Fig 1.
Model sketch. Each layer is composed of orientation selective cells (8 per location; only 2 shown for clarity).
The bottom layer processes image inputs. The top layer receives excitatory connections from the bottom layer, inversely proportional to distance and difference in preferred orientation (red lines). The top layer sends feedback connections to the bottom layer, with weights proportional to those of feedforward connections, but modulatory (multiplicative) rather than driving (additive). In addition, all cells receive divisive short-range inhibition from their neighbour, decaying quickly with distance (blue lines). For clarity, we only show connections to and from one single top-layer cell; other cells have similar connectivity.
Fig 2.
Explanation of model mechanisms.
Attentional modulation on top-layer cells extends the RF of other top-layer cells, and short-range inhibition automatically scales competition to RF size. Top panel (A): Attention expands RFs. Without attention, cell B1 is too far from T2 to excite it significantly, and thus falls outside T2’s RF (Left). In the presence of attention (Right), the top-down modulation is propagated through feedback connections to B1, making it respond more strongly to a given stimulus. As a result, B1 can now reliably excite T2, and thus is now part of its RF. Bottom panel (B): Short-range inhibition scales competition to RF size. A non-preferred stimulus in N1’s RF excites cells close to N1, which in turn inhibit N1 through short-range inhibition (Left). But if the same stimulus falls well outside N1’s RF, it will also fall outside the RF of cells close to N1, which are the only ones that can inhibit N1; therefore, N1 will not be inhibited by the non-preferred stimulus (Right). The only required assumptions are that neighbouring cells tend to have comparable RF sizes, and that the spatial extent of short-range lateral inhibition is small relative to RF size.
Fig 3.
Response of a top-layer cell selective for vertically-oriented stimuli. Response to two opposite stimuli in the RF (third bar) is intermediate between the cell’s responses to either stimulus in isolation (first and second bar). Attending to one of the stimuli partially restores the response to that stimulus alone, without any change in the display (fourth and fifth bar). The numbers above the fourth and fifth bars indicate the magnitude of attentional modulation in comparison to the no-attention response to the exact same stimulus (third bar).
Fig 4.
Time course of attentional effects.
Cell activations as a function of time in the top and bottom layer, in the presence or absence of attention. Attentional modulation occurs earlier and is stronger in the top layer than in the bottom layer.
Fig 5.
Response of a model cell selective for vertically-oriented stimuli, for stimuli of varying orientation, with feature-based attention to the stimulus orientation (red) or in the absence of attention (blue). Dots represent model responses; lines are Gaussian fits. Compare Fig 4 of [12].
Fig 6.
Effect of attention on response curves as a function of stimulus intensity.
Top row (A): Similarly to Heeger & Reynolds’ normalization model of attention, response curves become more similar to a response gain or a contrast gain (respectively) when the attentional field is made smaller or larger in comparison to RF size. Middle row (B): In addition, the model predicts that attentional effects should shift from a response gain (first panel) to a contrast gain (second panel), and might also produce crossing curves (third panel), as the focus of attention shifts away from the center of the stimulus and of the cell’s RF. Note that the contrast-gain effect persists (though with decreasing magnitude) as attention shifts further away from the RF, due to the wide range of feedback connections between top and input layers. Compare with Fig 5 of [7].
Fig 7.
Spatial attention shifts receptive fields.
Reconstructed receptive fields obtained by mapping the response of the cell to a moving probe stimulus, under various attentional conditions. Compare with Fig 2 of [13].
Fig 8.
Spatial attention resizes receptive fields.
Conventions are as in Fig 7. Focusing attention inside the receptive field shifts and shrinks the receptive field around the focus of attention (top row). Focusing attention just outside the receptive field expands it slightly towards the focus of attention (bottom row). Compare with Fig 6 of [15].
Fig 9.
Feature-based attention shifts the reconstructed receptive fields of top-layer cells in featural (spectral) space.
Top and Middle row: the reconstructed spectral preference (2D Fourier spectrum) of a horizontally-selective and vertically-selective cell, respectively, under attention to two different orientations. Note that both cells have preferred orientation equidistant from either attended orientation, and thus receive quantitatively similar attentional modulation in all conditions. The last column indicates the normalized difference (a-b) / (a+b) between the two attentional conditions, reflecting the shift caused by attention. Bottom panel: difference between attentional conditions, using the summed spectral receptive fields of both horizontally- and vertically-selective cells.