Matrix Multiplication Integrated Circuit Using Addition-Only Operations
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Solution Overview
Problem
Traditional matrix multiplication methods require significant space and time, especially for large matrices, due to the need for multiplier chips and scalar multiplication operations, which limits computational efficiency in applications like machine learning and graphics processing.
Innovation Solution
A special purpose integrated circuit that performs matrix multiplication using only addition, replacing scalar multiplication with a small number of additions, allowing for a single matrix-multiplier chip design without a multiplication unit, thus reducing space and processing time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional matrix multiplication methods are used with multiplier chips and scalar multiplication operations, then computational accuracy is maintained, but chip space consumption increases and processing time increases
Solution Approach 1:
The patent extracts and removes the multiplication unit from the matrix multiplier chip, keeping only the addition unit. This is achieved by transforming the matrix multiplication algorithm to use only addition operations through vector sorting and duplicate elimination, thereby reducing chip space while maintaining computational functionality.
Solution Approach 2:
The patent changes the computational parameter from multiplication operations to addition-only operations. By modifying the algorithm to sort vectors and eliminate duplicates before accumulation, the system transforms the mathematical operation type, enabling implementation with simpler addition-only hardware.
2Loss of time
If traditional matrix multiplication methods are used with scalar multiplication operations, then computational completeness is maintained, but processing time increases
Solution Approach 1:
The patent applies preliminary actions by sorting the vector and eliminating duplicates before performing the accumulation operation. This preprocessing step organizes the data in advance, enabling the subsequent addition-only accumulation to proceed more efficiently and complete faster than traditional multiplication methods.
3Productivity
If vector sorting and duplicate elimination are performed, then the number of additions required is reduced, but computational steps increase
Solution Approach 1:
The patent applies partial action by performing sorting and duplicate elimination only on the vector being multiplied, not on the entire matrix. This selective preprocessing reduces the number of additions required in the accumulation step while avoiding the excessive complexity of sorting entire matrices, achieving a balanced optimization.
Data Source
AI summary
Special purpose integrated circuits and methods for matrix multiplication are disclosed. In some embodiments, a special purpose integrated circuit is constructed to perform mathematical operations. For matrix A and matrix B, an outer product of each column i of matrix A [vector Ai] and a corresponding row i of matrix B [vector Bi], for all i, is used to calculate all the products used for determining matrices A and B. A product matrix C (where A×B=C) is assembled using additions of the elements of the calculated outer products. Each outer product of Ai and Bi may be calculated using a series of vector-scalar products. Each vector-scalar product is calculated using the vector Bi and a selected element of Ai as the scalar. Thus, calculating the vector-scalar product for all the elements of Ai will produce the outer product of Ai and Bi.