LFSR Random Number Generation for GPU Matrix Multiplication
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Solution Overview
Problem
The bottleneck in machine-learning algorithms is the performance impact caused by stochastic rounding during matrix multiplication, particularly due to inefficient random number generation, either pre-generated or generated on-the-fly in software, which limits AI performance.
Innovation Solution
Implementing hardware-accelerated random number generation using a linear-feedback shift register (LFSR) algorithm to generate random numbers on-the-fly, improving performance during down-conversion to low precision data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If random numbers are generated in software on-the-fly, then no additional hardware is required, but computational overhead increases and performance decreases
Solution Approach 1:
The patent replaces software-based random number generation with a hardware-based LFSR system. The LFSR circuit generates random numbers through bitwise operations and register shifts, substituting the software computational mechanism with a dedicated hardware circuit that operates in parallel with the matrix multiplication process, thereby eliminating software overhead and improving performance.
Solution Approach 2:
The patent introduces an LFSR-based random number generator as an intermediary component between the matrix multiplication unit and the stochastic rounding operation. This intermediary hardware module provides random numbers on-demand without burdening the main computational pipeline, resolving the conflict between performance and complexity by offloading random number generation to a specialized subsystem.
2Speed
If random numbers are pre-generated and stored, then random number generation is fast, but memory usage increases and may not meet performance requirements
Solution Approach 1:
The patent implements a dynamic random number generation system using LFSR that generates numbers on-demand rather than pre-generating and storing them. The LFSR state updates continuously with each clock cycle, providing a stream of random numbers that adapts to the computational needs of matrix multiplication without requiring static memory allocation, thus achieving fast generation speed with minimal memory usage.
Solution Approach 2:
The LFSR is initialized with a seed value before matrix multiplication begins, preparing the random number generation mechanism in advance. This preliminary setup allows the system to generate random numbers immediately during computation without delay, achieving fast generation speed while avoiding the need to pre-generate and store large quantities of random numbers.
3Productivity
If hardware-accelerated random number generation is implemented, then performance increases, but device complexity and area increase
Solution Approach 1:
The patent segments the random number generation function into a dedicated LFSR hardware module separate from the main matrix multiplication unit. This segmentation allows the LFSR to be optimized independently using efficient bitwise operations and register shifts, improving overall performance while containing the complexity increase to a localized, manageable component rather than distributing complexity throughout the entire system.
Solution Approach 2:
The patent optimizes the LFSR implementation by carefully selecting register widths and feedback polynomial parameters that balance randomness quality with hardware resource usage. By adjusting these parameters, the system achieves sufficient random number quality for stochastic rounding while minimizing the area and complexity overhead of the hardware circuit.
Data Source
AI summary
One embodiment provides a graphics processor comprising a memory interface and a processing resource coupled with the memory interface. The processing resource includes multiple processing lanes, each of the multiple processing lanes including circuitry dedicated to generation of one or more randomized numbers. The processing resource configured to receive an instruction to generate a two-dimensional matrix of randomized numbers, generate one or more hardware generated seed values for use by each of the multiple processing lanes, generate one or more randomized numbers at each of the multiple processing lanes based on the one or more hardware generated seed values and output the two-dimensional matrix of randomized numbers to a destination register.