Imagine you have lost your cell phone. Your eyes scan the cluttered table in front of you, searching for its familiar blue case. But what is happening within the visual areas of your brain while you search? One possibility is that neurons that represent relevant features such as 'blue' and 'rectangular' increase their activity. This might help you spot your phone among all the other objects on the table.

Paying attention to specific features improves our performance on visual tasks that require detecting those features. The 'feature similarity gain model' proposes that this is because attention increases the activity of neurons sensitive to specific target features, such as ‘blue’ in the example above. But is this how the brain solves such challenges in practice? Previous studies examining this issue have relied on correlations. They have shown that increases in neural activity correlate with improved performance on visual tasks. But correlation does not imply causation.

Lindsay and Miller have now used a computer model of the brain’s visual pathway to examine whether changes in neural activity cause improved performance. The model was trained to use feature similarity gain to detect an object within a set of photographs. As predicted, changes in activity like those that occur in the brain did indeed improve the model’s performance. Moreover, activity changes at later stages of the model's processing pathway produced bigger improvements than activity changes earlier in the pathway. This may explain why attention affects neural activity more at later stages in the visual pathway.

But feature similarity gain is not the only possible explanation for the results. Lindsay and Miller show that another pattern of activity change also enhanced the model’s performance, and propose an experiment to distinguish between the two possibilities. Overall, these findings increase our understanding of how the brain processes sensory information. Work is ongoing to teach computers to process images as efficiently as the human visual system. The computer model used in this study is similar to those used in state-of-the-art computer vision. These findings could thus help advance artificial sensory processing too.

Covert visual attention—applied according to spatial location or visual features—has been shown repeatedly to enhance performance on challenging visual tasks (Carrasco, 2011). To explore the neural mechanisms behind this enhancement, neural responses to the same visual input are compared under different task conditions. Such experiments have identified numerous neural modulations associated with attention, including changes in firing rates, noise levels, and correlated activity (Treue, 2001; Cohen and Maunsell, 2009; Fries et al., 2001; Maunsell and Cook, 2002). But how do these neural activity changes impact performance? Previous theoretical studies have offered helpful insights on how attention may work to enhance performance (Navalpakkam and Itti, 2007; Rolls and Deco, 2006; Tsotsos et al., 1995; Cave, 1999; Hamker and Worcester, 2002; Wolfe, 1994; Hamker, 1999; Eckstein et al., 2009; Borji and Itti, 2014; Whiteley and Sahani, 2012; Bundesen, 1990; Treisman and Gelade, 1980; Verghese, 2001; Chikkerur et al., 2010). However, much of this work is either based on small, hand-designed models or lacks direct mechanistic interpretability. Here, we utilize a large-scale model of the ventral visual stream to explore the extent to which neural changes like those observed experimentally can lead to performance enhancements on realistic visual tasks. Specifically, we use a deep convolutional neural network trained to perform object classification to test effects of the feature similarity gain model of attention (Treue and Martínez Trujillo, 1999).

Deep convolutional neural networks (CNNs) are popular tools in the machine learning and computer vision communities for performing challenging visual tasks (Rawat and Wang, 2017). Their architecture—comprised of layers of convolutions, nonlinearities, and response pooling—was designed to mimic the retinotopic and hierarchical nature of the mammalian visual system (Rawat and Wang, 2017). Models of a similar form have been used to study the biological underpinnings of object recognition for decades (Fukushima, 1988; Riesenhuber and Poggio, 1999; Serre et al., 2007). Recently it has been shown that when these networks are trained to successfully perform object classification on real-world images, the intermediate representations learned are remarkably similar to those of the primate visual system, making CNNs state-of-the-art models of the ventral stream (Yamins et al., 2014; Khaligh-Razavi et al., 2017; Khaligh-Razavi and Kriegeskorte, 2014; Kheradpisheh et al., 2016; Kar et al., 2017; Cadena et al., 2017; Tripp, 2017; Love et al., 2017; Kubilius et al., 2016). A key finding has been the correspondence between different areas in the ventral stream and layers in the deep CNNs, with early convolutional layers best able to capture the representation of V1 and middle and higher layers best able to capture V4 and IT, respectively (Güçlü and van Gerven, 2015; Eickenberg et al., 2017; Yamins et al., 2014). The generalizability of these networks is limited, however, and the models are not able to match all elements of visual behaviour (Ullman et al., 2016; Azulay and Weiss, 2018; Baker et al., 2018). But given that CNNs can reach near-human performance on some visual tasks and have architectural and representational similarities to the visual system, they are well-positioned for exploring how neural correlates of attention can impact behaviour.

