Differing effects of attention in single-units and populations are well predicted by heterogeneous tuning and the normalization model of attention

Single-unit measurements have reported many different effects of attention on contrast-response (e.g., contrast-gain, response-gain, additive-offset dependent on visibility), while functional imaging measurements have more uniformly reported increases in response across all contrasts (additive-offset). The normalization model of attention elegantly predicts the diversity of effects of attention reported in single-units well-tuned to the stimulus, but what predictions does it make for more realistic populations of neurons with heterogeneous tuning? Are predictions in accordance with population-scale measurements? We used functional imaging data from humans to determine a realistic ratio of attention-field to stimulus-drive size (a key parameter for the model) and predicted effects of attention in a population of model neurons with heterogeneous tuning. We found that within the population, neurons well-tuned to the stimulus showed a response-gain effect, while less-well-tuned neurons showed a contrast-gain effect. Averaged across the population, these disparate effects of attention gave rise to additive-offsets in contrast-response, similar to reports in human functional imaging as well as population averages of single-units. Differences in predictions for single-units and populations were observed across a wide range of model parameters (ratios of attention-field to stimulus-drive size and the amount of baseline response modifiable by attention), offering an explanation for disparity in physiological reports. Thus, by accounting for heterogeneity in tuning of realistic neuronal populations, the normalization model of attention can not only predict responses of well-tuned neurons, but also the activity of large populations of neurons. More generally, computational models can unify physiological findings across different scales of measurement, and make links to behavior, but only if factors such as heterogeneous tuning within a population are properly accounted for.