Quantized LUT Approximation for Accurate Neural Network Nonlinear Functions
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Solution Overview
Problem
Conventional neural network operations using Look Up Tables (LUTs) suffer from errors due to rapid changes in output values for non-linear functions, leading to reduced prediction accuracy and increased hardware costs due to the need for a large number of LUT indexes.
Innovation Solution
A neural network operation apparatus that includes a receiver and processor to perform scale-up and quantization of LUT parameters based on a scale factor, using a quantized LUT to approximate non-linear functions, thereby reducing errors and hardware costs while maintaining accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a conventional LUT is used to approximate non-linear functions, then hardware cost is reduced, but prediction accuracy deteriorates due to errors in approximating high fluctuation sections
Solution Approach 1:
The patent divides the LUT into multiple sections based on the fluctuation characteristics of the non-linear function. Each section is approximated separately using linear functions with different slopes, allowing for more accurate representation of high fluctuation regions without requiring a uniformly dense LUT across the entire range. This segmentation approach improves prediction accuracy while controlling hardware cost.
Solution Approach 2:
The patent applies different LUT densities and approximation methods to different sections of the non-linear function based on their fluctuation rates. Sections with high fluctuation rates receive more detailed approximation (higher LUT density), while sections with low fluctuation rates use coarser approximation. This local quality adjustment maintains prediction accuracy where needed while reducing overall hardware requirements.
2Measurement precision
If more LUT indexes are used to approximate high fluctuation sections, then prediction accuracy is improved, but hardware cost increases
Solution Approach 1:
The patent dynamically adjusts the LUT indexing strategy based on the slope of the non-linear function at different regions. By calculating the slope and using it to determine the appropriate LUT density, the system adapts the hardware resources to the actual computational needs of each function section, improving accuracy where the function changes rapidly while minimizing hardware usage where the function is stable.
Solution Approach 2:
The patent changes the LUT parameter (index quantity, density) based on the slope parameter of the approximating linear function. By establishing a relationship between the slope magnitude and the required LUT resolution, the system optimizes the balance between prediction accuracy and hardware cost, using fewer indexes when the slope is small and more indexes when the slope is large.
3Measurement precision
If scale-up operation is performed on input data, then prediction accuracy is maintained, but computational complexity increases
Solution Approach 1:
The patent performs scale-up operation as a preliminary step before LUT lookup, transforming the input data to a scaled range that matches the LUT's expected input domain. This preliminary scaling ensures that the subsequent LUT lookup operates on appropriately normalized data, maintaining accuracy while keeping the overall computation efficient. The scaling operation is performed once at the beginning rather than repeatedly during computation.
Data Source
AI summary
A neural network operation apparatus may include a receiver configured to receive input data to perform the neural network operation and a quantized Look Up Table (LUT) corresponding to a non-linear function comprised in the neural network operation, and a processor configured to perform scale-up on the input data based on a scale factor, to extract a quantized LUT parameter from the quantized LUT based on scaled-up input data, and to generate an operation result by performing a neural network operation based on the quantized LUT parameter.