Artificial intelligence is increasingly integrated throughout everyday life. However, recent studies document reluctance to interact with A.I. systems. This challenges both the deployment of beneficial A.I. technology and the development of deep learning systems that depend on humans for oversight, direction, and training. Previously neglected but fundamental, social-cognitive processes guide human interactions with A.I. systems. In five behavioral studies (_N_ = 3,099), warmth and competence feature prominently in participants’ impressions of artificially intelligent systems. Judgments of warmth and competence systematically depend on human-A.I. interdependence. In particular, systems that optimized interests aligned with human interests were perceived as warmer and systems that operated independently from human direction were perceived as more competent. Finally, a prisoner’s dilemma game shows that warmth and competence judgments predict participants’ willingness to cooperate with a deep learning system. These results highlight the need for researchers and developers to consider the degree and alignment of interdependence between humans and artificial intelligence.