Autonomous robots are increasingly becoming a strong fixture in social environments. Effective crowd navigation requires not only safe yet fast planning, but should also enable interpretability and computational efficiency for working in real-time on embedded devices. In this work, we advocate for hyperbolic learning to enable crowd navigation and we introduce Hyp2Nav. Different from conventional reinforcement learning-based crowd navigation methods, Hyp2Nav leverages the intrinsic properties of hyperbolic geometry to better encode the hierarchical nature of decision-making processes in navigation tasks. We propose a hyperbolic policy model and a hyperbolic curiosity module that results in effective social navigation, best success rates, and returns across multiple simulation settings, using up to 6 times fewer parameters than competitor state-of-the-art models. With our approach, it becomes even possible to obtain policies that work in 2-dimensional embedding spaces, opening up new possibilities for low-resource crowd navigation and model interpretability. Insightfully, the internal hyperbolic representation of Hyp2Nav correlates with how much attention the robot pays to the surrounding crowds, e.g. due to multiple people occluding its pathway or to a few of them showing colliding plans, rather than to its own planned route.

Image retrieval has become an increasingly appealing technique with broad multimedia application prospects, where deep hashing serves as the dominant branch towards low storage and efficient retrieval. In this paper, we carried out in-depth investigations on metric learning in deep hashing for establishing a powerful metric space in multi-label scenarios, where the pair loss suffers high computational overhead and converge difficulty, while the proxy loss is theoretically incapable of expressing the profound label dependencies and exhibits conflicts in the constructed hypersphere space. To address the problems, we propose a novel metric learning framework with Hybrid Proxy-Pair Loss (HyP$^2$ Loss) that constructs an expressive metric space with efficient training complexity w.r.t. the whole dataset. The proposed HyP$^2$ Loss focuses on optimizing the hypersphere space by learnable proxies and excavating data-to-data correlations of irrelevant pairs, which integrates sufficient data correspondence of pair-based methods and high-efficiency of proxy-based methods. Extensive experiments on four standard multi-label benchmarks justify the proposed method outperforms the state-of-the-art, is robust among different hash bits and achieves significant performance gains with a faster, more stable convergence speed. Our code is available at https://github.com/JerryXu0129/HyP2-Loss.