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A quantitative model of ensemble perception as summed activation in feature space

Nature Human Behaviour volume 7, pages 1638–1651 (2023)Cite this article

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Abstract

Ensemble perception is a process by which we summarize complex scenes. Despite the importance of ensemble perception to everyday cognition, there are few computational models that provide a formal account of this process. Here we develop and test a model in which ensemble representations reflect the global sum of activation signals across all individual items. We leverage this set of minimal assumptions to formally connect a model of memory for individual items to ensembles. We compare our ensemble model against a set of alternative models in five experiments. Our approach uses performance on a visual memory task for individual items to generate zero-free-parameter predictions of interindividual and intraindividual differences in performance on an ensemble continuous-report task. Our top-down modelling approach formally unifies models of memory for individual items and ensembles and opens a venue for building and comparing models of distinct memory processes and representations.

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Fig. 1: Laboratory ensemble tasks.
Fig. 2: TCC framework for memory of individual items and ensembles.
Fig. 3: TCC ensemble models.
Fig. 4: Non-TCC ensemble models.
Fig. 5: Colour, shape and sequential memory tasks.
Fig. 6: Comparison in predictive accuracy between the Perceptual Summation model and competing models of ensemble memory for colour with set size manipulation.
Fig. 7: The Perceptual Summation model predicts ensemble memory for colour with set size manipulation.
Fig. 8: Comparison in predictive accuracy between the Perceptual Summation model and competing models of ensemble memory for colour with colour range manipulation.

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Data availability

The data are publicly available at the following OSF link: https://osf.io/mt29p/.

Code availability

The code is publicly available on OSF (https://osf.io/mt29p/).

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Acknowledgements

We acknowledge funding from the National Institutes of Health (National Research Service Award Fellowship No. 1F32MH127823-01 to M.M.R.) and the National Science Foundation (grant nos. BCS-1653457 and BCS-2146988 to T.F.B.). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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Authors and Affiliations

  1. Psychology Department, University of California, San Diego, La Jolla, CA, USA

    Maria M. Robinson & Timothy F. Brady

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Contributions

M.M.R. and T.F.B. conceived and designed the experiments, developed the material and analytic tools and models, and wrote the paper. M.M.R. implemented the main experiments and modelling analyses.

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Correspondence to Maria M. Robinson or Timothy F. Brady.

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Extended data

Extended Data Fig. 1 The Perceptual Summation model predicts ensemble memory for color with a range manipulation.

Graphical representation of TCC models’ fit and prediction of data in Experiment 2. In this experiment participants had to remember colors of simultaneously presented circles, and the range of colors was manipulated in the ensemble task. The top row of panel A shows the fits of the TCC model for individual items to aggregate data from the visual working memory task for six items. The bottom row of panel A shows results from the predictive analysis in which d’ estimates from the visual working memory task were substituted into the TCC Perceptual Summation (blue), Post-perceptual (red) and Automatic Averaging (green) models to predict the ensemble data. The bottom panel (B) shows model predictions for a few example participants. Schurgin et al.35).

Extended Data Fig. 2 Comparison in predictive accuracy between Perceptual Summation model and competing models of ensemble memory for shape with the set size manipulation.

The top panel shows violin plots for the difference in predicted negative log likelihood scores between each of the six alternative competing models (PNLLAlt) and the main Perceptual Summation model (PNLLPerSum) for Experiment 3 (n = 50 participants). Lower values of PNLL indicate higher predictive accuracy, therefore, PNLL difference scores higher (or lower) than zero indicate support for the Perceptual Summation (or a competing) model. In both experiments, the vast majority of participants are better predicted by the Perceptual Summation model than any of the alternatives. The bottom panel shows a table with a summary of descriptive and inferential statistics from all comparisons in Experiment 3, including the mean and standard error of the mean across participants. PNLL values were compared with a paired two-tailed t-test, corrected for multiple comparisons and all p-values were statistically significant (p < 0.001).

Extended Data Fig. 3 The Perceptual Summation model predicts ensemble memory for shape with a set size manipulation.

