Curve Function Device Using Segmented Lookup Tables
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Solution Overview
Problem
Existing electronic circuits require a large number of logic gates and complex calculations to compute Sigmoid and Tanh functions, leading to increased hardware costs and potential calculation errors when using approximation algorithms, which can decrease the accuracy of neural network models.
Innovation Solution
A curve function device and method that uses a lookup table, weight calculation circuit, and linear function circuit to calculate an approximate value of curve functions by partitioning the input value range into segments, extracting bias values, and calculating weight values to reduce calculation complexity while minimizing errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If approximation algorithms are used to simplify curve function operations, then hardware costs and calculation complexity are reduced, but calculation error increases
Solution Approach 1:
The input range is divided into multiple segments, each with its own pre-stored bias value. This segmentation allows the system to use simpler linear approximations for each segment while maintaining overall accuracy through the piecewise linear combination of these segments.
Solution Approach 2:
Bias values for multiple segments are pre-stored in the lookup table during system initialization or offline processing. This preliminary action eliminates the need for complex real-time calculations, reducing both hardware requirements and calculation complexity while maintaining accuracy.
2Measurement precision
If more logic gates and complex calculation circuits are used to implement curve functions, then calculation accuracy is improved, but hardware costs increase
Solution Approach 1:
Instead of implementing complex exponential and division operations using numerous logic gates, the system creates a simplified copy of the curve function behavior using piecewise linear approximations with pre-stored bias values. This copying approach maintains functional accuracy while dramatically reducing hardware requirements.
Solution Approach 2:
The system replaces expensive, complex calculation circuits with a simpler, more economical approach using lookup tables and basic arithmetic operations. The pre-stored bias values act as disposable lookup data that eliminates the need for costly real-time complex calculations.
3Device complexity
If approximation algorithms are used to reduce calculation amount, then hardware costs are reduced, but system efficacy decreases due to increased error
Solution Approach 1:
By segmenting the input range into multiple intervals with different bias values, the system achieves a balance between simplicity and accuracy. Each segment uses a simple linear approximation, but the collective effect of all segments maintains high reliability for the overall function evaluation.
Solution Approach 2:
The system implicitly uses feedback from the lookup table to correct approximation errors. The pre-stored bias values are derived from the actual curve function characteristics, allowing the linear approximations to automatically compensate for inherent simplification errors and maintain system efficacy.
Data Source
AI summary
A curve function device and an operation method thereof are provided. The curve function device includes a lookup table, a weight calculation circuit, and a linear function circuit. According to first partial bits of an input value, a bias value of a current segment and a bias value of a next segment can be extracted from the lookup table. The weight calculation circuit can calculate a weight value of the current segment according to the bias value of the current segment and the bias value of the next segment. The linear function circuit can calculate a linear function value by using the bias value of the current segment, the weight value of the current segment, and second partial bits of the input value. This linear function value can be used as an approximate value of the curve function.