Fig. 4
Dual adaptation pathways following rule reversal. Demonstration of the two adaptation pathways, depending on the violation magnitude, when the rule changes from \(\alpha\) to \(-\alpha\). (a) Example image pairs before and after the rule reversal for a large violation (\(\alpha = 0.8\), left) and a small violation (\(\alpha = 0.2\), right). (b) Performance across 100 networks as a function of examples (shaded regions: 95% CI). (c) Representative demonstration of the evolution of \(\Delta Z\) (red) and \(\theta\) (blue) for each violation magnitude. Initially, both networks converge to the positive solution (\(\theta , \Delta Z > 0\)). After reversal, \(\Delta Z\) flips immediately due to the change in the image order. Optimization drives \(\Delta Z\) and \(\theta\) towards each other, approaching \(\Delta Z=0\) and \(\theta =0\). For large violations (left), the representation module “wins” and adaptation restores \(\Delta Z\) while keeping \(\theta\) unchanged. For small violations (right), adaptation eventually occurs via the relational module, flipping the sign of \(\theta\) to match the negative \(\Delta Z\).
