Title: PAYING MORE ATTENTION TO ATTENTION: IMPROVING THE PERFORMANCE OF CONVOLUTIONAL NEURAL NETWORKS VIA ATTENTION TRANSFER

Abstract: Attention plays a critical role in human visual experience. Furthermore, it has recently been demonstrated that attention can also play an important role in the context of applying artificial neural networks to a variety of tasks from fields such as computer vision and NLP. In this work we show that, by properly defining attention for convolutional neural networks, we can actually use this type of information in order to significantly improve the performance of a student CNN network by forcing it to mimic the attention maps of a powerful teacher network.
To that end, we propose several novel methods of transferring attention, showing consistent improvement across a variety of datasets and convolutional neural network architectures. Code and models for our experiments are available at https://github.com/szagoruyko/attention-transfer.

1. INTRODUCTION:

As humans, we need to pay attention in order to be able to adequately perceive our surroundings. Attention is therefore a key aspect of our visual experience, and closely relates to perception -we need to keep attention to build a visual representation, possessing detail and coherence.

As artificial neural networks became more popular in fields such as computer vision and natural language processing in the recent years, artificial attention mechanisms started to be developed as well. Artificial attention lets a system "attend" to an object to examine it with greater detail. It has also become a research tool for understanding mechanisms behind neural networks, similar to attention used in psychology.

One of the popular hypothesis there is that there are non-attentional and attentional perception processes. Non-attentional processes help to observe a scene in general and gather high-level information, which, when associated with other thinking processes, helps us to control the attention processes and navigate to a certain part of the scene. This implies that different observers with different knowledge, different goals, and therefore different attentional strategies can literally see the same scene differently. This brings us to the main topic of this paper: how attention differs within artificial vision systems, and can we use attention information in order to improve the performance of convolutional neural networks ? More specifically, can a teacher network improve the performance of another student network by providing to it information about where it looks, i.e., about where it concentrates its attention into ?

To study these questions, one first needs to properly specify how attention is defined w.r.t. a given convolutional neural network. To that end, here we consider attention as a set of spatial maps that essentially try to encode on which spatial areas of the input the network focuses most for taking its output decision (e.g., for classifying an image), where, furthermore, these maps can be defined w.r.t. various layers of the network so that they are able to capture both low-, mid-, and high-level representation information. More specifically, in this work we define two types of spatial attention maps: activation-based and gradient-based. We explore how both of these attention maps change over various datasets and architectures, and show that these actually contain valuable information that can be used for significantly improving the performance of convolutional neural network architectures (of various types and trained for various different tasks). To that end, we propose several novel ways of transferring attention from a powerful teacher network to a smaller student network with the goal of improving the performance of the latter (Fig. 1 ).

To summarize, the contributions of this work are as follows:

• We propose attention as a mechanism of transferring knowledge from one network to another

• We propose the use of both activation-based and gradient-based spatial attention maps

• We show experimentally that our approach provides significant improvements across a variety of datasets and deep network architectures, including both residual and non-residual networks

• We show that activation-based attention transfer gives better improvements than fullactivation transfer, and can be combined with knowledge distillation

The rest of the paper is structured as follows: we first describe related work in section 2, we explain our approach for activation-based and gradient-based attention transfer in section 3, and then present experimental results for both methods in section 4. We conclude the paper in section 5.

2. RELATED WORK:

Early work on attention based tracking Larochelle & Hinton (2010) , Denil et al. (2012) was motivated by human attention mechanism theories Rensink (2000) and was done via Restricted Bolzmann Machines. It was recently adapted for neural machine translation with recurrent neural networks, e.g. Bahdanau et al. (2014) as well as in several other NLP-related tasks. It was also exploited in computer-vision-related tasks such as image captioning Xu et al. (2015) , visual question answering Yang et al. (2015) , as well as in weakly-supervised object localization Oquab et al. (2015) and classification Mnih et al. (2014) , to mention a few characteristic examples. In all these tasks attention proved to be useful. Due to the above fact and due to that thin deep networks are less parallelizable than wider ones, we think that knowledge transfer needs to be revisited, and take an opposite to FitNets approachwe try to learn less deep student networks. Our attention maps used for transfer are similar to both gradient-based and activation-based maps mentioned above, which play a role similar to "hints" in FitNets, although we don't introduce new weights.

