Multiview Self-Supervised Studying (MSSL) relies on studying invariances with respect to a set of enter transformations. Nonetheless, invariance partially or completely removes transformation-related info from the representations, which could hurt efficiency for particular downstream duties that require such info. We suggest 2D strUctured and EquivarianT representations (coined DUET), that are 2nd representations organized in a matrix construction, and equivariant with respect to transformations performing on the enter knowledge. DUET representations keep details about an enter transformation, whereas remaining semantically expressive. In comparison with SimCLR (Chen et al., 2020) (unstructured and invariant) and ESSL (Dangovski et al., 2022) (unstructured and equivariant), the structured and equivariant nature of DUET representations allows managed technology with decrease reconstruction error, whereas controllability will not be doable with SimCLR or ESSL. DUET additionally achieves greater accuracy for a number of discriminative duties, and improves switch studying.