One popular framework to describe attention’s effects on firing rates is the feature similarity gain model (FSGM). This model, introduced by Treue and Martinez-Trujillo, claims that a neuron’s activity is multiplicatively scaled up (or down) according to how much it prefers (or doesn’t prefer) the properties of the attended stimulus (Treue and Martínez Trujillo, 1999; Martinez-Trujillo and Treue, 2004). Attention to a certain visual attribute, such as a specific orientation or color, is generally referred to as feature-based attention (FBA). FBA effects are spatially global: if a task performed at one location in the visual field activates attention to a particular feature, neurons that represent that feature across the visual field will be affected (Zhang and Luck, 2009; Saenz et al., 2002). Overall, this leads to a general shift in the representation of the neural population towards that of the attended stimulus (Çukur et al., 2013; Kaiser et al., 2016; Peelen and Kastner, 2011). Spatial attention implies that a particular portion of the visual field is being attended. According to the FSGM, spatial location is treated as an attribute like any other. Therefore, a neuron’s modulation due to attention can be predicted by how well it’s preferred features and spatial receptive field align with the features or location of the attended stimulus. The effects of combined feature and spatial attention have been found to be additive (Hayden and Gallant, 2009).

A debated issue in the attention literature is where in the visual stream attention effects can be seen. Many studies of attention focus on V4 and MT/MST (Treue, 2001), as these areas have reliable attentional effects. Some studies do find effects at earlier areas (Moro et al., 2010), though they tend to be weaker and occur later in the visual response (Kastner and Pinsk, 2004). Therefore, a leading hypothesis is that attention signals, coming from prefrontal areas (Moore and Armstrong, 2003; Monosov et al., 2011; Bichot et al., 2015; Kornblith and Tsao, 2017), target later visual areas, and the feedback connections that those areas send to earlier ones cause the weaker effects seen there later (Buffalo et al., 2010; Luck et al., 1997).

In this study, we define the FSGM of attention mathematically and implement it in a deep CNN. By applying attention at different layers in the network and for different tasks, we see how neural changes at one area propagate through the network and change performance.

The network used in this study—VGG-16, (Simonyan and Zisserman, 2014)—is shown in Figure 1A and explained in Materials and methods, 'Network Model'. Briefly, at each convolutional layer, the application of a given convolutional filter results in a feature map, which is a 2-D grid of artificial neurons that represent how well the bottom-up input at each location aligns with the filter. Each layer has multiple feature maps. Therefore a 'retinotopic’ layout is built into the structure of the network, and the same visual features are represented across that retinotopy (akin to how cells that prefer a given orientation exist at all locations across the V1 retinotopy). This network was explored in (Güçlü and van Gerven, 2015), where it was shown that early convolutional layers of this CNN are best at predicting activity of voxels in V1, while late convolutional layers are best at predicting activity of voxels in the object-selective lateral occipital area (LO).

