Stimuli and protocols of the profile experiment.

a, Left: the auditory cue, comprising either a low- or high-frequency tone, predicted the orientation of the first grating with equal validity in the baseline experiment. B20°: Baseline 20°; B70°: Baseline 70°. Right: in the main experiment, the low- or high-frequency tone predicted 20° or 70° (expected) orientation of the first grating with 75% validity. In the remaining 25% of trials, this orientation was chosen randomly and equally from four non-predicted orientations (30°, 40°, 50°, and 60°). There were two types of expected conditions: Expect 20° (E20°) and Expect 70° (E70°), and for both conditions, there were 5 possible distances in orientation space between the expected and test gratings, ranging from Δ0° through Δ40° with a step size of 10°. b, In both baseline and main experiments, each trial began with an auditory cue, followed by an 1800 ms fixation interval. Then, two consecutive gratings were each presented for 150-ms and separated by a 300-ms blank interval. Participants were first asked to make a 2AFC judgment of either the orientation (clockwise or anticlockwise) or the spatial frequency (lower or higher) of the second grating relative to the first on orientation discrimination (OD, purple) and spatial frequency discrimination (SFD, blue) tasks, respectively. Then, participants were asked to make another 2AFC judgment on the tone of auditory cue, either low or high. CW: clockwise; CCW: counterclockwise; HF: higher frequency; LF: lower frequency; HT: high tone; LT: low tone. c, Left: expectation operates by the sharpening model with suppressing unexpected information, under this configuration, the profile of expectation could display as a center-surround inhibition, with an inhibitory zone surrounding the focus of expectation. Right: expectation operates by the cancelation model with highlighting unexpected information, under this configuration, the profile of expectation could display as a monotonic gradient, without the inhibitory zone.

Results of the profile experiment.

The discrimination thresholds of OD (top) and SFD (bottom) tasks during baseline (a) and main (b) experiments. B20°: Baseline 20°; B70°: Baseline 70°; E20°: Expect 20°; E70°: Expect 70°. c, The averaged discrimination sensitivity (DS) of each distance on OD (top) and SFD (bottom) tasks, and the best fitting Gaussian and Mexican-hat functions to these DSs across distances. G, Gaussian model; M, Mexican-hat model. d, R2of the best fitting Gaussian and Mexican-hat functions for individual participants in OD (top) and SFD (bottom) tasks. For both tasks, most dots located in the upper-left zone, demonstrating that the Mexican-hat model was favored over the Gaussian model. Open symbols represent the data from each participant and filled colored dots represented the mean across participants. Error bars indicate 1 SEM calculated across participants.

Results of computational modeling.

a, Illustration of the Tuning sharpening model (left) and the Tuning shift model (right). The Tuning sharpening model postulates that expectation sharpens the tuning of individual neurons (thick curves) towards the expected orientation, which results in a center-surround population response profile (black curve) centered at the expected orientation. The Tuning shift model postulates that expectation attracts the tuning of individual neurons (thick curves) from unexpected orientation towards the expected orientation, which also results in a center-surround population response profile. b, The fitted discrimination thresholds on OD (left) and SFD (right) tasks in the baseline (top) and main (bottom) experiments. c, The averaged DSs using Tuning sharpening model on OD (left) and SFD (right) tasks. d, R2 of the best fitting Gaussian and Mexican-hat functions for individual participants based on the fitted DSs using Tuning sharpening model on OD (left) and SFD (right) tasks. Open symbols represent the data from each participant and filled colored dots represented the mean across participants. e-g, The results from Tuning shift model, see caption for (b-d) for a description of each type of graph. The amplitude A (vertical stripes) and width σ (diagonal stripes) differences between the baseline and main experiments using Tuning sharpening model in Δ0° (h) and Δ10°-Δ40° (i) conditions, on OD (left) and SFD (right) tasks. The location x0 differences between the baseline and main experiments using Tuning shift model in Δ0° (j) and Δ10°-Δ40° (k) conditions, on OD (left) and SFD (right) tasks. Open symbols represent the data from each participant and error bars indicate 1 SEM calculated across participants. B20°: Baseline 20°; B70°: Baseline 70°; E20°: Expect 20°; E70°: Expect 70° (*p < 0.05; **p < 0.005; ***p < 0.001).

RMSDs of Tuning sharpening and Tuning shift models.

RMSDs of Tuning sharpening and Tuning shift models during the baseline (top) and main (bottom) experiments, on OD (a) and SFD (b) tasks. B20°: Baseline 20°; B70°: Baseline 70°; E20°: Expect 20°; E70°: Expect 70°. Open symbols represent the data from each participant and filled colored dots represented the mean across participants. Error bars indicate 1 SEM calculated across participants.

