Matrix Multiplication Approximation by Dropping Insignificant Products

Solution Overview

Problem

Matrix multiplication operations in high performance computing and machine learning are time-consuming and expensive due to the large number of calculations involved, necessitating more efficient methods to reduce computational time and energy costs.

Innovation Solution

The method involves dynamically determining a target number of product values to be kept for matrix multiplication by approximating the products as sums of exponents, dropping the least significant products, and using hardware components to perform the remaining calculations, without the need for sorting the elements.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If all products of element pairs are calculated in matrix multiplication, then calculation accuracy is maintained, but computational time and energy costs increase

Engineering Contradiction:

Improvecalculation accuracyVSAvoidcomputational time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent extracts and removes insignificant products from the matrix multiplication calculation. By approximating products as sums of exponents and dropping the least significant products (those with smallest exponent sums), the system eliminates unnecessary calculations while preserving accuracy for significant products. This selective extraction resolves the contradiction by removing only the non-essential computational burden.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent changes the parameter representation by using exponent sums to approximate product values. Instead of calculating full product values, the system transforms the parameter representation to exponents, enabling efficient identification and removal of insignificant products based on exponent sum comparisons. This parameter transformation allows accuracy preservation for significant products while eliminating time-consuming calculations of insignificant ones.

Inventive Principle:

Principle #35Parameter changes

2Measurement precision

If all products of element pairs are calculated in matrix multiplication, then calculation accuracy is maintained, but energy costs increase

Engineering Contradiction:

Improvecalculation accuracyVSAvoidenergy costs

Core Design Contradiction:

Measurement precisionVSUse of energy by moving object

Solution Approach 1:

The patent extracts and removes insignificant products from the matrix multiplication calculation. By approximating products as sums of exponents and dropping the least significant products (those with smallest exponent sums), the system eliminates unnecessary calculations while preserving accuracy for significant products. This selective extraction resolves the contradiction by removing only the non-essential computational burden.

Inventive Principle:

Principle #2Taking out (Extraction)

Solution Approach 2:

The patent changes the parameter representation by using exponent sums to approximate product values. Instead of calculating full product values, the system transforms the parameter representation to exponents, enabling efficient identification and removal of insignificant products based on exponent sum comparisons. This parameter transformation allows accuracy preservation for significant products while eliminating energy-consuming calculations of insignificant ones.

Inventive Principle:

Principle #35Parameter changes

3Measurement precision

If products are sorted by value to identify insignificant ones, then accuracy is maintained, but device complexity increases

Engineering Contradiction:

ImproveaccuracyVSAvoidhardware complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent inverts the traditional approach by not sorting products in ascending order to find insignificant ones, but rather using exponent sum approximation to directly identify and drop insignificant products. Instead of full sorting which requires complex hardware, the system uses the inverted logic of approximating with exponents to efficiently identify insignificant products without complex sorting networks.

Inventive Principle:

Principle #13The other way round (Inversion)

Solution Approach 2:

The patent changes the parameter representation by using exponent sums to approximate product values. Instead of calculating full product values, the system transforms the parameter representation to exponents, enabling efficient identification and removal of insignificant products based on exponent sum comparisons. This parameter transformation allows accuracy preservation for significant products while eliminating energy-consuming calculations of insignificant ones.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentEP4315044B1Approximation of matrices for matrix multiply operations

Publication Date: 2026.02.04 ADVANCED MICRO DEVICES INC

Figure 1
Figure 2
Figure 3

AI summary

A processing device is provided which comprises memory configured to store data and a processor configured to receive a portion of data of a first matrix comprising a first plurality of elements and receive a portion of data of a second matrix comprising a second plurality of elements. The processor is also configured to determine values for a third matrix by dropping a number of products from products of pairs of elements of the first and second matrices based on approximating the products of the pairs of elements as a sum of the exponents of the pairs of elements and performing matrix multiplication on remaining products of the pairs of elements of the first and second matrices.