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While deep neural networks (DNNs) have achieved impressive classification performance in closed-world learning scenarios, they typically fail to generalize to unseen categories in dynamic open-world environments, in which the number of concepts is unbounded. In contrast, human and animal learners have the ability to incrementally update their knowledge by recognizing and adapting to novel observations. In particular, humans characterize concepts via exclusive (unique) sets of essential features, which are used for both recognizing known classes and identifying novelty. Inspired by natural learners, we introduce a Sparse High-level-Exclusive, Low-level-Shared feature representation (SHELS) that simultaneously encourages learning exclusive sets of high-level features and essential, shared low-level features. The exclusivity of the high-level features enables the DNN to automatically detect out-of-distribution (OOD) data, while the efficient use of capacity via sparse low-level features permits accommodating new knowledge. The resulting approach uses OOD detection to perform class-incremental continual learning without known class boundaries. We show that using SHELS for novelty detection results in statistically significant improvements over state-of-the-art OOD detection approaches over a variety of benchmark datasets. Further, we demonstrate that the SHELS model mitigates catastrophic forgetting in a class-incremental learning setting,enabling a combined novelty detection and accommodation framework that supports learning in open-world settings