Fig. 3

Illustration of the two adaptation pathways. (a) The two equivalent solutions for the relational task. One solution is to encode the size of the objects and expect that the size increases (positive \(\Delta Z\) and \(\theta\), marked by a star). In the other solution, the smallness decreases (negative \(\Delta Z\) and \(\theta\)). The diagonal line all solutions in which \(\Delta Z=\theta\). (b) Adaptation pathways following rule reversal. Without loss of generality, we consider an agent that has learned the positive solution. After learning the initial rule, the rule is reversed, flipping the sign of \(\Delta Z\), making it inconsistent with positive \(\theta\) (marked by a star). There are two adaptation pathways: relational adaptation—maintaining the sign of \(\Delta Z\) but reversing the sign of the expectation \(\theta\); or representational adaptation - changing the sign of \(\Delta Z\) to encode the smallness of objects, while maintaining the expectation that the relevant feature increases (\(\theta >0\)). The dashed diagonal line represent expectations that are opposite to the observations (\(\theta = -\Delta Z\)).