Article Figures & Data
Figures
- Figure 1.
Experimental design of the hidden target task employed to study the statistical learning of a spatial prior in two different visuo-motor contexts. A, B, Main task of the experiment. A, Participants were told to estimate the location of a hidden treasure on a ring by observing and combining information provided by the visual hints across trials. The hidden target location was defined as the mean of a von Mises distribution and the hints, presented at each trial, were samples drawn from this underlying distribution. Participants had 20 trials to estimate the location of the hidden target, after which a new hidden target had to be found. Participants used their gaze to indicate their responses. B, Each trial started with a fixation period, after which the hint was presented, and participants had to indicate their guess about the location of the hidden target by either looking at it (pro-saccade response) or by looking exactly opposite to it (anti-saccade response). In half of the trials (i.e., consecutive 10 trials), participants had to use pro-saccades, and in the other half they used anti-saccades, with a randomized order across blocks. C, D, Calibration task used to estimate the motoric error of each participant for pro-saccades and anti-saccades. Participants had to directly look either at the lines (pro-saccade response) or exactly opposite to the lines (anti-saccade response). E, Block-design of the experiment. F, We compared learning across two levels of difficulty and two different response types. Task difficulty was varied by changing the concentration of the von Mises distribution (compare Materials and Methods). Finally, we tested whether knowledge could be transferred from one visuo-motor context to the other. For this, we also varied the order of pro-saccade and anti-saccade responses across blocks.
- Figure 2.
Participants successfully accumulate information and learn on a short time scale. A, The angular difference between the participant’s guess and the true location of the hidden target was used to measure learning. B, Example block. To test learning, we compared the performance in trials 1–5 (first half) to the performance in trials 6–10 (second half). C, The absolute angular error in the second half is lower than in the first half (paired t test: t = 7.25, p < 0.0001, N = 20). D, Participants’ confidence is higher in the second half than in the first half (paired t test: t = −4.39, p = 0.0003, N = 20). E, The absolute angular error of participants is lower than the absolute angular error of the visual hints, i.e., participants’ guesses are closer to the center of the von Mises distribution compared with the presented visual hints (paired t test: t = 4.92, p = 0.0001, N = 20).
- Figure 3.
Similarity of learning curves across response modalities. A, The distribution of the angular error for pro-saccade and anti-saccade response in the calibration task. B, The distribution of the angular error for pro-saccade and anti-saccade response in the hidden target task. C, The modality difference index quantifies the difference between the absolute angular error in pro-saccade and anti-saccade trials. The shaded area indicates the SEM. D, Time course of the absolute angular error for each of the four different conditions (two response types × two difficulties). Here and in the following panels, except stated otherwise, shaded areas represent the SEM (N = 20). E, Time course of the confidence ratings for each of the four different conditions. F–J, Participants’ learning curves compared with the lower bound. The lower bound is given by taking the cumulative average of all hints presented so far and adding the error because of motoric noise, estimated from the calibration task.
- Figure 4.
Learning strategy is similar across response modalities. A, Different predictors used to explain the participants’ single trial estimates (i.e., angular error). B, Model comparison between various single and multiple predictor models. Shown are the weights ω, which represent the probability that a model is the best among the ones considered. Error bars indicate SEM (N = 20). C, D, Same as B but performed on two different datasets, one consisting only of pro-saccade response trials (C), the other consisting only of anti-saccade response trials (D). E–H, Regression weights for a model including participants’ last three guesses and the current and last three visual hints. Shaded area indicates SEM (N = 20). E, Regression weights put on the last three guesses. F, Regression weights put on the current, as well as the last three hints. G, H, Participants put similar weight on guesses and hints in pro-saccade and anti-saccade response trials (paired t test for previous guess: t = −0.38 p = 0.70; paired t test for hint: t = −0.26 p = 0.79). The weights put on previous hints and guesses were validated using separate models for hints and guesses (Extended Data Fig. 4-1). To select the relevant number of time steps in the past to include in the model comparison in B (see Table 1 for model definitions), we used a stepwise regression approach (Extended Data Fig. 4-2). Results shown in B were validated by varying the dataset used to fit the models (Extended Data Fig. 4-3), looking at best single subject models (Extended Data Fig. 4-4), and splitting the data according to task difficulty and response type (Extended Data Fig. 4-5).
- Figure 5.