3. ATTENTION TRANSFER:

In this section we explain the two methods that we use for defining the spatial attention maps of a convolutional neural network as well as how we transfer attention information from a teacher to a student network in each case.

3.1. ACTIVATION-BASED ATTENTION TRANSFER:

Let us consider a CNN layer and its corresponding activation tensor A ∈ R C×H×W , which consists of C feature planes with spatial dimensions H × W . An activation-based mapping function F (w.r.t. that layer) takes as input the above 3D tensor A and outputs a spatial attention map, i.e., a flattened 2D tensor defined over the spatial dimensions, or

EQUATION

To define such a spatial attention mapping function, the implicit assumption that we make in this section is that the absolute value of a hidden neuron activation (that results when the network is evaluated on given input) can be used as an indication about the importance of that neuron w.r.t. the specific input. By considering, therefore, the absolute values of the elements of tensor A, we can construct a spatial attention map by computing statistics of these values across the channel dimension (see Fig. 3 ). More specifically, in this work we will consider the following activation-based spatial attention maps:

• sum of absolute values:

F sum (A) = C i=1 |A i | • sum of

absolute values raised to the power of p (where p > 1):

F p sum (A) = C i=1 |A i | p • max of

absolute values raised to the power of p (where p > 1):

F p max (A) = max i=1,C |A i | p

where A i = A(i, :, :) (using Matlab notation), and max, power and absolute value operations are elementwise (e.g. |A i | p is equivalent to abs(A i ). ∧ p in Matlab notation). We visualized activations of various networks on several datasets, including ImageNet classification and localization, COCO object detection, face recognition, and fine-grained recognition. We were mostly focused on modern architectures without top dense linear layers, such as Network-In-Network, ResNet and Inception, which have streamlined convolutional structure. We also examined networks of the same architecture, width and depth, but trained with different frameworks with significant difference in performance. We found that the above statistics of hidden activations not only have spatial correlation with predicted objects on image level, but these correlations also tend to be higher in networks with higher accuracy, and stronger networks have peaks in attention where weak networks don't (e.g., see Fig. 4 ). Furthermore, attention maps focus on different parts for different layers in the network. In the first layers neurons activation level is high for low-level gradient points, in the middle it is higher for the most discriminative regions such as eyes or wheels, and in the top layers it reflects full objects. For example, mid-level attention maps of a network trained for face recognition Parkhi et al. (2015) will have higher activations around eyes, nose and lips, and top level activation will correspond to full face (Fig. 2 ).

Concerning the different attention mapping functions defined above, these can have slightly different properties. E.g.:

• Compared to F sum (A), the spatial map F p sum (A) (where p > 1) puts more weight to spatial locations that correspond to the neurons with the highest activations, i.e., puts more weight to the most discriminative parts (the larger the p the more focus is placed on those parts with highest activations).

• Furthermore, among all neuron activations corresponding to the same spatial location, F p max (A) will consider only one of them to assign a weight to that spatial location (as opposed to F p sum (A) that will favor spatial locations that carry multiple neurons with high activations). To further illustrate the differences of these functions we visualized attention maps of 3 networks with sufficient difference in classification performance: Network-In-Network (62% top-1 val accuracy), ResNet-34 (73% top-1 val accuracy) and ResNet-101 (77.3% top-1 val accuracy).

