We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information---the class-attribute matrix---and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

We first prove the second part of the Theorem. Now, we will prove the first part of the Theorem. The proof is by induction. The following auxiliary proposition is crucial to prove the theorem. A for the first attribute.

We develop a rigorous mathematical analysis of zero-shot learning with attributes.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information---the class-attribute matrix---and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

Abstract: Compositional Zero-Shot Learning (CZSL) aims to recognize unseen compositions formed from seen state and object during training. Since the same state may be various in the visual appearance while entangled with different objects, CZSL is still a challenging task. Some methods recognize state and object with two trained classifiers, ignoring the impact of the interaction between object and state; the other methods try to learn the joint representation of the state-object compositions, leading to the domain gap between seen and unseen composition sets. Considering the entanglement between state and object, we embed the visual feature into a Siamese Contrastive Space to capture prototypes of them separately, alleviating the interaction between state and object. In addition, we design a State Transition Module (STM) to increase the diversity of training compositions, improving the robustness of the recognition model.

Zero-shot classification is a promising paradigm to solve an applicable problem when the training classes and test classes are disjoint. Achieving this usually needs experts to externalize their domain knowledge by manually specifying a class-attribute matrix to define which classes have which attributes. Designing a suitable class-attribute matrix is the key to the subsequent procedure, but this design process is tedious and trial-and-error with no guidance. This paper proposes a visual explainable active learning approach with its design and implementation called semantic navigator to solve the above problems. This approach promotes human-AI teaming with four actions (ask, explain, recommend, respond) in each interaction loop. The machine asks contrastive questions to guide humans in the thinking process of attributes. A novel visualization called semantic map explains the current status of the machine. Therefore analysts can better understand why the machine misclassifies objects. Moreover, the machine recommends the labels of classes for each attribute to ease the labeling burden. Finally, humans can steer the model by modifying the labels interactively, and the machine adjusts its recommendations. The visual explainable active learning approach improves humans' efficiency of building zero-shot classification models interactively, compared with the method without guidance. We justify our results with user studies using the standard benchmarks for zero-shot classification.