Drop in performance after response switch. A, To test the knowledge transfer hypothesis, we analyzed all trials within a block, encompassing trials before and after the response switch. We specifically focused on the difference between trial 10 (before response switch) and trial 11 (after response switch). The same example block as in Figure 2 is shown. B, If knowledge is transferred, we expect similar performance in trial 11 and trial 10. In contrast, if no knowledge is transferred, we expect similar performance in trial 11 and trial 1. To analyze the difference because of statistical learning only, we subtracted the motor error estimated from the calibration task to make pro-saccade and anti-saccade trials more comparable. C, Comparison of performance in trial 10 and 11 for the four different experimental conditions (difficulty × pro/anti order). Each dot represents one subject and horizontal bars indicate mean and extreme values. D, Same as C but for comparison between trial 1 and trial 11; ***p < 0.001, **p < 0.01, *p < 0.05, n.s. p > 0.05. E–H, Performance time course for different difficulty levels and pro-/anti-saccade orders. Dashed colored lines represent performance in trials 1–10. Shaded area indicates the SEM (N = 20). The results for performance were corroborated by analyzing confidence levels, which showed a similar drop from trial 10 to trial 11 (Extended Data Fig. 5-1, Fig. 5-2). We tested whether the drop in performance was related to the fact that subjects might have misunderstood the task. A control experiment (see Materials and Methods, experiment 2) confirmed that although subjects were aware that all 20 trials belonged to the same hidden target location, they were not able to integrate information across the response switch (Extended Data Fig. 5-3). Furthermore, we validated that the subtraction of the motor error is plausible and that there is no temporarily increased motor error after the response switch (Extended Data Fig. 5-4).
- Figure 6
Almost no knowledge transfer between visuo-motor modalities. A, To test whether there is any knowledge transferred from the experience with one response type to the other, we regressed the current guess against previous guesses/current hint. B, Participants’ estimates at trial 11 (after response switch) are independent of the estimates at trials 10 (before response switch). In contrast, at every other time point, participants use previous experience to inform their current guess. Shaded area here and in the remaining panels indicates the SEM (N = 20). C, At trial 11, participants highly rely on the information coming from the current hint. D, E, Similar to the lack of transfer from one trial to the next (B), there is also no transfer from trials further in the past across the response switch (trials 11–12 for t-2; trials 11–13 for t-3). In B, D, E, non-significant regression weights with a p > 0.05 are shown in opaque.
Tables
Name Equation 1 Hint 2 Prev. hint 3 Cum. avg. hint 4 Prev. guess 5 Cum. avg. guess 6 Cum. avg. hint+guess 7 Hintt:t-3 8 Guesst-1:t-3 9 Guesst-1:t-2+Hintt 10 Guesst-1:t-3+Hintt 11 Guesst-1:t-3+Hintt:t-3 Task Modality Mean SD Absolute angular error Calibration Pro-saccade −0.1° 6.3° 3.5° Calibration Anti-saccade 0.7° 9.5° 7.1° Hidden target Pro-saccade 1.1° 16.9° 12.1° Hidden target Anti-saccade 0.1° 18.4° 13.4° Hidden target Hints 0.1° 20.6° 14.7° Mean and SD for distributions shown in Figure 3A,B. The rightmost column indicates the average absolute angular error in each task condition, estimated from the subjects’ guess, or, for the last row, from the distribution of visual hints.
Extended Data Figure 4-1
Memory traces for previous guesses and hints. This figure is supplementary to Figure 4 in the main text. Here, we quantified how much weight is put on previous hints or guesses, tested in separate models each including either only the guesses or only the visual hints. Data were pooled across all experimental conditions, so from pro-saccade and anti-saccade, as well as from easy and hard task condition. A, Regression weights of the model including previous guesses as a predictor. B, Same as A for a separate model including visual hints as a predictor. C, Comparison of the model shown in A against the model shown in B. It can be seen that the previous guess models consistently outperformed the visual information/hints models, confirming the finding that subjects’ behavior is better predicted by previous actions than external visual information. D, E, Same as A, B, but showing the single subject regression weights instead of the average weights. Download Figure 4-1, TIF file.
Extended Data Figure 4-2
Stepwise regression to select relevant predictors for model comparison. This figure is supplementary to Figure 4 in the main text. Here, we used stepwise linear regression (train function with method “leapForward” from the Caret package in R) to estimate the relevant number of past trials that should be included in our main model comparison analyses (Fig. 4; Table 1). We tried to predict the angular error in trial 10 from either all previous guesses (A), all observed visual hints (B), or a combination of both (C, D). Shown is the cross-validated fit accuracy (10-fold), measured as the root-mean-squared error (RMSE). Thereby, we found for each individual subject the number of trials (=predictors) that were included in the best fitting model (red dot), indicated by the lowest RMSE. To identify not only the number, but also the type of information that best predicted performance in trial 10, we analyzed which timesteps of previous guesses and current and previous hints were included in the best combined model (C) and created a histogram indicating for how many subjects the specific predictor (either guess: G or hint: H) was included in the best model (D). Using this approach, we found that for most subjects a model with six or less predictors, including a combination of previous guesses and visual hints, is best in predicting the angular error of the current trial. Thereby, we focused our main analysis (Fig. 4; Table 1) on three timesteps in the past (up to t-3). This allowed us to predict not only the behavior in trial 10, as done here, but also the behavior from trial 4 to trial 10. A general trend in the main analysis, which is also apparent here, is that previous guesses are better in predicting current behavior, compared to current or previous visual hints [lower errors for models including guesses (A) compared to hints (B)]. Download Figure 4-2, TIF file.
