Vector-Vector Multiplication Threshold Skipping
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Solution Overview
Problem
Current computing systems face significant computational workloads due to the need for extensive calculations in rectified linear vector-vector and matrix-matrix multiplication operations, which are common in artificial intelligence tasks.
Innovation Solution
Implementing a method that computes a partial product using most-significant-bits of vectors and determines if it's below a threshold, allowing for the skipping of unnecessary calculations by setting the result to zero if the partial product is below the threshold, thereby reducing the computational workload.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If complete vector-vector multiplication is performed, then computation accuracy is maintained, but computational workload increases
Solution Approach 1:
The patent performs a preliminary computation of a first portion of the vector-vector multiplication product before completing the full calculation. This preliminary result is used to determine whether subsequent computation passes are necessary, allowing the system to skip unnecessary calculations while maintaining accuracy when needed.
Solution Approach 2:
The vector-vector multiplication computation is divided into multiple portions or passes. The first portion is computed separately and used for threshold comparison, while remaining portions are computed conditionally. This segmentation allows the system to potentially skip computing remaining portions, reducing overall computational workload.
2Reliability
If all computation passes are executed, then computation completeness is ensured, but processing time increases
Solution Approach 1:
The first portion of the vector-vector multiplication product is computed as a preliminary action before executing remaining computation passes. This preliminary computation enables the control unit to determine whether subsequent passes are necessary, allowing the system to skip them when the threshold condition is met, thereby reducing processing time while maintaining completeness when required.
3Productivity
If threshold-based skipping is implemented, then computational workload is reduced, but computation accuracy may deteriorate
Solution Approach 1:
The patent computes only a first portion of the vector-vector multiplication product as a partial action, rather than completing the full computation. This partial computation is sufficient to determine whether the threshold condition is met, allowing the system to skip remaining passes when appropriate. The approach accepts that the partial computation may not always yield the complete accurate result, but the trade-off is justified by the significant reduction in computational workload.
Data Source
AI summary
Vector-vector multiplication or matrix-matrix multiplication computation on computing systems can include computing a first portion of a vector-vector multiplication product based on a most-significant-bit set of a first vector and a most-significant-bit set of a second vector, and determining if the first portion of the vector-vector multiplication product is less than a threshold. If the first partial vector-vector multiplication product is not less than the threshold, a remaining portion of the vector-vector multiplication product can be computed, and a rectified linear vector-vector multiplication product can be determined for the sum of the first portion of the vector-vector multiplication product and the remaining portion of the vector-vector multiplication product. If the first portion of the vector-vector multiplication product is less than the threshold, computation of the remaining portion of the vector-vector multiplication product can be skipped and the rectified linear vector-vector multiplication product can be set to a zero scalar.