  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.