Figure 1

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The relationship between tuning and classification

The feature similarity gain model of attention posits that neural activity is modulated by attention in proportion to how strongly a neuron prefers the attended features, as assessed by its tuning. However, the relationship between a neuron’s tuning and its ability to influence downstream readouts remains a difficult one to investigate biologically. We use our hierarchical model to explore this question. We do so by using back propagation to calculate 'gradient values', which we compare to tuning curves (see Materials and methods, 'Object category gradient calculations' and 'Tuning values' for details). Gradient values indicate the ways in which feature map activities should change in order to make the network more likely to classify an image as being of a certain object category. Tuning values represent the degree to which the feature map responds preferentially to images of a given category. If there is a correspondence between tuning and classification, a feature map that prefers a given object category (that is, responds strongly to it) should also have a high positive gradient value for that category. In Figure 2A we show gradient values and tuning curves for three example feature maps. In Figure 2C, we show the average correlation coefficients between tuning values and gradient values for all feature maps at each of the 13 convolutional layers. As can be seen, tuning curves in all layers show higher correlation with gradient values than expected by chance (as assayed by shuffled controls), but this correlation is relatively low, increasing across layers from about .2 to .5. Overall tuning quality also increases with layer depth (Figure 2B), but less strongly.

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Object tuning curves and gradients.

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Even at the highest layers, there can be serious discrepancies between tuning and gradient values. In Figure 2D, we show the gradient values of feature maps at the final four convolutional layers, segregated according to tuning value. In red are gradient values that correspond to tuning values greater than one (for example, category 12 for the feature map in the middle pane of Figure 2A). As these distributions show, strong tuning values can be associated with weak or even negative gradient values. Negative gradient values indicate that increasing the activity of that feature map makes the network less likely to categorize the image as the given category. Therefore, even feature maps that strongly prefer a category (and are only a few layers from the classifier) still may not be involved in its classification, or even be inversely related to it. This is aligned with a recent neural network ablation study that shows category selectivity does not predict impact on classification (Morcos et al., 2018).

Feature-based attention improves performance on challenging object classification tasks

To determine if manipulation according to tuning values can enhance performance, we created challenging visual images composed of multiple objects for the network to classify. These test images are of two types: merged (two object images transparently overlaid, such as in Serences et al., 2004) or array (four object images arranged on a grid) (see Figure 1C examples). The task for the network is to detect the presence of a given object category in these images. It does so using a series of binary classifiers trained on standard images of these objects, which replace the last layer of the network (Figure 1B). The performance of these classifiers on the test images indicates that this is a challenging task for the network (64.4% on merged images and 55.6% on array, Figure 1D. Chance is 50%), and thus a good opportunity to see the effects of attention.

We implement feature-based attention in this network by modulating the activity of units in each feature map according to how strongly the feature map prefers the attended object category (see Materials and methods, 'Tuning values' and 'How attention is applied'). A schematic of this is shown in Figure 3A. The slope of the activation function of units in a given feature map is scaled according to the tuning value of that feature map for the attended category (positive tuning values increase the slope while negative tuning values decrease it). Thus the impact of attention on activity is multiplicative and bi-directional.

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Performance changes with attention.

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The effects of attention are measured when attention is applied in this way at each layer individually (Figure 3B; solid lines) or all layers simultaneously (Figure 3—figure supplement 1A, red). For both image types (merged and array), attention enhances performance and there is a clear increase in performance enhancement as attention is applied at later layers in the network (numbering is as in Figure 1A). In particular, attention applied at the final convolutional layer performs best, leading to an 18.8% percentage point increase in binary classification on the merged images task and 22.8% increase on the array images task. Thus, FSGM-like effects can have large beneficial impacts on performance.

Attention applied at all layers simultaneously does not lead to better performance than attention applied at any individual layer (Figure 3—figure supplement 1A). We also performed a control experiment to ensure that nonspecific scaling of activity does not alone enhance performance (Figure 3—figure supplement 1C).

Some components of the FSGM are debated, for example whether attention impacts responses multiplicatively or additively (Boynton, 2009; Baruni et al., 2015; Luck et al., 1997; McAdams and Maunsell, 1999 ), and whether the activity of cells that do not prefer the attended stimulus is actually suppressed (Bridwell and Srinivasan, 2012; Navalpakkam and Itti, 2007). Comparisons of different variants of the FSGM can be seen in Figure 3—figure supplement 2. In general, multiplicative and bidirectional effects work best.

