Superhard materials are among the most scarce functional inorganic solids in existence. Indeed, recent research suggested that less than 0.1% of all known materials are likely to have a Vickers hardness ≥40 GPa. Here, an anomaly detection framework is created to treat these materials as rare occurrences by encoding and reconstructing the input composition and crystal structure information without supervision. The resulting model can quantitatively identify outliers from "normal" behaving materials, leading to the discovery of materials with exceptional properties such as a superhard response. Moreover, examining the difference between the encoded and decoded crystal structure provides fundamental insights into the crystal-chemical origin of hardness. The presented methodology is ultimately generalizable, enabling the design of other outlier materials with rare and unexpected physical properties.