Matrix Multiply Cell Array With Width-Adaptive Dot Product Tiling
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing matrix multiplication techniques are computationally intensive, particularly for large matrices, and there is a need for more efficient methods to accelerate these computations.
Innovation Solution
A matrix multiply engine is implemented with a first and second operand buffer and a cell array that computes dot products of multiple elements in an operating cycle, utilizing a cell array with accumulator circuitry to increase arithmetic intensity, and supports operand width-dependent patch thickness for efficient matrix multiplication.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional scalar multiplication operations are used for matrix multiplication, then computational accuracy is maintained, but computational intensity and processing time increase significantly
Solution Approach 1:
The matrix multiplication operation is segmented into smaller dot product computations that can be performed in parallel. Each cell in the cell array processes a specific portion of the matrix multiplication by computing dot products of column vectors, dividing the overall computational task into manageable segments that execute simultaneously
Solution Approach 2:
Multiple scalar multiplication operations are merged into parallel dot product computations. The cell array combines multiple multiplication and addition operations into unified dot product calculations, increasing arithmetic intensity and reducing the total number of sequential operations required
2Productivity
If operand width is decreased to improve arithmetic intensity, then processing efficiency increases, but the number of operations required increases
Solution Approach 1:
The system dynamically adjusts the patch thickness TK based on the operand width. When operand width decreases, the patch thickness is increased to maintain optimal arithmetic intensity. This dynamic adaptation ensures that the cell array processes data efficiently across different precision levels
Solution Approach 2:
The patch thickness parameter TK is changed according to operand width to optimize performance. The system modifies this critical parameter to balance the trade-off between arithmetic intensity and operation count, ensuring efficient processing across different data types
3Speed
If parallel processing is used to accelerate matrix multiplication, then processing speed increases, but hardware complexity increases
Solution Approach 1:
The parallel processing architecture is segmented into multiple identical cells arranged in a grid. Each cell performs the same dot product computation independently, allowing for simple parallel execution without complex coordination logic between processing units
Solution Approach 2:
The cell array provides a universal processing unit that can handle different matrix sizes and precision levels. Each cell is designed to perform the same function across multiple operations, simplifying the hardware design compared to specialized parallel processors
Data Source
AI summary
A matrix multiply engine can include a first operand buffer and a second operand buffer, each of which can store multiple operand elements arranged in rows and columns. A cell array can be formed of cells, where each cell includes a memory and accumulator circuitry to receive operand elements column-wise from each of the first operand buffer and the second operand buffer, to compute a dot product of the received operand elements, and to accumulate the dot product into a corresponding tile state element in the memory. Matrix elements of the operand matrices to be multiplied can be loaded row-wise into rows of the operand buffers and read column-wise into the cells. The number of elements for which a dot product is computed can be selected depending on operand element width.