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We present flight patterns for a collision-free passage of swarms of drones through one or more openings. The narrow openings provide drones with access to an infrastructure component such as charging stations to charge their depleted batteries and hangars for storage. The flight patterns are a staging area (queues) that match the rate at which an infrastructure component and its openings consume drones. They prevent collisions and may implement different policies that control the order in which drones pass through an opening. We illustrate the flight patterns with a 3D display that uses drones configured with light sources to illuminate shapes. 

Today's robotic laboratories for drones are housed in a large room. At times, they are the size of a warehouse. These spaces are typically equipped with permanent devices to localize the drones, e.g., Vicon Infrared cameras. Significant time is invested to fine-tune the localization apparatus to compute and control the position of the drones. One may use these laboratories to develop a 3D multimedia system with miniature sized drones configured with light sources. As an alternative, this brave new idea paper envisions shrinking these room-sized laboratories to the size of a cube or cuboid that sits on a desk and costs less than 10K dollars. The resulting Dronevision (DV) will be the size of a 1990s Television. In addition to light sources, its Flying Light Specks (FLSs) will be network-enabled drones with storage and processing capability to implement decentralized algorithms. The DV will include a localization technique to expedite development of 3D displays. It will act as a haptic interface for a user to interact with and manipulate the 3D virtual illuminations. It will empower an experimenter to design, implement, test, debug, and maintain software and hardware that realize novel algorithms in the comfort of their office without having to reserve a laboratory. In addition to enhancing productivity, it will improve safety of the experimenter by minimizing the likelihood of accidents. This paper introduces the concept of a DV, the research agenda one may pursue using this device, and our plans to realize one. 

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the complexity of concepts becomes diverse. Specifically, at the representational level, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) build an inverted-U relation. Leveraging the Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the computational level, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity out-perform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization. 

Inspired by humans’ exceptional ability to master arithmetic and generalize to new problems, we present a new dataset, Handwritten arithmetic with INTegers (HINT), to examine machines’ capability of learning generalizable concepts at three levels: perception, syntax, and semantics. In HINT, machines are tasked with learning how concepts are perceived from raw signals such as images (i.e., perception), how multiple concepts are structurally combined to form a valid expression (i.e., syntax), and how concepts are realized to afford various reasoning tasks (i.e., semantics), all in a weakly supervised manner. Focusing on systematic generalization, we carefully design a five-fold test set to evaluate both the interpolation and the extrapolation of learned concepts w.r.t. the three levels. Further, we design a few-shot learning split to determine whether or not models can rapidly learn new concepts and generalize them to more complex scenarios. To comprehend existing models’ limitations, we undertake extensive experiments with various sequence-to-sequence models, including RNNs, Transformers, and GPT-3 (with the chain of thought prompting). The results indicate that current models struggle to extrapolate to long-range syntactic dependency and semantics. Models exhibit a considerable gap toward human-level generalization when evaluated with new concepts in a few-shot setting. Moreover, we discover that it is infeasible to solve HINT by merely scaling up the dataset and the model size; this strategy contributes little to the extrapolation of syntax and semantics. Finally, in zero-shot GPT-3 experiments, the chain of thought prompting exhibits impressive results and significantly boosts the test accuracy. We believe the HINT dataset and the experimental findings are of great interest to the learning community on systematic generalization. 

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TABMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TABMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TABMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TABMWP. To mitigate this, we further propose a novel approach, PROMPTPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples.