A key challenge to understanding self-awareness has been a principled way of quantifying whether an intelligent system has a concept of a "self", and if so how to differentiate the "self" from other cognitive structures. We propose that the "self" can be isolated by seeking the invariant portion of cognitive process that changes relatively little compared to more rapidly acquired cognitive knowledge and skills, because our self is the most persistent aspect of our experiences. We used this principle to analyze the cognitive structure of robots under two conditions: One robot learns a constant task, while a second robot is subjected to continual learning under variable tasks. We find that robots subjected to continual learning develop an invariant subnetwork that is significantly more stable (p < 0.001) compared to the control, and that this subnetwork is also functionally important: preserving it aids adaptation while damaging it impairs performance. We suggest that this principle can offer a window into exploring selfhood in other cognitive AI systems

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