Protocol and error distributions of the orientation adjustment experiment.

a, The protocol of orientation adjustment experiment was similar with that of the profile experiment, except for two aspects. First, there were 4 possible (20°, 40°, 50°, and 70°) orientations for the first grating: 20°/70° (Δ0° deviated from the expected orientation) and 40°/50° (Δ20°/Δ30° deviated from the expected orientation). Second, in both baseline and main experiments, the second grating was set as a random orientation within the range of 0° to 90°, and participants were required to rotate the orientation of the second grating to match the first. HT: high tone; LT: low tone. b, Three-component mixture model to the adjusted errors from baseline (left) and main (middle) experiments. In current study, the shift towards to 20° was (arbitrarily) considered to be the negative value (‘-’), whereas the shift towards to 70° was thus the positive value (‘+’). The mean shift was calculated as: mean shift = (shift towards to 70°-shift towards to 20°)/2. The shaded error bars indicate 1 SEM calculated across participants. B20°: Baseline 20°; B70°: Baseline 70°; E20°: Expect 20°; E70°: Expect 70°.

Results of the orientation adjustment experiment.

a, The adjusted orientation difference between the baseline and main experiments in both expected (20°/70°, i.e. Δ0°, middle) and unexpected (40°/50°, i.e. Δ20°/Δ30°, right) conditions. B20°: Baseline 20°; B70°: Baseline 70°; E20°: Expect 20°; E70°: Expect 70°. b-d, The parameter estimates difference between the baseline and main experiments in both expected (Δ0°, middle) and unexpected (Δ20°/Δ30°, right) orientations. The parameter estimates were obtained by fitting a three-component mixture model to adjusted errors in different conditions. b, mu reflects the response distribution shift away from the presented grating orientation. c, s.d. reflects precision of responses (with higher values indicating worse precision). d, g estimates the probability that the participant produced a random response (i.e., the guess). Open symbols represent the data from each participant and error bars indicate 1 SEM calculated across participants (*p < 0.05; **p < 0.005; ***p < 0.001).

Protocol and results of the orientation discrimination experiment.

a, The protocol of orientation discrimination experiment was similar with that of the orientation adjustment experiment, except for two aspects. First, there were 3 possible (20°, 45°, and 70°) orientations for the first grating: 20°/70° (Δ0° deviated from the expected orientation) and 45° (Δ25° deviated from the expected orientation). Second, in both baseline and main experiments, the second grating were 1°, 3°, 5°, 7°, and 9° deviated from the first grating, either clockwise (CW) or counterclockwise (CCW). Participants were asked to make a 2AFC judgment of the orientation of the second grating relative to the first, either clockwise or anticlockwise. HT: high tone; LT: low tone. Psychometric functions showing orientation judgements in each condition for Δ0° (b) and Δ25° (c). Data points averaged across participants were fit using a cumulative normal function. The abscissa refers to ten orientation differences between the first and second gratings. The ordinate refers to the percentage of trials in which participants indicated the orientation of second grating that was anticlockwise or clockwise to the first for expected 20° (left) and 70° (right) conditions, respectively. The slope (an index for the Tuning sharpening model, d) and shift (an index for the Tuning shift model, e) differences between the baseline and main experiments for expected 20° and 70° conditions. Negative: shift to left; Positive: shift to right. Open symbols represent the data from each participant and error bars indicate 1 SEM calculated across participants. B20°: Baseline 20°; B70°: Baseline 70°; E20°: Expect 20°; E70°: Expect 70° (*p < 0.05; **p < 0.005).

Results of artificial neural networks.

a, Model structure and stimulus examples for deep predictive coding neural network (DPCNN) and standard feedforward CNN, on both OD (purple) and SFD (blue) tasks. DPCNN consisted of 6 feedforward encoding layers (e1-e6), 5 generative feedback decoding layers (d1-d5), and 3 fully connected (fc) layers. The reconstruction error (E1-E5) is computed and used for the proposed predictive coding updates, denoting by P.C. loops. The CNN is the same with DPCNN but removing feedback predictive coding iterations. The accuracy of each distance during the pre- (b) and post- (c) training for DPCNN (left) and CNN (right), on the OD task. d, The training effect (i.e., the ACC difference between pre- and post-training) of each distance in DPCNN (left) and CNN (right), and the best fitting Mexican-hat and Gaussian functions to these training effects across distances, on the OD task. M, Mexican-hat model; G, Gaussian model. e, R2 of the best fitting Mexican-hat and Gaussian functions from individual data in DPCNN (left) and CNN (right) on the OD task. Open symbols represent individual data and filled colored dots represented the mean across data. Error bars indicate 1 SEM calculated across data. f-i, The results from the SFD task, see caption for (b-e) for a description of each type of graph.