Examples of stimulus arrays for each task and the procedure in Experiment 1. (A) Stimulus examples of the collinearity discrimination task (left), the parallelism discrimination task (middle), the orientation discrimination task (right). (B) The procedure of Experiment 1.

Results of Experiment 1, RTs of each discrimination tasks measured at Pre-test and Post-test were compared by one-tailed, paired sample t-test. (A) Results from the group trained on the collinearity task (n=15). Performances of the collinearity task were improved after training (p = 0.0008). (B) Results from the group trained on the parallelism task (n=15). Performances of the collinearity (p = 0.008) and parallelism (p < 0.0001) task were improved after training. (C) Results from the group trained on the orientation task (n=14). Performances of the collinearity (p = 0.0007), parallelism (p = 0.002) and orientation task (p = 0.0002) were improved after training. (***p < 0.001, **p < 0.01, *p < 0.05). Error bars denote 1 SEM across subjects.

Figure 2—figure supplement 1. Accuracies for the three discrimination tasks measured at Pre-test and Post-test.

Figure 2—figure supplement 2. The learning indexes of the three geometrical invariants in Experiment 1.

Figure 2—source data 1. RTs and accuracies at Pre-test and Post-test, and learning indexes in the course of training for each participant.

Examples of the layout of a stimulus frame. The top line demonstrates trials with a “target” (surrounded by orange dashed box), and the bottom line demonstrates the catch trials without “target”. The blue dashed lines represent the “base” orientation for each stimulus, and 𝜃 is the angle separation of the discrimination task. (A) Stimulus examples of the collinearity (colli.) task, the upper example shows a “target” (a pair of non-collinear lines) located at the lower right quadrant. (B) Stimulus examples of the parallelism (para.) task, the upper example shows a “target” (a pair of unparallel lines) located at the lower right quadrant. (C) Stimulus examples of the orientation (ori.) task, the upper example shows a “target” (the more clockwise line) located at the upper right quadrant.

Figure 3—figure supplement 1. Examples of stimuli in Experiment 2.

Examples of stimulus arrays for each task and the procedure in Experiment 1. (A) Stimulus examples of the collinearity discrimination task (left), the parallelism discrimination task (middle), the orientation discrimination task (right). (B) The procedure of Experiment 1

Results of Experiment 2, Thresholds of each discrimination task measured at Pre-test and Post-test were compared by one-tailed, paired sample t-test. (A) Results from the group trained on the collinearity task (n = 15). Performances of the collinearity task were improved after training (p = 0.026). (B) Results from the group trained on the parallelism task (n = 15). Performances of the collinearity (p = 0.007) and parallelism (p = 0.003) task were improved after training. (C) Results from the group trained on the orientation task (n = 15). Performances of the collinearity (p = 0.008), parallelism (p = 0.036) and orientation task (p < 0.0001) were improved after training. (***p < 0.001, **p < 0.01, *p < 0.05). Error bars denote 1 SEM across subjects.

Figure 5—figure supplement 1. The learning indexes of the three geometrical invariants in Experiment 2.

Performance of the model when trained under different discrimination tasks. (A) Accuracy trajectories against training iterations from the models trained on collinearity (left), parallelism (middle), and orientation task (right), with the error bar representing 1 SEM. 𝑡95 is the iteration where the fully plastic network reached 95% accuracy, depicted by green dashed lines. The numbers located at the end of each curve are the final accuracies of the last iteration. (B) The learning speed which was indexed by 𝑡95 of the three tasks. The learning speed of the collinearity task was faster than the parallelism (p = 0.018) and orientation task (p < 0.0001). The learning speed of the parallelism task was faster than the orientation task (p < 0.0001). Statistical significance was calculated by paired t-test with FDR correction. (***p < 0.001, **p < 0.01, *p < 0.05). Error bars denote 1 SEM across subjects. (C) Final mean accuracies when the network was trained and tested on all combinations of tasks

Figure 6—figure supplement 1. Model structure and stimulus examples in Experiment 3.

Layer change under different training tasks. (A) Layer change trajectories during learning. (B) Iteration at which the rate of change peaked (PSI) in layers 1-5. (C) Final layer change in layers 1-5. The error bar representing 1 SEM.

Accuracies for the three discrimination task measured at Pre-test and Post-test. Accuracy was defined as the average percentage correct per block. At Pre-test, the accuracies of the collinearity task were significantly higher than that in the parallelism (p < 0.0001) and orientation task (p = 0.0001). At Post-test, the accuracies of the collinearity task were still significantly higher than the other two tasks (p < 0.0001 for the parallelism task, p = 0.0001 for the orientation task). Statistical significance was calculated by paired t-test with FDR correction. (***p < 0.001, **p < 0.01, *p < 0.05). Error bars denote 1 SEM across subjects.

The learning indexes of the three geometrical invariants in Experiment 1. Error bars denote 1 SEM across subjects.

Examples of stimuli in Experiment 2. Sample stimuli in the collinearity (left), parallelism (middle) and orientation (right) discrimination task. The blue dashed lines represent the "base" orientation for each stimulus, and 𝜃 is the angle separation of the discrimination task.

The learning indexes of the three geometrical invariants in Experiment 2. Error bars denote 1 SEM across subjects.

Stimulus examples in Experiment 3. Examples of the pairs of stimulus images for the three discrimination tasks in Experiment 3. The examples here are selected from the stimulus condition with the following parameters: angle separation (10° for colli. & para. and 20° for ori.), distance for para. (40 pixels), location of gap for colli. (the front one-third).