Benchmarks for kernel matrix vector products, inversions and attention layers

This website provides a benchmarking environment for operations on kernel matrices. Please visit our GitHub repository for a guided tour of the platform. Note that this is an open project: you are welcome to make a pull request to improve the benchmarking system or add support for a new algorithm.

Results are split by dataset and algorithm. The plots depict the root mean squared error against total run time for both kernel matrix products and solvers. Click on the images to access detailed interactive plots with numerous performance metrics and Latex code to include in your paper.

Datasets:
• product-cube-D3-E1-M1000-N1000-gaussian
• product-cube-D3-E1-M10000-N10000-gaussian
• product-cube-D3-E1-M2000-N2000-gaussian
• product-cube-D3-E1-M5000-N5000-gaussian
• product-sphere-D3-E1-M1000-N1000-inverse-distance
• product-sphere-D3-E1-M10000-N10000-inverse-distance
• product-sphere-D3-E1-M2000-N2000-inverse-distance
• product-sphere-D3-E1-M5000-N5000-inverse-distance
• solver-cube-D3-E1-M1000-N1000-gaussian
• solver-cube-D3-E1-M10000-N10000-gaussian
• solver-cube-D3-E1-M2000-N2000-gaussian
• solver-cube-D3-E1-M5000-N5000-gaussian
• solver-sphere-D3-E1-M1000-N1000-inverse-distance
• solver-sphere-D3-E1-M10000-N10000-inverse-distance
• solver-sphere-D3-E1-M2000-N2000-inverse-distance
• solver-sphere-D3-E1-M5000-N5000-inverse-distance

Algorithms:
• bruteforce-product-blas
• bruteforce-solver-blas
• htool-product

Results by Dataset

Product on the sphere, gaussian (N=1000, D=3)

Product on the sphere, gaussian (N=10000, D=3)

Product on the sphere, gaussian (N=2000, D=3)

Product on the sphere, gaussian (N=5000, D=3)

Product on the sphere, inverse-distance (N=1000, D=3)

Product on the sphere, inverse-distance (N=10000, D=3)

Product on the sphere, inverse-distance (N=2000, D=3)

Product on the sphere, inverse-distance (N=5000, D=3)

Solver on the sphere, gaussian (N=1000, D=3)

Solver on the sphere, gaussian (N=10000, D=3)

Solver on the sphere, gaussian (N=2000, D=3)

Solver on the sphere, gaussian (N=5000, D=3)

Solver on the sphere, inverse-distance (N=1000, D=3)

Solver on the sphere, inverse-distance (N=10000, D=3)

Solver on the sphere, inverse-distance (N=2000, D=3)

Solver on the sphere, inverse-distance (N=5000, D=3)

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Results by Algorithm

bruteforce-product-blas

bruteforce-solver-blas

htool-product

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Contact

Please use Github to submit your implementations and improvements.