We also measure performance when attention is applied using gradient values rather than tuning values (these gradient values are calculated to maximize performance on the binary classification task, rather than classify the image as a given category; therefore technically they differ from those shown in Figure 2, however in practice they are strongly correlated. See Materials and methods, 'Object category gradient calculations' and 'Gradient values' for details). Attention applied using gradient values shows the same layer-wise trend as when using tuning values. It also reaches the same performance enhancement peak when attention is applied at the final layers. The major difference, however, comes when attention is applied at middle layers of the network. Here, attention applied according to gradient values outperforms that of tuning values.

Attention strength and the trade-off between increasing true and false positives

In the previous section, we examined the best possible effects of attention by choosing the strength for each layer and category that optimized performance. Here, we look at how performance changes as we vary the overall strength ($\beta$) of attention.

In Figure 4A we break the binary classification performance into true and false positive rates. Here, each colored line indicates a different category and increasing dot size represents increasing strength of attention. Ideally, true positives would increase without an equivalent increase (and possibly with a decrease) in false positive rates. If they increase in tandem, attention does not have a net beneficial effect. Looking at the effects of applying attention at different layers, we can see that attention at lower layers is less effective at moving the performance in this space and that movement is in somewhat random directions, although there is an average increase in performance with moderate attentional strength. With attention applied at later layers, true positive rates are more likely to increase for moderate attentional strengths, while substantial false positive rate increases occur only with higher strengths. Thus, when attention is applied with modest strength at layer 13, most categories see a substantial increase in true positives with only modest increases in false positives. As strength continues to increase however, false positives increase substantially and eventually lead to a net decrease in overall classifier performance (representing as crossing the dotted line in Figure 4A).

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Applying attention according to negated tuning values leads to a decrease in true and false positive values with increasing attention strength, which decreases overall performance (Figure 4—figure supplement 1A). This verifies that the effects of attention are not from non-specific changes in activity.

Experimentally, when switching from no or neutral attention, neurons in MT showed an average increase in activity of 7% when attending their preferred motion direction (and similar decrease when attending the non-preferred) (Martinez-Trujillo and Treue, 2004). In our model, when $\beta =.75$ (roughly the value at which performance peaks at later layers; Figure 4—figure supplement 1B), given the magnitude of the tuning values (average magnitude: .38), attention scales activity by an average of 28.5%. This value refers to how much activity is modulated in comparison to the $\beta =0$ condition, which is probably more comparable to passive or anesthetized viewing, as task engagement has been shown to scale neural responses generally (Page and Duffy, 2008). This complicates the relationship between modulation strength in our model and the values reported in the data.

To allow for a more direct comparison, in Figure 4B, we collected the true and false positive rates obtained experimentally during different object detection tasks (explained in Materials and methods, 'Experimental data'), and plotted them in comparison to the model results when attention is applied at layer 13 using tuning values (pink line) or gradient value (brown line). Five experiments (second through sixth studies) are human studies. In all of these, uncued trials are those in which no information about the upcoming visual stimulus is given, and therefore attention strength is assumed to be low. In cued trials, the to-be-detected category is cued before the presentation of a challenging visual stimulus, allowing attention to be applied to that object or category.

The majority of these experiments show a concurrent increase in both true and false positive rates as attention strength is increased. The rates in the uncued conditions (smaller dots) are generally higher than the rates produced by the $\beta =0$ condition in our model, consistent with neutrally cued conditions corresponding to ${\displaystyle \beta >0}$. We find (see Materials and methods, 'Experimental data'), that the average corresponding $\beta$ value for the neutral conditions is .37 and for the attended conditions .51. Because attention scales activity by $1+\beta f_c^{lk}$ (where $f_c^{lk}$ is the tuning value), these changes correspond to a $\approx$5% change in activity.

