Article Figures & Data
Figures
- Figure 1.
Stimuli and simulation results. A, The stimuli were the same in the simulations and in the human experiments. The items were displayed at opposite sides of the screen (either 45° and 225° or −45° and −225°). Both item positions were jittered by a random amount in both the x- and y-axes (Δx and Δy in the picture) to make the task non-trivial for human participants (i.e., preventing participants from performing the SR task considering only the position of one item, thus ignoring the SR between the two items). The items used are hexominoes (right panel). Minimum and maximum item height and width are 1.2–3.6° and 1.2–2.7° of visual angle, respectively, and 2–5 pixels used for the simulations (image size was 50 × 80 pixels). B, Example of stimuli position for the SD task (left column) and spatial relation task (SR, right column). For the sake of illustration, the ratio between the screen and hexominoes size has been modified (stimuli here look bigger than in the real experiment). C, D, Accuracy of the CNN network on the SD (light red) and SR (blue) tasks, and of a Siamese network trained on the SD task (dark red). The Siamese network mimics segmentation in a feedforward network, by separating the items in two distinct channels of the network (see D). The left panel shows the training curves for each network (accuracy over epochs during training); we stopped the training when the validation accuracy reached 90%. In the right panel, we show the training accuracy at the last epoch and the test accuracy. The latter was evaluated using novel items never used for training, and it reveals that the CNN seems to only learn the required rule for the SR but not for the SD task, as shown in a previous study. Conversely, the Siamese network (CNN with segmentation) can solve the SD task, demonstrating that segmentation can allow the CNN to successfully accomplish this task. In both panels we show average values ± SE over 10 repetitions using different random initializations.
- Figure 2.
Experimental design and human behavioral results. A, At the beginning of each trial, a black fixation cross was displayed for 350 ms. After two stimuli were shown for 30 ms, participants waited an additional 970 ms before providing the answer. The response was cued by the fixation cross turning blue. After the response, the color of the fixation cross provided feedback: green if the response was correct, red otherwise. B, Humans performed the SD and SR tasks with comparable levels of performance. In the left and right panels are shown the averages ± SE for accuracy and RTs, respectively. Each pair of connected markers represent an individual subject. The results for the SD (in red) and SR (in blue) conditions are further broken down for each condition separately (SD and vertical-horizontal). BF indicates the BF against the null hypothesis (difference between the two conditions). C, Changes over blocks of ρ (the distance between the stimuli, left panel) and θ (the angle between the stimuli and the meridian, right panel) as adjusted by the QUEST algorithm.
- Figure 3.
ERPs results. Each panel represents the difference between ERPs elicited in the SD and SR conditions for the seven midline electrodes (average ± SE). Shown in red are the points for which a significant difference was found against zero. The results reveal a significant difference from 250 ms after stimuli onset until the response cue (at 1000 ms) in central parietal regions, and an opposite effect after 750 ms in frontal regions. In the bottom-right panel, the topography, computed over the 250- to 1000-ms interval, confirmed a larger activity in the SD than in the SR condition (positive difference, warmer colors) in the central-parietal regions, and an opposite effect (negative difference, colder colors) in the frontal regions (which, although not significantly, also included occipital regions).
- Figure 4.
Time-frequency results. A, The difference between SD and SR power spectra is shown in the first panel. White lines indicate the onset of the fixation cross, the stimuli and the response cue. B, The second panel shows the corresponding t values (when testing the difference against zero). We observed a significant region in the low β band (16–24 Hz), between 250 and 950 ms after stimulus onset. C, The topography of the significant time-frequency window reveals the involvement of occipital-parietal regions.
- Figure 5.
Pilot experiment results. A, Behavioral results of the pilot experiment: left and right panel show accuracy and RTs for SD (red) and SR (blue) tasks. Differently than in the main task, in the pilot experiment participants performed significantly better in the SD than in the SR task (compare the accuracy between A and Fig. 2B). ***indicates Bayes Factor > 100. B, Difference between SD and SR EPs. Red asterisk indicates time window significantly different from zero. C, Difference between SD and SR power spectra: white lines indicate the stimulus onset and the response cue. D, Testing the SD-SR difference against zero reveals a significant region in the low β band (13–21 Hz), before the response cue, in agreement with the results of the main experiment (Fig. 4). We reported a large effect size for this effect (one sample t test against zero averaging per each participant the values within the significant region, t(13) = 7.049, p < 0.001, Cohen’s d = 1.820). E, As in the main experiment, the SD-SR difference mostly involves occipital-parietal regions.
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