In each network we took last pre-downsampling activation maps, on the left for mid-level and on the right for top pre-average pooling activations in fig. 4 . Top-level maps are blurry because their original spatial resolution is 7 × 7. It is clear that most discriminative regions have higher activation levels, e.g. face of the wolf, and that shape details disappear as the parameter p (used as exponent) increases.

In attention transfer, given the spatial attention maps of a teacher network (computed using any of the above attention mapping functions), the goal is to train a student network that will not only make correct predictions but will also have attentions maps that are similar to those of the teacher. In general, one can place transfer losses w.r.t. attention maps computed across several layers. For instance, in the case of ResNet architectures, one can consider the following two cases, depending on the depth of teacher and student:

• Same depth: possible to have attention transfer layer after every residual block • Different depth: have attention transfer on output activations of each group of residual blocks Similar cases apply also to other architectures (such as NIN, in which case a group refers to a block of a 3 × 3, 1 × 1, 1 × 1 convolutions). In fig. 5 we provide a schematic illustration of the different depth case for residual network architectures.

Without loss of generality, we assume that transfer losses are placed between student and teacher attention maps of same spatial resolution, but, if needed, attention maps can be interpolated to match their shapes. Let S, T and W S , W T denote student, teacher and their weights correspondingly, and let L(W, x) denote a standard cross entropy loss. Let also I denote the indices of all teacher-student activation layer pairs for which we want to transfer attention maps. Then we can define the following total loss:

EQUATION

where Q j S = vec(F (A j S )) and Q j T = vec(F (A j T )) are respectively the j-th pair of student and teacher attention maps in vectorized form, and p refers to norm type (in the experiments we use p = 2). As can be seen, during attention transfer we make use of l 2 -normalized attention maps, i.e., we replace each vectorized attention map Q with Q Q 2 (l 1 normalization could be used as well). It is worth emphasizing that normalization of attention maps is important for the success of the student training.

Attention transfer can also be combined with knowledge distillation Hinton et al. (2015) , in which case an additional term (corresponding to the cross entropy between softened distributions over labels of teacher and student) simply needs to be included to the above loss. When combined, attention transfer adds very little computational cost, as attention maps for teacher can be easily computed during forward propagation, needed for distillation.

3.2. GRADIENT-BASED ATTENTION TRANSFER:

In this case we define attention as gradient w.r.t. input, which can be viewed as an input sensitivity map Simonyan et al. (2014) , i.e., attention at an input spatial location encodes how sensitive the output prediction is w.r.t. changes at that input location (e.g., if small changes at a pixel can have a large effect on the network output then it is logical to assume that the network is "paying attention" to that pixel). Let's define the gradient of the loss w.r.t input for teacher and student as:

EQUATION

Then if we want student gradient attention to be similar to teacher attention, we can minimize a distance between them (here we use l 2 distance but other distances can be employed as well):

EQUATION

As W T and x are given, to get the needed derivative w.r.t. W S :

EQUATION

So to do an update we first need to do forward and back propagation to get J S and J T , compute the second error β 2 ||J S -J T || 2 and propagate it second time. The second propagation is similar to forward propagation in this case, and involves second order mixed partial derivative calculation ∂ 2 ∂W S ∂x . The above computation is similar to the double backpropagation technique developed by Drucker & LeCun (1992) (where the l 2 norm of the gradient w.r.t. input is used as regularizer). Furthermore, it can be implemented efficiently in a framework with automatic differentiation support, even for modern architectures with sophisticated graphs. The second backpropagation has approximately the same cost with first backpropagation, excluding forward propagation.

We also propose to enforce horizontal flip invariance on gradient attention maps. To do that we propagate horizontally flipped images as well as originals, backpropagate and flip gradient attention maps back. We then add l 2 losses on the obtained attentions and outputs, and do second backpropagation:

EQUATION

where flip(x) denotes the flip operator. This is similar to Group Equivariant CNN approach by Cohen & Welling (2016), however it is not a hard constraint. We experimentally find that this has a regularization effect on training.

