Adaptive Interval Segmentation: An Algorithmic Approach for Optimal SORN Datatypes

The Sets Of Real Numbers (SORN) format is an interval-based number representation to perform fast and low-complex arithmetic operations. Since the implemented arithmetic is based on lookup tables, the applied SORN datatypes are not standardized and can be highly application specific. Because the formats precision is rather low in general, the evaluation of suitable SORN datatypes is one of the major challenges when applying the format, since not all datatypes guarantee sufficient results for the implemented algorithms. Therefore, this paper presents an algorithmic approach to determine the optimized interval distribution for a SORN datatype for specific applications. The Adaptive Interval Segmentation (AIS) algorithm is gradient based and applies directional nested intervals to adapt a floating point functionality by SORN arithmetic. This approach is used to evaluate SORN datatypes for Hybrid SORN k-Nearest Neighbor (kNN) classification. For the MNIST dataset, the AIS algorithm provides seven SORN datatypes that show better classification results for Hybrid SORN kNN classification, compared to floating point implementations. This is particular evident in a four and a five bit SORN datatype leading to an accuracy increase of \(0.24\%\) and \(0.26\%\) , respectively.