Continuous Arrays
summary
Proposes a Continuous Tensor abstraction with real-valued indices and continuous for loops that assume tensors are piecewise-constant (finite axis-aligned constant regions). Introduces two reduction semantics, integral vs summation, so interval regions integrate to length-weighted values while pinpoints sum. Builds a compiler by extending Finch to lower continuous loops to executable code. Demonstrations: radius search and ray trilinear sampling expressed in 9 lines versus ~80 lines in PyTorch; single-threaded CPU generic code outperforms the reference PyTorch; point-cloud convolution lags due to dense kernels.
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chapters (9)
- 0:00Introduction
- 1:50Continuous tensor abstraction
- 3:15Pinpoint and interval coordinates
- 5:23Summation and integral reduction
- 6:25Radius search in continuous tensors
- 8:12Compiler design for continuous loops
- 9:15Trilinear interpolation
- 10:41Beyond numerical computing
- 12:24Q&A
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