A Neural Net Approach to Improving Interval Arithmetic

Abstract—Interval arithmetic has become a popular tool for general optimization problems such as robust root finding and global maximum/minimum finding. This has been effectively applied in many computer fields, such as computer graphics. However, interval arithmetic suffers from two significant weaknesses. First, its evaluations are often very conservative, making it useless in many practical situations. Second, it can be much slower than traditional arithmetic. In this paper we present a new approach to computing interval arithmetic: neural network approximation. This naturally provides more accuracy since each traditional interval operation can introduce errors that compound, but a neural emulation approach requires only one approximation. Further, greater overall speed can be achieved