Arithmetic Circuit Sigmoid Function Base Transformation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Implementing the sigmoid function in hardware is challenging due to its complex calculation formula, leading to high circuit scale, prolonged arithmetic operation time, and increased power consumption.
Innovation Solution
An arithmetic operation circuit is designed with a configuration that includes a multiplier, power and square root extraction arithmetic operator, adder, divider, subtractor, and multiplexer, which replaces reciprocal operations with subtraction and transforms the exponential function of base e to base 2, reducing circuit scale and power consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the sigmoid function is implemented using its original complex calculation formula, then calculation accuracy is maintained, but circuit scale increases and arithmetic operation time is prolonged
Solution Approach 1:
The patent transforms the base of the exponential function from e to 2, changing the mathematical parameter to enable hardware-friendly calculation. This allows the sigmoid function to be computed using binary exponentiation and lookup tables, significantly reducing circuit complexity while maintaining calculation accuracy through controlled approximation.
Solution Approach 2:
The patent creates simplified computational models by using lookup tables that pre-store calculated sigmoid values. Instead of performing complex real-time calculations, the system copies pre-computed results from tables, reducing the arithmetic operation time and circuit scale while maintaining sufficient accuracy for neural network applications.
2Measurement precision
If the sigmoid function is implemented using its original complex calculation formula, then calculation accuracy is maintained, but power consumption increases
Solution Approach 1:
By changing the exponential base from e to 2, the patent enables more efficient hardware implementation using binary arithmetic operations. This parameter change reduces the number of computational steps required, directly lowering power consumption while maintaining acceptable calculation accuracy through the use of lookup tables and approximation techniques.
Solution Approach 2:
The use of pre-computed lookup tables eliminates the need for power-intensive real-time exponential calculations. The system copies stored values from memory rather than performing complex arithmetic operations, significantly reducing dynamic power consumption during inference operations in neural networks.
3Measurement precision
If the sigmoid function is implemented using its original complex calculation formula, then mathematical precision is maintained, but arithmetic operation time is prolonged
Solution Approach 1:
Transforming the exponential base to 2 enables the use of efficient binary exponentiation algorithms and hardware-friendly computation methods. This parameter transformation, combined with lookup table approaches, reduces arithmetic operation time by avoiding complex transcendental function calculations while maintaining sufficient mathematical precision for practical neural network applications.
Solution Approach 2:
The patent performs sigmoid function calculations in advance and stores results in lookup tables during system initialization or training phases. During actual inference, the system retrieves pre-computed values instead of calculating in real-time, dramatically reducing arithmetic operation time while maintaining the precision needed for accurate neural network processing.
Data Source
AI summary
An artificial intelligence system includes a neural network layer including an arithmetic operation circuit that performs an arithmetic operation of a sigmoid function. The arithmetic operation circuit includes a first circuit configured to perform an exponent arithmetic operation using a Napier's constant e as a base and output a first calculation result when an exponent in the exponent arithmetic operation is a negative number, wherein an absolute value of the exponent is used in the exponent arithmetic operation, and a second circuit configured to subtract the first calculation result obtained by the first circuit from 1 and output the subtracted value.