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As far as DLPack is concerned, sparse tensors are currently not supported. However, as the Data API Standard Consortium starts considering standardizing sparse tensors (scipy/scipy#18915), at some point we'll need to have a DLPack-like in-memory data exchange format. We're not there yet, though.
For sparse arrays, binsparse is being developed as an on-disk storage spec, which should capture all the needed details/formats that are sparse-specific. There's also an open discussion about in-memory storage that is relevant: GraphBLAS/binsparse-specification#4.
Should DLPack also define a stable format for sparse arrays?
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