Extended Data Figure 4-3
Model comparison results of single predictor models tested on trials 2–10. This figure is supplementary to Figure 4B in the main text. Our main modeling results were based on models that included up to three timesteps in the past (n = 3), where n was determined based on a model search approach (Extended Data Fig. 4-2). To this end, we included trials 4–10, allowing us to test the models on a consistent dataset. To test whether our results hold when we include earlier trials in a block, we repeated our analysis focusing only on single predictor models (Table 1, models 1–5), which allowed us to use the data from trial 2 to trial 10. Similar to our main results, the best single predictor model was the one based on the cumulative average of past guesses. Download Figure 4-3, TIF file.
Extended Data Figure 4-4
Model comparison results for single subjects. This figure is supplementary to Figure 4B in the main text. Here, we show the model comparison results for each single subject individually. Download Figure 4-4, TIF file.
Extended Data Figure 4-5
Dependency of model comparison results on experimental condition. This figure is supplementary to Figure 4 in the main text. A–D, Model comparison results for data split according to pro-/anti-saccades and easy/hard task difficulty. Overall model comparison results did not depend on the response type or task difficulty. E, Example model prediction for a held-out data block. Data were pooled across experimental conditions, identical to the procedure used in Figure 4. F, Summary of model performance on held-out data, calculated using 10-fold cross-validation and the Caret package in R. Data were pooled across experimental conditions, as in Figure 4. Model performance was measured as the root-mean-squared-error (RMSE) for the difference between the true and the predicted angular error in the held-out data. The null model (also in the Caret package) corresponds to not using any predictor, but only fitting the intercept. Download Figure 4-5, TIF file.
Extended Data Figure 5-1
Time course of confidence rating. Download Figure 5-1, TIF file.
Extended Data Figure 5-2
Confidence drops after response switch. Figures 5-1 and Figures 5-2 are supplementary to Figure 5 in the main text. The confidence ratings demonstrated the same results as observed by analyzing the absolute angular errors of the eye movements, as there was a decrement in confidence from trial 10 to trial 11 (as shown in Extended Data Fig. 5-1A for experiment 1 as well as in Extended Data Fig. 5-1B for experiment 2), in all experimental conditions. The drop in confidence between trial 10 and trial 11 was significant (Extended Data Fig. 5-2A; paired t test; t = 3.67, p = 0.0016, N = 20). The confidence of trial 11 was not different from trial 1 (Extended Data Fig. 5-2B; paired t test; t = –1.78, p = 0.0906, N = 20). These results support the observation that after a switch in response modality, learning starts from an almost naive level. Download Figure 5-2, TIF file.
Extended Data Figure 5-3
Second experiment with reinforced instructions shows similar results. This figure is supplementary to Figures 5, 6 in the main text. These results demonstrate that we obtained similar results when participants were explicitly instructed that the location of the hidden target remained the same after a switch. Additionally, participants had to report whether they were aware of this rule, thus reinforcing the instructions. A, Also, in this experiment, performance dropped to almost naive levels after a switch in response type. B, The majority of participants reported to be aware of the rule. C, The weighting of previous guesses dropped between trial 10 and trial 11 (when the switch occurred), and instead (D), more weight was put on visual hints. Download Figure 5-3, TIF file.
Extended Data Figure 5-4
Motor error estimation. This figure is supplementary to Figures 3, 5 in the main text. Here, we tested whether our assumption that participants’ estimation error in the hidden target task calculated as a combination of two independent sources of uncertainty, i.e., the motor noise (estimated from the calibration task) and statistical uncertainty (estimated from the distribution of visual hints in the hidden target task), was plausible. A, Time course of motor error in the calibration task. B, In the following, we examined trial 1 of the hidden target task and compared subjects’ actual performance to the theoretical prediction of adding motor noise and statistical uncertainty. If our assumption that both noise sources are independent and thus can be added is plausible, we would expect that the actual (x-axis) and predicted (y-axis) data would match. C–F, Results for all four experimental conditions. Each dot represents one subject (N = 20). Paired t tests were performed to test whether there is a significant difference between the theoretical prediction and the actual data and results are shown in the respective panels. Download Figure 5-4, TIF file.
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