Sparse Linear Operation Graphs for GPU Interior Point Execution
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Solution Overview
Problem
Traditional Interior Point Methods for solving linear programs are laborious and resource-intensive, necessitating the development of a novel, efficient method that can be executed on Central Processing Units (CPUs) with accelerated computing co-processors like GPUs or TPUs.
Innovation Solution
A novel Interior Point Method algorithm optimized for GPUs or TPUs, transforming linear operations into graphs and iteratively optimizing them for specific hardware characteristics such as topological depth, memory footprint, and cache hierarchy utilization, enabling efficient execution on parallel processing hardware.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Traditional Interior Point Methods are used to solve linear programs, then mathematical programming can be performed, but the process becomes laborious and resource-intensive
Solution Approach 1:
The patent segments the linear program into a chain of linear operations, where each operation is represented as a node in a graph. This segmentation allows the complex computation to be divided into smaller, manageable units that can be processed in parallel on GPU or TPU hardware, significantly improving execution speed and reducing resource intensity compared to traditional monolithic Interior Point Methods
Solution Approach 2:
The patent transforms the traditional sequential computation approach into a parallel dimension by representing operations as a graph structure. This dimensional change enables simultaneous execution of multiple linear operations on GPU/TPU hardware, converting a laborious sequential process into an efficient parallel computation that maintains mathematical correctness while dramatically improving productivity
2Productivity
If linear operations are represented as graphs and optimized for parallel hardware, then execution speed improves, but algorithm complexity increases
Solution Approach 1:
The patent changes the representation parameters of linear operations from traditional matrix forms to graph-based node-edge structures. This parameter change enables the operations to be optimized for parallel hardware execution while maintaining mathematical equivalence. The graph representation allows for iterative optimization of topological depth and memory access patterns, improving execution speed without requiring complex manual algorithm design
Solution Approach 2:
The patent implements a system where the linear operation graph automatically optimizes itself by iteratively improving topological depth and memory access patterns. The algorithm self-adjusts the graph structure to minimize cache misses and maximize parallel hardware utilization, reducing the need for complex external optimization and simplifying the overall system architecture
3Productivity
If iterative optimization of linear operation graphs is performed, then execution characteristics improve, but computation time increases
Solution Approach 1:
The patent performs preliminary actions by representing linear operations as graphs before execution and iteratively optimizing the graph structure in advance. This preliminary optimization of topological depth and memory access patterns ensures that when the actual computation runs on GPU/TPU hardware, the execution is highly efficient. The iterative optimization happens before the main computation, so the optimization time is amortized over many subsequent efficient executions
Solution Approach 2:
The patent maintains continuity of useful action by implementing iterative optimization that continuously improves the linear operation graph structure. Each iteration refines the graph to better exploit parallel hardware capabilities, and this continuous improvement process is integrated into the execution flow. The useful action of optimizing execution characteristics is performed continuously alongside the main computation, ensuring that time is not lost but rather productively utilized
Data Source
AI summary
A platform that includes a plurality of CPU cores and a plurality of GPU cores that receive input of a chain of linear operations; represent or transform each linear operation in the chain to a respective linear operation graph; connect one or more input nodes of each component in the chain to one or more output nodes of a previous component in the chain, with an edge of weight one; iteratively optimize the linear operation graph, thereby improving one or more characteristics of each linear operation graph; map the linear operations graph into a runtime execution plan that is tailored for a specific processing hardware; iteratively optimize the runtime execution plan, thereby improving one or more specific processing hardware execution characteristics; and run the runtime execution plan that has been optimized on the specific processing hardware.