We should note that in this work we consider only gradients w.r.t. the input layer, but in general one might have the proposed attention transfer and symmetry constraints w.r.t. higher layers of the network.

4. EXPERIMENTAL SECTION:

In the following section we explore attention transfer on various image classification datasets. We 2016)), as they are most performant and set strong baselines in terms of number of parameters compared to AlexNet or VGG, and have been explored in various papers across small and large datasets. On Scenes, CUB and ImageNet we experimented with ResNet-18 and ResNet-34. As for gradient-based attention, we constrained ourselves to Network-In-Network without batch normalization and CIFAR dataset, due to the need of complex automatic differentiation.

4.1. CIFAR EXPERIMENTS:

We start with CIFAR dataset which has small 32 × 32 images, and after downsampling top activations have even smaller resolution, so there is not much space for attention transfer. Interestingly, even under this adversarial setting, we find that attention transfer seems to give reasonable benefits, offering in all cases consistent improvements. We use horizontal flips and random crops data augmentations, and all networks have batch normalization. We find that ZCA whitening has negative effect on validation accuracy, and omit it in favor of simpler meanstd normalization. We raise Knowledge Distillation (KD) temperature for ResNet transfers to 4, and use α = 0.9 (see Hinton et al. (2015) for an explanation of these parameters).

Results of attention transfer (using F 2 sum attention maps) for various networks on CIFAR-10 can be found in table 1. We experimented with teacher/student having the same depth (WRN-16-2/WRN-16-1), as well as different depth (WRN-40-1/WRN-16-1, WRN-40-2/WRN-16-2). In all combinations, attention transfer (AT) shows significant improvements, which are also higher when it is combined with knowledge distillation (AT+KD). To verify if having at least one activation-based attention transfer loss per group in WRN transfer is important, we trained three networks with only one transfer loss per network in group1, group2 and group3 separately, and compared to a network trained with all three losses. The corresponding results were 8.11, 7.96, 7.97 (for the separate losses) and 7.93 for the combined loss (using WRN-16-2/WRN-16-1 as teacher/student pair). Each loss provides some additional degree of attention transfer.

We also explore which attention mapping functions tend to work best using WRN-16-1 and WRN-16-2 as student and teacher networks respectively (table 2 ). Interestingly, sum-based functions work very similar, and better than max-based ones. From now on, we will use sum of squared attention mapping function F 2 sum for simplicity. As for parameter β in eq. 2, it usually varies about 0.1, as we set it to 10 3 divided by number of elements in attention map and batch size for each layer. In case of combinining AT with KD we decay it during traning in order to simplify learning harder examples.

4.1.2. ACTIVATION-BASED AT VS. TRANSFERRING FULL ACTIVATION:

To check if transferring information from full activation tensors is more beneficial than from attention maps, we experimented with FitNets-style hints using l 2 losses on full activations directly, with 1 × 1 convolutional layers to match tensor shapes, and found that improvements over baseline student were minimal (see column F-ActT in table 1). For networks of the same width different depth we tried to regress directly to activations, without 1 × 1 convolutions. We also use l 2 normalization before transfer losses, and decay β in eq. 2 during training as these give better performance. We find that AT, as well as full-activation transfer, greatly speeds up convergence, but AT gives much better final accuracy improvement than full-activation transfer (see fig. 7 (b), Appendix). It seems quite interesting that attention maps carry information that is more important for transfer than full activations. Table 3 : Performance of various gradient-based attention methods on CIFAR-10. Baseline is a thin NIN network with 0.2M parameters (trained only on horizontally flipped augmented data and without batch normalization), min-l 2 refers to using l 2 norm of gradient w.r.t. input as regularizer, symmetry norm -to using flip invariance on gradient attention maps (see eq. 6), AT -to attention transfer, and KD -to Knowledge Distillation (both AT and KD use a wide NIN of 1M parameters as teacher).

