Deep learning has shown great success in settings with massive amounts of data but has struggled when data is limited. Few-shot learning algorithms, which seek to address this limitation, are designed to generalize well to new tasks with limited data. Typically, models are evaluated on unseen classes and datasets that are defined by the same fundamental task as they are trained for (e.g. category membership). One can also ask how well a model can generalize to fundamentally different tasks within a fixed dataset (for example: moving from category membership to tasks that involve detecting object orientation or quantity). To formalize this kind of shift we define a notion of "independence of tasks" and identify three new sets of labels for established computer vision datasets that test a model's ability to generalize to tasks which draw on orthogonal attributes in the data. We use these datasets to investigate the failure modes of metric-based few-shot models. Based on our findings, we introduce a new few-shot model called Fuzzy Simplicial Networks (FSN) which leverages a construction from topology to more flexibly represent each class from limited data. In particular, FSN models can not only form multiple representations for a given class but can also begin to capture the low-dimensional structure which characterizes class manifolds in the encoded space of deep networks. We show that FSN outperforms state-of-the-art models on the challenging tasks we introduce in this paper while remaining competitive on standard few-shot benchmarks.
Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction
Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）；Max Planck Institute for Human Cognitive and Brain Sciences（马克斯·普朗克人类认知与脑科学研究所）；Max Planck School of Cognition（马克斯·普朗克认知学校）；ScaDS.AI (Center for Scalable Data Analytics and AI)（ScaDS.AI（可扩展数据与人工智能中心））；Santa Fe Institute for the Sciences of Complexity（复杂性科学圣菲研究所）
Binarizing Physics-Inspired GNNs for Combinatorial Optimization
Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University（计算机科学系，电气工程学院，捷克技术大学）；Quantum Technologies Group, HSBC Labs, Singapore（量子技术组，汇丰实验室，新加坡）；Archimedes Research Unit on AI, Data Science and Algorithms, Athena Research Center（人工智能、数据科学与算法研究单元，阿提卡研究中心）
Persistent Topological Structures and Cohomological Flows as a Mathematical Framework for Brain-Inspired Representation Learning
Dept. of Artificial Intelligence & Machine Learning（人工智能与机器学习系）；B.N.M Institute of Technology（B.N.M技术学院）；Dept. of Computer Science Engineering（计算机科学工程系）；Dept. of Electronics & Communications（电子与通信系）
