Polynomial Kernel Generation Using Fixed-Point Function Approximation
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Solution Overview
Problem
Existing processing units face challenges in balancing latency and throughput, with floating-point units being resource-intensive and leading to increased complexity, size, power consumption, and limited parallel computing capabilities due to their fixed architecture.
Innovation Solution
The use of polynomial-based kernels computed using scaled fixed-point units, which are dynamically adjusted through interconnected computing grids to minimize approximation errors while adhering to constraints such as accuracy, compute graph size, and hardware utilization, allowing for runtime adaptation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If floating-point units are used to compute functions, then accuracy is improved, but device complexity and hardware utilization increase
Solution Approach 1:
The patent transforms floating-point computation into fixed-point computation by changing the numerical representation parameter. Polynomial-based approximations are computed using fixed-point arithmetic with carefully selected scaling factors, maintaining sufficient accuracy while dramatically reducing hardware complexity and resource requirements compared to floating-point units.
Solution Approach 2:
The patent replaces expensive, complex floating-point units with simpler, cheaper fixed-point computational structures. The polynomial-based approximation approach uses basic arithmetic operations (addition, multiplication) that can be implemented with simple logic circuits, effectively substituting high-cost hardware with low-cost alternatives that achieve the required performance.
2Measurement precision
If floating-point units are used to compute functions, then accuracy is improved, but latency and power consumption increase
Solution Approach 1:
The patent changes the computational parameter from floating-point to fixed-point representation, which requires simpler arithmetic logic and consumes less power. The polynomial approximations are designed to work efficiently with fixed-point arithmetic, reducing the energy required for each computation while maintaining acceptable accuracy levels for the application.
Solution Approach 2:
The patent extracts and removes the complex floating-point unit from the system, replacing it with simpler fixed-point computational structures. This extraction eliminates the high power consumption associated with floating-point operations while retaining the essential computational functionality through polynomial-based approximations.
3Ease of manufacture
If fixed architecture processing units are used, then manufacturing is simplified, but adaptability and parallel computing capabilities are limited
Solution Approach 1:
The patent introduces dynamic adaptability into the fixed architecture by implementing runtime reconfigurable polynomial degree selection and coefficient loading. The processing unit can dynamically adjust the polynomial approximation parameters and reconfigure its computational structure based on the specific function being computed, enabling parallel processing of multiple different functions without requiring a completely reconfigurable architecture.
Solution Approach 2:
The patent segments the computational function into polynomial approximation components that can be independently computed in parallel. The polynomial-based approach allows the computation to be divided into separate stages (coefficient multiplication, term computation, summation) that can be executed concurrently, increasing parallel processing capability while maintaining a relatively simple fixed architecture.
Data Source
AI summary
An apparatus for computing functions using polynomial-based approximation, comprising one or more processing circuitries configured for computing a polynomial-based approximant approximating a function by executing one or more iterations. Each iteration comprising computing the polynomial-based approximant using scaled fixed-point unit(s) according to a constructed set of coefficients, minimizing an approximation error of the computed polynomial-based approximant compared to the function while complying with one or more constraints selected from a group comprising at least: an accuracy, a compute graph size, a computation complexity, and a hardware utilization of the processing circuitry(s), adjusting one or more of the coefficients in case the approximation error is incompliant with the constraint(s) and initiating another iteration. The polynomial-based approximant and its adjusted set of coefficients for which the computed polynomial-based approximant complies with the constraint(s) may be output to one or more processing circuitries configured to approximate the function by computing the polynomial-based approximant.