The Continuous Tensor Abstraction: Where Indices are Real
summary
Introduces a compiler and code generator that lets tensor indices be real numbers and represents data as piecewise-constant tensors so infinite domains execute in finite time; extends Einsum with measure-marked reductions (counting vs. integration) and supports continuous indices like A[3.14]. Implementation partitions space via a linear two‑finger merge plus sparse‑intersection pruning, fuses filters into single‑pass kernels, and matches or beats hand code: 9.20× on 2D radius search with ~60× fewer LoC, 1.22× on genomic interval overlap (~18× LoC saving), 1.69× on NeRF trilinear interpolation (~6× LoC saving).
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chapters (7)
- 0:00Continuous tensor abstraction intro
- 3:12Continuous tensors defined
- 5:41Einom for real indices
- 8:06Efficient compilation
- 10:37Radius search performance
- 12:47Benefits and future work
- 13:54Answering audience questions
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