The first dataset included in the plot (Ori-Change; yellow line in Figure 4B) comes from a macaque change detection study (see Materials and methods, 'Experimental data' for details). Because the attention cue was only 80% valid, attention strength could be of three levels: low (for the uncued stimuli on cued trials), medium (for both stimuli on neutrally-cued trials), or high (for the cued stimuli on cued trials). Like the other studies, this study shows a concurrent increase in both true positive (correct change detection) and false positive (premature response) rates with increasing attention strength. For the model to achieve the performance changes observed between low and medium attention a roughly 12% activity change is needed, but average V4 firing rates recorded during this task show an increase of only 3.6%. This discrepancy may suggest that changes in correlations (Cohen and Maunsell, 2009) or firing rate changes in areas aside from V4 also make important contributions to observed performance changes.

Thus, according to our model, the size of experimentally observed performance changes is broadly consistent with the size of experimentally observed neural changes. While other factors are likely also relevant for performance changes, this rough alignment between the magnitude of firing rate changes and magnitude of performance changes supports the idea that the former could be a major causal factor for the latter. In addition, the fact that the model can capture this relationship provides further support for its usefulness as a model of the biology.

Finally, we show the change in true and false positive rates when the threshold of the final layer binary classifier is varied (a ‘receiver operating characteristic’ analysis, Figure 4B, gray line; no attention was applied during this analysis). Comparing this to the pink line, it is clear that varying the strength of attention applied at the final convolutional layer has more favorable performance effects than altering the classifier threshold (which corresponds to an additive effect of attention at the classifier layer). This points to the limitations that could come from attention targeting only downstream readout areas.

Overall, the model roughly matches experiments in the amount of neural modulation needed to create the observed changes in true and false positive rates. However, it is clear that the details of the experimental setup are relevant, and changes aside from firing rate and/or outside the ventral stream also likely play a role (Navalpakkam and Itti, 2007).

Feature-based attention enhances performance on orientation detection task

Some of the results presented above, particularly those related to the layer at which attention is applied, may be influenced by the fact that we are using an object categorization task. To see if results are comparable using the simpler stimuli frequently used in macaque studies, we created an orientation detection task (Figure 5A). Here, binary classifiers trained on full-field oriented gratings are tested using images that contain two gratings of different orientation and color. The performance of these binary classifiers without attention is above chance (distribution across orientations shown in inset of Figure 5A). The performance of the binary classifier associated with vertical orientation (0 degrees) was abnormally high (92% correct without attention, other orientations average 60.25%. This likely reflects the over-representation of vertical lines in the training images) and this orientation was excluded from further performance analysis.

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Performance on orientation detection task.

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Performance on spatial and feature-based attention task.

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Attention is applied according to orientation tuning values of the feature maps (tuning quality by layer is shown in Figure 5B) and tested across layers. We find (Figure 5D, solid line and Figure 3—figure supplement 1B, red) that the trend in this task is similar to that of the object task: applying attention at later layers leads to larger performance increases (14.4% percentage point increase at layer 10). This is despite the fact that orientation tuning quality peaks in the middle layers.

We also calculate the gradient values for this orientation detection task. While overall the correlations between gradient values and tuning values are lower (and even negative for early layers), the average correlation still increases with layer (Figure 5C), as with the category detection task. Importantly, while this trend in correlation exists in both detection tasks tested here, it is not a universal feature of the network or an artifact of how these values are calculated. Indeed, an opposite pattern in the correlation between orientation tuning and gradient values is shown when using attention to orientation to classify the color of a stimulus with the attended orientation (see 'Recordings show how feature similarity gain effects propagate', and Materials and methods, 'Oriented grating attention tasks' and 'Gradient values').

The results of applying attention according to gradient values is shown in Figure 5D (dashed line). Here again, using gradient value creates similar trends as using tuning values, with gradient values performing better in the middle layers.

