Understanding the Energy and Precision Requirements for Online Learning

TL;DR

This paper derives analytical lower bounds on data and hyperparameter precision for online SVM training using SGD, linking precision requirements to classification accuracy and energy efficiency, and validates these bounds empirically.

Contribution

It introduces the first analytical bounds on precision for online SVM training, addressing limitations of prior empirical studies and enabling more energy-efficient implementations.

Findings

Lower bounds on data precision depend on classification accuracy.

Hyperparameter precision bounds are derived for SGD training.

Energy consumption is reduced by applying the precision bounds.

Abstract

It is well-known that the precision of data, hyperparameters, and internal representations employed in learning systems directly impacts its energy, throughput, and latency. The precision requirements for the training algorithm are also important for systems that learn on-the-fly. Prior work has shown that the data and hyperparameters can be quantized heavily without incurring much penalty in classification accuracy when compared to floating point implementations. These works suffer from two key limitations. First, they assume uniform precision for the classifier and for the training algorithm and thus miss out on the opportunity to further reduce precision. Second, prior works are empirical studies. In this article, we overcome both these limitations by deriving analytical lower bounds on the precision requirements of the commonly employed stochastic gradient descent (SGD) on-line learning algorithm in the specific context of a support vector machine (SVM). Lower bounds on the data precision are derived in terms of the the desired classification accuracy and precision of the hyperparameters used in the classifier. Additionally, lower bounds on the hyperparameter precision in the SGD training algorithm are obtained. These bounds are validated using both synthetic and the UCI breast cancer dataset. Additionally, the impact of these precisions on the energy consumption of a fixed-point SVM with on-line training is studied.