Artificial intelligence is advancing rapidly, with increasingly capable systems taking larger roles in reasoning, decision-making, scientific discovery, and autonomous development. As AI begins to participate in its own improvement, from model training and experience accumulation to agent evolution and automated AI development, the prospect of recursive self-improvement (RSI) is becoming increasingly relevant. This transition raises a fundamental safety question: how can safety be maintained when the system, its accumulated experience, and even the process producing its successors continue to change? We introduce Evolutionary Safety as a perspective for studying safety under persistent and recursive self-improvement. It concerns not only whether an AI system is safe at a particular moment, but how safety properties change, persist, accumulate, and propagate throughout evolution. We characterize recurring manifestations, including intent drift, error accumulation, experience contamination, safety-property erosion, evaluator drift, and risk propagation. We then develop a taxonomy spanning persistent agent state, model state, evaluation and environmental feedback, computational substrate, and meta-level update mechanisms. Building on this taxonomy, we examine how evolutionary risks can be discovered and evaluated across states, updates, trajectories, and lineages, and derive governance principles for modification, selection, authorization, provenance, and recovery. Finally, we outline open problems toward maintaining safety guarantees as AI systems become increasingly persistent, adaptive, and recursively self-improving. Project resources and proposed evaluation systems are available at https://chaunceykung.github.io/evolutionary-safety-rsi.

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