Recordings show how feature similarity gain effects propagate

To explore how attention applied at one location in the network impacts activity later on, we apply attention at various layers and 'record' activity at others (Figure 6A, in response to full field oriented gratings). In particular, we record activity of feature maps at all layers while applying attention at layers 2, 6, 8, 10, or 12 individually.

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Intercepts and slopes from gradient-applied attention.

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Intercepts and slopes from tuning curve-applied attention.

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To understand the activity changes occurring at each layer, we use an analysis from (Martinez-Trujillo and Treue, 2004) that was designed to test for FSGM-like effects and is explained in Figure 6B. Here, the activity of a feature map in response to a given orientation when attention is applied is divided by the activity in response to the same orientation without attention. These ratios are organized according to the feature map’s orientation preference (most to least) and a line is fit to them. According to the FSGM of attention, this ratio should be greater than one for more preferred orientations and less than one for less preferred, creating a line with an intercept greater than one and negative slope.

In Figure 6C, we plot the median value of the slopes and intercepts across all feature maps at a layer, when attention is applied at different layers (indicated by color). When attention is applied directly at a layer according to its tuning values (left), FSGM effects are seen by default (intercept values are plotted in terms of how they differ from one; comparable average values from (Martinez-Trujillo and Treue, 2004) are intercept: .06 and slope: 0.0166, but note we are using $\beta =0$ for the no-attention condition in the model which, as mentioned earlier, is not necessarily the best analogue for no-attention conditions experimentally. Therefore we use these measures to show qualitative effects). As these activity changes propagate through the network, however, the FSGM effects wear off, suggesting that activating units tuned for a stimulus at one layer does not necessarily activate cells tuned for that stimulus at the next. This misalignment between tuning at one layer and the next explains why attention applied at all layers simultaneously isn’t more effective (Figure 3—figure supplement 1). In fact, applying attention to a category at one layer can actually have effects that counteract attention at a later layer (see Figure 6—figure supplement 1).

In Figure 6C (right), we show the same analysis, but while applying attention according to gradient values. The effects at the layer at which attention is applied do not look strongly like FSGM, however FSGM properties evolve as the activity changes propagate through the network, leading to clear FSGM-like effects at the final layer. Finding FSGM-like behaviour in neural data could thus be a result of FSGM effects at that area or non-FSGM effects at an earlier area (here, attention applied according to gradients which, especially at earlier layers, are not aligned with tuning).

An alternative model of the neural effects of attention—the feature matching (FM) model—suggests that the effect of attention is to amplify the activity of a neuron whenever the stimulus in its receptive field matches the attended stimulus. In Figure 6D, we calculate the fraction of feature maps at a given layer that show feature matching behaviour (defined as having activity ratios greater than one when the stimulus orientation matches the attended orientation for both preferred and anti-preferred orientations). As early as one layer post-attention, some feature maps start showing feature matching behaviour. The fact that the attention literature contains conflicting findings regarding the feature similarity gain model versus the feature matching model (Motter, 1994; Ruff and Born, 2015) may result from this finding that FSGM effects can turn into FM effects as they propagate through the network. In particular, this mechanism can explain the observations that feature matching behaviour is observed more in FEF than V4 (Zhou and Desimone, 2011) and that match information is more easily read out from perirhinal cortex than IT (Pagan et al., 2013).

We also investigated the extent to which measures of attention’s neural effects correlate with changes in performance (see Materials and methods, 'Correlating activity changes with performance'). For this we developed a new, experimentally-feasible way of calculating attention’s effects on neural activity that is inspired by the gradient-based approach to attention (that is, it focuses on classification rather than tuning). We show (Figure 6—figure supplement 2) that this new measure better correlates with performance changes than the FSGM measure of activity changes, particularly at earlier layers.

