I think the ML community has just adopted the mathematicians’ definition of tensor, which is just “high-dimensional array”, though usually with some notion of underlying vector space for each dimension. In contrast, a physicist’s tensor is a multi-index object that transforms in a certain way under certain operations (e.g. rotations in 3D space), with a possible distinction of contravariant and covariant indices (especially in general relativity AFAIK). In practice, the mathematicians’ tensors are quite large, while the physicists’ tensors are quite small (please correct me if I’m wrong).
I’m also working on a rather specialized tensor package (it is too WIP to link to) and it’s also for “just” high-dimensional arrays. I think the majority of Julia tensor packages uses the term in this sense?
There is also a JuliaTensors Github organization but it looks pretty bare and might be abandoned. If there is general interest in tensors, maybe we could revive or expand on this? Although again, one would first need to clarify what kind of tensors…