Kernel Coefficient Quantization for Matrix Precision
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Solution Overview
Problem
Converting matrices from real numbers to fixed point representation often results in significant precision loss and increased processing resources, particularly when dealing with large kernel coefficients and matrices of arbitrary dimensions, which can lead to undesirable errors in mathematical operations.
Innovation Solution
The method involves converting matrices by representing each kernel coefficient as a mantissa and exponent, using a signed two's complement integer for the mantissa and a power of 2 exponent, while preserving the sum of values with minimal error by calculating C-values and adjusting mantissa values to minimize residue errors, thereby optimizing resource usage and reducing precision loss.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If kernel coefficients are converted from real number representation to fixed point representation, then processing resources are reduced and computational efficiency is improved, but precision loss occurs and error in the sum of values increases
Solution Approach 1:
The patent changes the representation parameters of kernel coefficients by introducing a hybrid format that combines elements of both real number and fixed point representations. Specifically, it uses a sign bit, integer part, and fractional part with configurable bit allocations, allowing optimization between precision and processing efficiency by adjusting the distribution of bits among these components.
Solution Approach 2:
The patent segments the kernel coefficient representation into distinct components: sign bit, integer part, and fractional part. This segmentation allows independent optimization of each component's bit allocation to balance precision requirements with processing resource constraints, resolving the contradiction between maintaining precision and reducing resource usage.
2Quantity of substance
If kernel coefficients are converted to fixed point representation with fewer bits, then storage space is optimized and processing resources are reduced, but loss of information increases
Solution Approach 1:
The patent optimizes storage space while minimizing information loss by changing the parameter allocation within the fixed point representation. It configurable bit distribution across sign, integer, and fractional parts allows tailoring the representation to specific application requirements, maximizing information retention within constrained storage resources.
Solution Approach 2:
The patent introduces dynamic bit allocation strategies where the number of bits assigned to integer and fractional parts can be adjusted based on the specific kernel coefficients being processed. This dynamic adaptation allows the system to maintain higher precision when needed while optimizing storage when precision requirements are lower, thus reducing overall information loss.
Data Source
AI summary
Apparatuses, systems, and techniques to optimize memory usage when performing matrix operations. In at least one embodiment, a matrix is optimized to limit memory and storage requirements while minimizing loss of precision for a sum of the members of the matrix.