation and matrix rank determination), that allows us to automatically check the state observability even in the presence of unknown inputs (Algorithm 6.1). A first solution of this problem was presented in the second part of the book: "Observability: A New Theory Based on the Group of Invariance" [45]. The solution presented by this paper completes the previous solution in [45]. In particular, the new solution exhaustively accounts for the systems that do not belong to the category of the systems that are "canonic with respect to their unknown inputs". The analytical derivations largely exploit several new concepts and analytical results introduced in [45]. Finally, as a simple consequence of the results here obtained, we also provide the answer to the problem of unknown input reconstruction which is intimately related to the problem of state observability. We illustrate the implementation of the new algorithm by studying the observability properties of a nonlinear system in the framework of visual-inertial sensor fusion, whose dynamics are driven by two unknown inputs and one known input.

We study how to generate captions that are not only accurate in describing an image but also discriminative across different images. The problem is both fundamental and interesting, as most machine-generated captions, despite phenomenal research progresses in the past several years, are expressed in a very monotonic and featureless format. While such captions are normally accurate, they often lack important characteristics in human languages - distinctiveness for each caption and diversity for different images. To address this problem, we propose a novel conditional generative adversarial network for generating diverse captions across images. Instead of estimating the quality of a caption solely on one image, the proposed comparative adversarial learning framework better assesses the quality of captions by comparing a set of captions within the image-caption joint space. By contrasting with human-written captions and image-mismatched captions, the caption generator effectively exploits the inherent characteristics of human languages, and generates more discriminative captions. We show that our proposed network is capable of producing accurate and diverse captions across images.