Graphical representation of the TCC models’ fit and prediction of data in Experiment 3. In this experiment participants had to remember different shapes, and the number of shapes was manipulated in the working memory and ensemble task. The top row of panel A shows the fits of the TCC model for individual items to aggregate data from the visual working memory task for six items and the second row of panel A shows results from the predictive analysis in which d’ estimates from the visual working memory task were substituted into the TCC Perceptual Summation (blue), Post-perceptual (red) and Automatic Averaging (green) models to predict the ensemble data. Panel B shows data and model predictions for a few example participants.

Extended Data Fig. 4 Comparison in predictive accuracy between Perceptual Summation model and competing models of ensemble memory for shape with the range manipulation.

The top panel shows violin plots with the difference in predicted negative log likelihood scores between each of the six alternative competing models (PNLLAlt) and the main Perceptual Summation model (PNLLPerSum) for Experiment 4 (n = 50 participants). Lower values of PNLL indicate higher predictive accuracy, therefore, PNLL difference scores higher (or lower) than zero indicate support for the Perceptual Summation (or a competing) model. In both experiments, the vast majority of participants are better predicted by the Perceptual Summation model than any of the alternatives. The bottom panel shows a table with a summary of descriptive and inferential statistics from all comparisons in Experiment 4, including the mean and standard error of the mean across participants. PNLL values were compared with a paired two-tailed t-test, corrected for multiple comparisons and all p-values were statistically significant (p < 0.001).

Extended Data Fig. 5 The Perceptual Summation model predicts ensemble memory for shape with a range manipulation.

Graphical representation of TCC model’s fit and prediction of data in Experiment 4. In this experiment participants had to remember simultaneously presented shapes, and the range of shapes was manipulated in the ensemble task. The top row of panel A shows the fits of the TCC model for individual items to aggregate data from the visual working memory task for six items, and the second row of panel A shows results from the predictive analysis in which d’ estimates from the visual working memory task were substituted into the TCC Perceptual Summation (blue), Post-perceptual (red) and Automatic Averaging (green) models to predict the ensemble data. Panel B shows data and model predictions for a few example participants.

Extended Data Fig. 6 Comparison in predictive accuracy between Sequential Perceptual Summation model and competing models of ensemble memory for sequentially presented stimuli.

The top panel shows violin plots of the difference in predicted negative log likelihood scores between each of the eight alternative competing models (PNLLAlt) and the main Sequential Perceptual Summation model (PNLLPerSum) (n = 50 participants). Lower values of PNLL indicate higher predictive accuracy, therefore, PNLL difference scores higher (or lower) than zero indicate support for the Sequential Perceptual Summation (or a competing) model. The vast majority of participants are better predicted by the Sequential Perceptual Summation model than any of the alternatives. Note that the baseline here is the Sequential Perceptual Summation model that relies on fitting a decay rate. The independent d’ Perceptual Summation model, the last model above, is the same model but without this parametric assumption about how d’ changes across the items in the working memory task. This independent model is instead one in which we used separate d’ estimates to quantify familiarity of items as a function of serial position, rather than a single d’ and rate parameter. This model is marked with an * because it is also a version of the Sequential Perceptual Summation model and so shows comparable predictive accuracy to the main Sequential Perceptual Summation model we use, as expected. The bottom panel shows a table with a summary of descriptive and inferential statistics from all comparisons in Experiment 5, including the mean and standard error of the mean across participants. PNLL values were compared with a paired two-tailed t-test, corrected for multiple comparisons and for all comparisons between competing models p-values were statistically significant (p < 0.001).

Extended Data Fig. 7 The Perceptual Summation model predicts ensemble memory for sequentially presented stimuli.

Summary of results from Experiment 5, in which participants had to remember colors of sequentially presented real-world objects. The top row of panel A shows the fits of the Sequential TCC model to individual data and the second row of panel A shows the TCC Sequential Perceptual Summation (blue), Post-perceptual (red) and Automatic Averaging (green) models’ predictions of the ensemble data in two conditions. In the clockwise (counterclockwise) condition the most recently shown items were from the clockwise (counterclockwise) direction from the mean color, producing a clockwise (counterclockwise) bias. Panel B shows data and model predictions for a few example participants.

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Robinson, M.M., Brady, T.F. A quantitative model of ensemble perception as summed activation in feature space. Nat Hum Behav 7, 1638–1651 (2023). https://doi.org/10.1038/s41562-023-01602-z

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