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Neat!

however, as a C guy, I really don't want to give up the control of my data structures.

A key idea of this language is that you _don't_ give up control over your data structures. You program your algorithm against abstract data structures, as in most high-performance DSLs, but then you _explicitly control_ the implementation of those abstract data structures as physical hierarchical structures. (You can get a taste for this in the `layout` block in Fig. 1.)
So you're working on both Halide and Taichi?
Very cool. Seems to be another tool in the same vein as halide-lang.org, now extended for sparse data.
Looks like cool stuff.

Am I right this language compiles to GPU code?

I'm thinking of a similar project myself and I'm curious what consideration besides loop vectorization goes into such stuff, especially, what about caches and access issues (OK, I ask the same question for any project like this)?

Also, isn't one factor in sparse representations that if you aren't careful, the data becomes un-sparse and slows down a lot?

It compiles to both CPU and GPU. GPU is faster and headline numbers are for GPU.
Cool stuff, but I would have found it more useful as a python library, to allow integration with existing tools like Pytorch.
I would have found it more useful as a python library

Today is you lucky day! Taichi is also a C++ library with first class python bindings: https://github.com/yuanming-hu/taichi

That's awesome, I'll give it a try. Do the python bindings include the Sparse Data functionality? I can't find it in the docs.