We introduce the isoperimetric loss as a regularization criterion for learning the map from a visual representation to a semantic embedding, to be used to transfer knowledge to unknown classes in a zero-shot learning setting. We use a pre-trained deep neural network model as a visual representation of image data, a Word2Vec embedding of class labels, and linear maps between the visual and semantic embedding spaces. However, the spaces themselves are not linear, and we postulate the sample embedding to be populated by noisy samples near otherwise smooth manifolds. We exploit the graph structure defined by the sample points to regularize the estimates of the manifolds by inferring the graph connectivity using a generalization of the isoperimetric inequalities from Riemannian geometry to graphs. Surprisingly, this regularization alone, paired with the simplest baseline model, outperforms the state-of-the-art among fully automated methods in zero-shot learning benchmarks such as AwA and CUB. This improvement is achieved solely by learning the structure of the underlying spaces by imposing regularity.

该论文介绍了等周损失（isoperimetric loss）作为图像表示到语义嵌入的映射的正则化标准，提出了一种使用预训练的深度神经网络模型作为图像数据的视觉表示的方法，并使用线性映射将视觉和语义嵌入空间结合起来，此方法通过利用样本空间中定义的图结构来正则化样本嵌入和结构，进而将零样本学习的性能提高到了目前的最高水平。

利用等周损失进行零样本学习