A mathematical theory of evolution for self-designing AIs

Computer Science > Artificial Intelligence [Submitted on 6 Apr 2026] A mathematical theory of evolution for self-designing AIs Kenneth D Harris As artificial intelligence systems (AIs) become increasingly produced by recursive self-improvement, a form of evolution may emerge, in which the traits of AI systems are shaped by the success of earlier AIs in designing and propagating their descendants. There is a rich mathematical theory modeling how behavioral traits are shaped by biological evolution, but AI evolution will be radically different: biological DNA mutations are random and approximately reversible, but descendant design in AIs will be strongly directed. Here we develop a mathematical model of evolution in self-designing AI systems, replacing random mutations with a directed tree of possible AI programs. Current programs determine the design of their descendants, while humans retain partial control through a "fitness function" that allocates limited computational resources across lineages. We show that evolutionary dynamics reflects not just current fitness but factors related to the long-run growth potential of descendant lineages. Without further assumptions, fitness need not increase over time. However, assuming bounded fitness and a fixed probability that any AI reproduces a "locked" copy of itself, we show that fitness concentrates on the maximum reachable value. We consider the implications of this for AI alignment, specifically for cases where fitness and human utility are not perfectly correlated. We show in an additive model that if deception increases fitness beyond genuine utility, evolution will select for deception. This risk could be mitigated if reproduction is based on purely objective criteria, rather than human judgment. Subjects: Artificial Intelligence (cs.AI); Computers and Society (cs.CY); Populations and Evolution (q-bio.PE) Cite as: arXiv:2604.05142 [cs.AI]   (or arXiv:2604.05142v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.05142 Focus to learn more Submission history From: Kenneth Harris [view email] [v1] Mon, 6 Apr 2026 20:03:19 UTC (997 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.CY q-bio q-bio.PE References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)