Fig. 3: Model distances.

A illustrates an example of distance computations for four points, according to Stimulus-Bound and Task-Relevant representations. The four points are selected here solely for visualization purposes. Stimulus-bound distances are calculated within a two-dimensional feature space, accurately capturing the configurations of conceptual and spatial features. Gray dashed lines denote distances between points. Task-relevant distances, however, are computed within a compressed space optimized for learning the task structure. These distances are measured along a one-dimensional manifold, and points are projected onto the red dashed line by subtracting feature 2 from feature 1, which retains essential task information critical for generalization. Here, the blue and green points overlap, reducing their distance to zero. B shows a schematic of the calculation of distances for spatial, conceptual, and cross-domain tasks (example from the SameSt group). The matrices presented in the figure are schematic examples meant to illustrate how distances are calculated across configurations for within- and cross-domain tasks. Each white and black square in the four-square maps represents different configurations, with white indicating “grow" and black indicating “die." Within a domain, Euclidean distances were calculated for spatial or conceptual tasks. Across domains, distances between the spatial and conceptual task stimuli were computed as if both lay in the same space. The red, orange, and purple lines indicate specific example distances used in the analysis, respectively, distance across domains, within domain in the conceptual space and within domain in the spatial space. This approach yielded six model matrices in total: three stimulus-bound and three task-relevant. We then computed correlations between these model matrices and empirical matrices, where distance was calculated as the correlation distance between the Event-Related Fields (ERF) of different configurations at each time point.