There is a simple experiment that would distinguish whether factors beyond tuning, such as gradients, play a role in guiding attention. It requires using two tasks with very different objectives (which should produce different gradients) but with the same attentional cue. An example is described in Figure 7. Here, the two tasks used would be an orientation-based color classification task (two gratings each with their own color and orientation are simultaneously shown, and the task is to report the color of the grating with the attended orientation) and an orientation detection task (report if the attended orientation is present or absent in the image). In both cases, attention is cued according to orientation. But gradient-based attention will produce different neural modulations for the two tasks, while the FSGM predicts identical modulations (Figure 7C). Thus, an experiment that recorded from the same neurons during both tasks could distinguish between tuning-based and gradient-based attention.

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Orientation tuning curves and gradients.

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In this work, we utilized a deep convolutional neural network (CNN) as a model of the visual system to probe the relationship between modulation of neural activity, as in attention, and performance. Specifically, we formally define the feature similarity gain model (FSGM) of attention (the basic tenets of which have been described in several experimental studies) as a multiplicative modulation of neuronal activity proportional to the neuron’s mean-subtracted feature tuning. This formalization allows us to investigate the FSGM’s ability to enhance a CNN’s performance on challenging visual tasks. We found that, across a variety of tasks, neural activity changes matching the type and magnitude of those observed experimentally can indeed lead to performance changes of the kind and magnitude observed experimentally.

We used the full observability of the model to investigate the relationship between tuning and function. We compared attention applied according to feature tuning (the FSGM) with attention designed to optimally modulate activity to improve performance (as determined by the gradient of performance with respect to the neural activity). Attention applied according to tuning does not successfully propagate from lower or middle to higher layers; that is, enhancing the activity of neurons that most prefer a given category at lower layers need not selectively enhance the activity of neurons preferring that category at higher layers. As a result, attention applied according to the FSGM performs poorly when applied at early to middle layers, while attention applied according to gradients at these layers performs better.

Attention is most effective applied at later layers (e.g., layers 9–13), where tuning and gradient values are better correlated. According to (Güçlü and van Gerven, 2015), these layers correspond most to areas V4 and LO. Such areas are known and studied for reliably showing attentional effects, whereas earlier areas such as V1 are generally not (Luck et al., 1997; Abdelhack and Kamitani, 2018). In a study involving detection of objects in natural scenes, the strength of category-specific preparatory activity in object selective cortex was correlated with performance, whereas such preparatory activity in V1 was anti-correlated with performance (Peelen and Kastner, 2011). This is in line with our finding that feature-based attention effects at earlier areas can counter the beneficial effects of that attention at later areas (Figure 6—figure supplement 1).

Our work raises the question: is attention applied simply according to tuning or is it targeted to best optimize function on a given task? We suggested a simple experiment (Figure 7) that would reveal whether non-tuning factors, such as gradients, guide attentional modulation. In (Chelazzi et al., 1998) the correlation coefficient between an index of tuning and an index of attentional modulation was .52 for a population of V4 neurons, suggesting factors other than selectivity influence attention. Furthermore, many attention studies, including that one, use only preferred and anti-preferred stimuli and therefore don’t include a thorough investigation of the relationship between tuning and attentional modulation. (Martinez-Trujillo and Treue, 2004) uses multiple stimuli to provide support for the FSGM, however the interpretation is limited by the fact that they only report population averages. (Ruff and Born, 2015) investigated the relationship between tuning strength and the strength of attentional modulation on a cell-by-cell basis. While they did find a correlation (particularly for binocular disparity tuning), it was relatively weak, which leaves room for the possibility that tuning is not the primary factor that determines attentional modulation. Local connectivity is also likely to play a role, as a correlation between normalization and attentional modulation has been shown (Ni et al., 2012).

