Top-down attention has often been separately studied in the contexts of either optimal population coding or biasing of visual search. Yet, both are intimately linked, as they entail optimally modulating sensory variables in neural populations according to top-down goals. Designing experiments to probe top-down attentional modulation is difficult because non-linear population dynamics are hard to predict in the absence of a concise theoretical framework. Here, we describe a unified framework that encompasses both contexts. Our work sheds light onto the ongoing debate on whether attention modulates neural response gain, tuning width, and/or preferred feature. We evaluate the framework by conducting simulations for two tasks: (1) classification (discrimination) of two stimuli sa and sb and (2) searching for a target T among distractors D. Results demonstrate that all of gain, tuning, and preferred feature modulation happen to different extents, depending on stimulus conditions and task demands. The theoretical analysis shows that task difficulty (linked to difference Δ between sa and sb, or T, and D) is a crucial factor in optimal modulation, with different effects in discrimination vs. search. Further, our framework allows us to quantify the relative utility of neural parameters. In easy tasks (when Δ is large compared to the density of the neural population), modulating gains and preferred features is sufficient to yield nearly optimal performance; however, in difficult tasks (smaller Δ), modulating tuning width becomes necessary to improve performance. This suggests that the conflicting reports from different experimental studies may be due to differences in tasks and in their difficulties. We further propose future electrophysiology experiments to observe different types of attentional modulation in a same neuron.
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