Tensor Processor Matrix-Matrix Batching for Combinatorial Optimization
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Solution Overview
Problem
Conventional computing systems face challenges in efficiently solving large-scale combinatorial optimization problems, particularly those involving more than 100 constrained variables, due to exponential growth in processing time and resource consumption, and existing algorithms like Ising processors and Tabu search are inefficient for NP-hard problems.
Innovation Solution
Utilizing simulated bifurcation optimization techniques on tensor processors, specifically the Language Processing Unit (LPU), by converting matrix-vector operations into matrix-matrix operations and incorporating mixed-integer quadratic programming with linear constraints transformed into quadratic penalty terms, and employing batched computations on tensor processors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional algorithms (linear programming, Ising processors, Tabu search) are used to solve combinatorial optimization problems, then the problems can be addressed, but processing time and resource consumption grow exponentially for problems with more than 100 constrained variables
Solution Approach 1:
The patent merges multiple vector-matrix operations into a single combined matrix-matrix operation. By batching k vector-matrix operations (where k > 1) into one matrix-matrix multiplication, the system leverages the parallel processing capability of tensor processors to perform multiple computations simultaneously, thereby reducing total computational time and resolving the exponential growth problem.
Solution Approach 2:
The patent employs a universal matrix-matrix operation that can handle multiple different vector-matrix operations through a single unified computation. The combined operation processes multiple right-hand side vectors and multiple output vectors simultaneously, making the system highly versatile for solving various combinatorial optimization problems without requiring separate computations for each operation type.
2Productivity
If conventional computing systems are used for combinatorial optimization, then existing algorithms can be applied, but resource consumption increases exponentially
Solution Approach 1:
By combining k separate vector-matrix operations into one matrix-matrix operation, the system reduces the total number of computational operations required. This merging strategy directly decreases resource consumption (energy, memory bandwidth, processing cycles) while maintaining the ability to solve the same optimization problem, thereby resolving the contradiction between computational efficiency and resource consumption.
3Loss of time
If tensor processors with matrix-matrix operations are used, then computational time is reduced significantly, but the system complexity increases
Solution Approach 1:
The patent segments the combinatorial optimization problem into a series of matrix-matrix operations that can be executed in parallel on tensor processor functional units. By breaking down the complex optimization into standardized matrix operation blocks, the system manages complexity through structured computation while achieving significant time reduction through parallel execution.
Solution Approach 2:
The patent transforms the problem representation by changing from vector-matrix operations to matrix-matrix operations, fundamentally altering the computational parameters. This parameter transformation enables the use of highly optimized matrix multiplication hardware on tensor processors, achieving faster computation while managing system complexity through standardized mathematical operations.
Data Source
AI summary
The present disclosure relates to systems and methods for obtaining a problem specification file descriptive of a combinatorial optimization problem; identifying a plurality of combinable vector-matrix operations of the combinatorial optimization problem; generating an instruction set for the one or more processors, wherein the instruction set includes a first instruction that, when implemented, causes the one or more processors to perform a combined matrix-matrix operation replacing the plurality of combinable vector-matrix operations; and executing the instruction set.