We introduce a new deep generative model useful for uncertainty quantification: the Morse neural network, which generalizes the unnormalized Gaussian densities to have modes of high-dimensional submanifolds instead of just discrete points. Fitting the Morse neural network via a KL-divergence loss yields 1) a (unnormalized) generative density, 2) an OOD detector, 3) a calibration temperature, 4) a generative sampler, along with in the supervised case 5) a distance aware-classifier. The Morse network can be used on top of a pre-trained network to bring distance-aware calibration w.r.t the training data. Because of its versatility, the Morse neural networks unifies many techniques: e.g., the Entropic Out-of-Distribution Detector of (Mac\^edo et al., 2021) in OOD detection, the one class Deep Support Vector Description method of (Ruff et al., 2018) in anomaly detection, or the Contrastive One Class classifier in continuous learning (Sun et al., 2021). The Morse neural network has connections to support vector machines, kernel methods, and Morse theory in topology.

翻译：我们提出了一种适用于不确定性量化的新型深度生成模型：Morse神经网络。该模型将非归一化高斯密度泛化为具有高维子流形模态（而非仅离散点）的形式。通过KL散度损失拟合Morse神经网络可同时获得：1)（非归一化的）生成密度，2) 分布外检测器，3) 校准温度，4) 生成采样器，以及在监督情形下的5) 距离感知分类器。Morse神经网络可叠加于预训练网络之上，实现对训练数据的距离感知校准。由于其多功能性，Morse神经网络统一了多种技术：例如(Macêdo等, 2021)提出的熵式分布外检测器（用于OOD检测）、(Ruff等, 2018)提出的单类深度支持向量描述方法（用于异常检测），以及(Sun等, 2021)提出的连续学习中的对比式单类分类器。该模型与支持向量机、核方法及拓扑学中的Morse理论存在理论关联。