For simplicity we use thin Network-In-Network model in these experiments, and don't apply random crop data augmentation with batch normalization, just horizontal flips augmentation. We also only use deterministic algorithms and sampling with fixed seed, so reported numbers are for single run experiments. We find that in this setting network struggles to fit into training data already, and turn off weight decay even for baseline experiments. In future we plan to explore gradient-based attention for teacher-student pairs that make use of batch normalization, because it is so far unclear how batch normalization should behave in the second backpropagation step required during gradientbased attention transfer (e.g., should it contribute to batch normalization parameters, or is a separate forward propagation with fixed parameters needed).

We explored the following methods:

• Minimizing l 2 norm of gradient w.r.t. input, i.e. the double backpropagation method Drucker & LeCun (1992) ;

• Symmetry norm on gradient attention maps (see eq. 6);

• Student-teacher gradient-based attention transfer;

• Student-teacher activation-based attention transfer.

Results for various methods are shown in table 3 . Interestingly, just minimizing l 2 norm of gradient already works pretty well. Also, symmetry norm is one the best performing attention norms, which we plan to investigate in future on other datasets as well. We also observe that, similar to activationbased attention transfer, using gradient-based attention transfer leads to improved performance. We also trained a network with activation-based AT in the same training conditions, which resulted in the best performance among all methods. We should note that the architecture of student NIN without batch normalization is slightly different from teacher network, it doesn't have ReLU activations before pooling layers, which leads to better performance without batch normalization, and worse with. So to achieve the best performance with activation-based AT we had to train a new teacher, with batch normalization and without ReLU activations before pooling layers, and have AT losses on outputs of convolutional layers.

4.2. LARGE INPUT IMAGE NETWORKS:

In this section we experiment with hidden activation attention transfer on ImageNet networks which have 224 × 224 input image size. Presumably, attention matters more in this kind of networks as spatial resolution of attention maps is higher. In both cases attention transfer provides significant improvements, closing the gap between ResNet-18 and ResNet-34 in accuracy. On Scenes AT works as well as KD, and on CUB AT works much better, which we speculate is due to importance of intermediate attention for fine-grained recognition. Moreover, after finetuning, student's attention maps indeed look more similar to teacher's (Fig. 6 , Appendix).

4.2.2. IMAGENET:

To showcase activation-based attention transfer on ImageNet we took ResNet-18 as a student, and ResNet-34 as a teacher, and tried to improve ResNet-18 accuracy. We added only two losses in the 2 last groups of residual blocks and used squared sum attention F 2 sum . We also did not have time to tune any hyperparameters and kept them from finetuning experiments. Nevertheless, ResNet-18 with attention transfer achieved 1.1% top-1 and 0.8% top-5 better validation accuracy (Table . 5 and Fig. 7 (a), Appendix), we plan to update the paper with losses on all 4 groups of residual blocks.

We were not able to achieve positive results with KD on ImageNet. With ResNet-18-ResNet-34 student-teacher pair it actually hurts convergence with the same hyperparameters as on CIFAR. As it was reported that KD struggles to work if teacher and student have different architecture/depth (we observe the same on CIFAR), so we tried using the same architecture and depth for attention transfer. On CIFAR both AT and KD work well in this case and improve convergence and final accuracy, on ImageNet though KD converges significantly slower (we did not train until the end due to lack of computational resources). We also could not find applications of FitNets, KD or similar methods on ImageNet in the literature. Given that, we can assume that proposed activation-based AT is the first knowledge transfer method to be successfully applied on ImageNet.

5. CONCLUSIONS:

We presented several ways of transferring attention from one network to another, with experimental results over several image recognition datasets. It would be interesting to see how attention transfer works in cases where spatial information is more important, e.g. object detection or weaklysupervised localization, which is something that we plan to explore in the future.

Overall, we think that our interesting findings will help further advance knowledge distillation, and understanding convolutional neural networks in general. 

