Machine Learning Stabilizer for Numerical Roundoff Error
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Solution Overview
Problem
Numerical methods in high-performance computing are limited by the accumulation of roundoff error in lower-precision datatypes, such as float16 and bfloat16, which leads to instability in computations and violations of physical conservation laws, reducing the motivation to develop novel datatypes.
Innovation Solution
A machine learning model is trained using pairs of low precision and high precision data to predict compensation values, which are then used to correct for roundoff errors in algorithmic computations, enabling the use of lower precision datatypes in high-performance computing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If lower-precision datatypes (float16, bfloat16) are used in numerical computations, then computational efficiency and hardware utilization are improved, but numerical stability deteriorates due to accumulated roundoff error
Solution Approach 1:
A machine learning model is introduced as an intermediary component that receives low-precision computational results and predicts compensation values. The model acts as a mediator between the low-precision arithmetic operations and the final corrected results, transforming unstable low-precision outputs into stable corrected values without requiring the entire computation to be performed in high precision.
Solution Approach 2:
The precision parameter of the datatype is dynamically adjusted through the machine learning compensation process. The system performs computations in low precision (float16/bfloat16) to maintain speed, then applies learned compensation parameters to correct the results, effectively changing the precision characteristics of the final output without changing the precision used during computation.
2Reliability
If single-precision or double-precision datatypes are used, then numerical stability is improved, but computational efficiency and hardware utilization deteriorate
Solution Approach 1:
Instead of applying high precision throughout the entire computation process, the system applies precision correction only where needed - specifically to the final results of low-precision computations. This partial application of high precision (only for correction, not for the entire computation chain) achieves numerical stability while maintaining the computational efficiency of low-precision arithmetic.
3Productivity
If low precision computations are performed, then hardware utilization is improved, but measurement precision deteriorates due to roundoff error accumulation
Solution Approach 1:
The machine learning model is trained using high-precision reference computations as ground truth, creating a feedback mechanism where the model learns to predict the difference between low-precision and high-precision results. During execution, this learned feedback is applied to correct low-precision computations, allowing the system to achieve high-precision accuracy through low-precision hardware operations.
Data Source
AI summary
An approach is provided for using machine learning to provide compensation for roundoff error in algorithmic computations. The approach includes training a machine learning model based low precision data and corresponding high precision data. The low precision data includes pairs of low precision values of a specific datatype that correspond to pairs of high precision values from the high precision data. The high precision data includes pairs of high precision values of a specific datatype that correspond to the pairs of low precision values from the low precision data. When the machine learning model has been trained, the machine learning model is used as a basis for determining a compensation value is used to compensate for roundoff error in a particular algorithmic computation. Techniques discussed herein provide compensation for roundoff error during otherwise unstable computations, enabling high-performance computing and other scientific applications to use lower precision data types more readily.