Abstract
Recursive self-improvement (RSI) seeks to turn gains in an AI system into a stronger capacity to produce subsequent gains. Foundation models make parts of this process practical through generated training data, program revision and automated experimentation, but repeated optimization alone does not establish recursive improvement. This survey organizes the field around two overlapping goals: automated design of AI infrastructure, and repair and optimization of existing systems. We relate these goals to AutoML, meta-learning and program search, and formulate their objectives alongside criteria for task gains, retained capabilities and improved update procedures. A common account of update targets, feedback, inheritance and external control connects self-training, memory and skills, agent design, editable improvers and automated research. We synthesize methods by shared mechanisms and compare their evidence under independent testing, resource controls, transfer probes and multi-round evaluation. Existing studies show that systems can retain useful changes and, in limited settings, improve how they produce subsequent updates. They do not yet establish unrestricted or reliably accelerating self-improvement. We identify feedback quality, interacting updates and independent validation as central constraints, and develop testable directions for more reliable, transferable improvement loops.