Toward tractable universal induction through recursive program learning

Abstract

Since universal induction is a central topic in artificial general intelligence (AGI), it is argued that compressing all sequences up to a complexity threshold should be the main thrust of AGI research. A measure for partial progress in AGI is suggested along these lines. By exhaustively executing all two and three state Turing machines a benchmark for low-complexity universal induction is constructed. Given the resulting binary sequences, programs are induced by recursively constructing a network of functions. The construction is guided by a breadthfirst search departing only from leaves of the lowest entropy programs, making the detection of low entropy (“short”) programs efficient. This way, all sequences (80% of the sequences) generated by two (three) state machines could be compressed back roughly to the size defined by their Kolmogorov complexity.