Systems, methods, and media for implementing tensor-trains in graphics processing unit tensor cores

A method of implementing tensor-trains, comprising:

• performing at least one of:
• partitioning a first matrix into a first plurality of blocks along a column dimension and partitioning a second matrix into a second plurality of blocks along a row dimension;
• loading a first block of the first plurality of blocks and a second block of the second plurality of blocks into a first graphics processing unit (GPU) tensor core;
• performing a multiplication of the first block and the second block to produce a first product;
• loading a third block of the first plurality of blocks and a fourth block of the second plurality of blocks into a second GPU tensor core;
• performing a multiplication of the third block and the fourth block to produce a second product;
• and
• summing at least the first product and the second product to produce a first sum;
• and
• partitioning a third matrix into a third plurality of blocks along a column dimension;
• loading a fourth matrix and a fifth block of the third plurality of blocks into a third graphics processing unit tensor core;
• and
• performing a multiplication of the fourth matrix and the fifth block to produce a third product.

A non-transitory computer-readable medium containing computer executable instructions that, when collectively executed by at least one processor, a first graphics processing unit (GPU) tensor core, and a second GPU tensor core, cause the at least one processor, the first GPU tensor core, and the second GPU tensor core to collectively perform a method of implementing tensor-trains, the method comprising:

• partitioning a first matrix into a first plurality of blocks along a column dimension and partitioning a second matrix into a second plurality of blocks along a row dimension;
• loading a first block of the first plurality of blocks and a second block of the second plurality of blocks into a first GPU tensor core;
• performing a multiplication of the first block and the second block to produce a first product;
• loading a third block of the first plurality of blocks and a fourth block of the second plurality of blocks into a second GPU tensor core;
• performing a multiplication of the third block and the fourth block to produce a second product;
• and
• summing at least the first product and the second product to produce a first sum;
• partitioning a third matrix into a third plurality of blocks along a column dimension;
• loading a fourth matrix and a fifth block of the third plurality of blocks into a third graphics processing unit tensor core;
• and
• performing a multiplication of the fourth matrix and the fifth block to produce a third product.