A Finite-Time Technological Singularity Model With Artificial Intelligence Self-Improvement

Recent advances in the development of artificial intelligence, technological progress acceleration, long-term trends of macroeconomic dynamics increase the relevance of technological singularity hypothesis. In this paper, we build a model of finite-time technological singularity assuming that artificial intelligence will replace humans for artificial intelligence engineers after some point in time when it is developed enough. This model implies the following: let A be the level of development of artificial intelligence. Then, the moment of technological singularity n is defined as the point in time where artificial intelligence development function approaches infinity. Thus, it happens in finite time. Although infinite level of development of artificial intelligence cannot be reached practically, this approximation is useful for several reasons, firstly because it allows modeling a phase transition or a change of regime. In the model, intelligence growth function appears to be hyperbolic function under relatively broad conditions which we list and compare. Subsequently, we also add a stochastic term (Brownian motion) to the model and investigate the changes in its behavior. The results can be applied for the modeling of dynamics of various processes characterized by multiplicative growth.