A major challenge for understanding the biological implementation of selective attention is determining how such a precise attentional signal is carried by feedback connections. We believe that it is plausible that the visual system can learn the connections needed to carry out gradient-based attention. For example, if a high-level neuron related to the classification of an image sends a feedback connection to lower areas, an anti-Hebbian post-pre spike timing-dependent learning rule would strengthen the connection from the high level neuron to the low level one, if the lower level one causes the firing of the higher. In this way, neurons in later areas can learn to target the cells in earlier areas that caused them to fire. In contrast, it is actually more difficult to imagine how higher areas could learn the connections needed to target neurons according to their tuning, as in the FSGM. The machine learning literature on attention and learning may inspire other useful hypotheses on underlying brain mechanisms (Xu et al., 2015; Lillicrap et al., 2016).

The concept of attention has been introduced in these models previously in the machine learning literature (Mnih et al., 2014). Generally, this kind of attention relates to what would be called overt spatial attention in the neuroscience literature. That is, the attention mechanism serially selects areas of the input image for further processing, rather than modulating the activity of neurons representing those areas (as in our model of spatial attention). Other work has been done using attention to selectively process image features (Stollenga et al., 2014) and it would be interesting to compare the workings of that model to the feature-based attention used in our study.

While CNNs have representations that are similar to the ventral stream, they lack many biological details including recurrent connections, dynamics, cell types, and noisy responses. Preliminary work has shown that these elements can be incorporated into a CNN structure, and attention can enhance performance in this more biologically-realistic architecture (Lindsay et al., 2017). Furthermore, while the current work does not include neural noise independent of the stimulus, the fact that a given image is presented in many contexts (different merged images or different array images) can be thought of as a form of highly structured noise that does produce variable responses to the same image.

Another biological detail that this model lacks is 'skip connections,’ where one layer feeds into both the layer directly after it and deeper layers after that (He et al., 2016; Huang et al., 2017) as in connections from V2 to V4 or V4 to parietal areas (Ungerleider et al., 2008). Our results regarding propagation of changes through the network suggest that synaptic distance from the classifier is a relevant feature—one that is less straight forward to determine in a network with skip connections.

Because experimenters can easily control the image, defining a cell’s function in terms of how it responds to stimuli makes practical sense. However, it may be that thinking about visual areas in terms of their synaptic distance from decision-making areas such as prefrontal cortex (Heekeren et al., 2004) can be more useful for the study of attention than thinking in terms of their distance from the retina. Thus far, coarse stimulation protocols have found a relationship between the tuning of neural populations and their impact on perception (Moeller et al., 2017; DeAngelis et al., 1998; Salzman et al., 1990). However, studies of the relationship between tuning and choice probabilities suggest that a neuron’s preferred stimulus is not always an indication of its causal role in classification (Zaidel et al., 2017; Purushothaman and Bradley, 2005), though see (Katz et al., 2016). Targeted stimulation protocols and a more fine-grained ability to determine both upstream drivers of, and downstream responses driven by, stimulated neurons will be needed to better address these issues.

The weights for the model used are linked to in the study. The data resulting from simulations have been packaged and are available on Dryad (doi:10.5061/dryad.jc14081). The analysis code are available on GitHub (https://github.com/gwl2108/CNN_attention; copy archived at https://github.com/elifesciences-publications/CNN_attention).

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Author details

1. Grace W Lindsay

   1. Center for Theoretical Neuroscience, College of Physicians and Surgeons, Columbia University, New York, United States
   2. Mortimer B. Zuckerman Mind Brain Behaviour Institute, Columbia University, New York, United States

   Contribution

   Conceptualization, Funding acquisition, Investigation, Visualization, Methodology, Writing—original draft

   For correspondence

   gracewlindsay@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9904-7471

2. Kenneth D Miller

   1. Center for Theoretical Neuroscience, College of Physicians and Surgeons, Columbia University, New York, United States
   2. Mortimer B. Zuckerman Mind Brain Behaviour Institute, Columbia University, New York, United States
   3. Swartz Program in Theoretical Neuroscience, Kavli Institute for Brain Science, New York, United States
   4. Department of Neuroscience, Columbia University, New York, United States

   Contribution

   Supervision, Funding acquisition, Methodology, Writing—review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-1433-0647

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