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Compositional zero-shot learning aims to recognize unseen compositions of seen visual primitives of object classes and their states. While all primitives (states and objects) are observable during training in some combination, their complex interaction makes this task especially hard. For example, wet changes the visual appearance of a dog very differently from a bicycle. Furthermore, we argue that relationships between compositions go beyond shared states or objects. A cluttered office can contain a busy table; even though these compositions don't share a state or object, the presence of a busy table can guide the presence of a cluttered office. We propose a novel method called Compositional Attention Propagated Embedding (CAPE) as a solution. The key intuition to our method is that a rich dependency structure exists between compositions arising from complex interactions of primitives in addition to other dependencies between compositions. CAPE learns to identify this structure and propagates knowledge between them to learn class embedding for all seen and unseen compositions. In the challenging generalized compositional zero-shot setting, we show that our method outperforms previous baselines to set a new state-of-the-art on three publicly available benchmarks.