Generative artificial intelligence (AI) is interacting with people at an unprecedented scale, offering new avenues for immense positive impact, but also raising widespread concerns around the potential for individual and societal harm. Today, the predominant paradigm for human-AI safety focuses on fine-tuning the generative model's outputs to better agree with human-provided examples or feedback. In reality, however, the consequences of an AI model's outputs cannot be determined in an isolated context: they are tightly entangled with the responses and behavior of human users over time. In this position paper, we argue that meaningful safety assurances for these AI technologies can only be achieved by reasoning about how the feedback loop formed by the AI's outputs and human behavior may drive the interaction towards different outcomes. To this end, we envision a high-value window of opportunity to bridge the rapidly growing capabilities of generative AI and the dynamical safety frameworks from control theory, laying a new foundation for human-centered AI safety in the coming decades.

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