Conformity refers to phenomena where people match their behavior to others. Much research has focused on cases where people observe others in identical situations, saying little about its depth or generalizability. When conforming, do people revise behaviors only in that specific situation, or do they update more deeply to maintain consistent behaviors across situations? Using simulations, we first show that deep and shallow conformity leads to contrasting group dynamics; only with deep conformity can groups accumulate improvements beyond individual lifespans. We further conduct an experiment using an estimation task to examine the depths of conformity in humans. People generally extended conformist social influence to new situations without direct reference to others. However, those who simply averaged their answer with that of the direct reference showed notable failures in this generalization. Collectively, our research highlights the importance of distinguishing different depths of conformity when studying social influence and resulting group outcomes.