:



Figures and Tables:

Figure1: (a) An input image and a corresponding spatial attention map of a convolutional network that shows where the network focuses in order to classify the given image. Surely, this type of map must contain valuable information about the network. The question that we pose in this paper is the following: can we use knowledge of this type to improve the training of CNN models ? (b) Schematic representation of attention transfer: a student CNN is trained so as, not only to make good predictions, but to also have similar spatial attention maps to those of an already trained teacher CNN.

Figure 2: Sum of absolute values attention maps F sum over different levels of a network trained for face recognition. Mid-level attention maps have higher activation level around eyes, nose and lips, high-level activations correspond to the whole face.

Figure 3: Attention mapping over feature dimension.

Figure 4: Activation attention maps for various ImageNet networks: Network-In-Network (62% top-1 val accuracy), ResNet-34 (73% top-1 val accuracy), ResNet-101 (77.3% top-1 val accuracy). Left part: mid-level activations, right part: top-level pre-softmax acivations group1 group2 group3

split the section in two parts, in the first we include activation-based attention transfer and gradientbased attention transfer experiments on CIFAR, and in the second activation-based attention trans-fer experiments on larger datasets. For activation-based attention transfer we used Network-In-Network Lin et al. (2013) and ResNet-based architectures (including the recently introduced Wide Residual Networks (WRN) Zagoruyko & Komodakis (

Figure 6: Top activation attention maps for different Scenes networks: original pretrained ResNet-18 (ResNet-18-ImageNet), ResNet-18 trained on Scenes (ResNet-18-scenes), ResNet-18 trained with attention transfer (ResNet-18-scenes-AT) with ResNet-34 as a teacher, ResNet-34 trained on Scenes (ResNet-34-scenes). Predicted classes for each task are shown on top. Attention maps look more similar after transfer (images taken from test set).

Attention transfer on ImageNet between ResNet-18 and ResNet-34. Solid lines represent top-5 validation error, dashed -top-5 training error. Two attention transfer losses were used on the outputs of two last groups of residual blocks respectively, no KD losses used. Activation attention transfer on CIFAR-10 from WRN-16-2 to WRN-16-1. Test error is in bold, train error is in dashed lines. Attention transfer greatly speeds up convergence and improves final accuracy.

Figure 7



Table content: <table><tr><td>student</td><td>teacher</td><td>student</td><td>AT</td><td colspan="4">F-ActT KD AT+KD teacher</td></tr><tr><td>NIN-thin, 0.2M</td><td>NIN-wide, 1M</td><td>9.38</td><td>8.93</td><td>9.05</td><td>8.55</td><td>8.33</td><td>7.28</td></tr><tr><td colspan="2">WRN-16-1, 0.2M WRN-16-2, 0.7M</td><td>8.77</td><td>7.93</td><td>8.51</td><td>7.41</td><td>7.51</td><td>6.31</td></tr><tr><td colspan="2">WRN-16-1, 0.2M WRN-40-1, 0.6M</td><td>8.77</td><td>8.25</td><td>8.62</td><td>8.39</td><td>8.01</td><td>6.58</td></tr><tr><td colspan="2">WRN-16-2, 0.7M WRN-40-2, 2.2M</td><td>6.31</td><td>5.85</td><td>6.24</td><td>6.08</td><td>5.71</td><td>5.23</td></tr></table>

Finetuning with attention transfer error on Scenes and CUB datasets 4.2.1 TRANSFER LEARNING To see how attention transfer works in finetuning we choose two datasets: Caltech-UCSD Birds-200-2011 fine-grained classification (CUB) byWah et al. (2011), and MIT indoor scene classification (Scenes) byQuattoni & Torralba (2009), both containing around 5K images training images. We took ResNet-18 and ResNet-34 pretrained on ImageNet and finetuned on both datasets. On CUB we crop bounding boxes, rescale to 256 in one dimension and then take a random crop. Batch normalization layers are fixed for finetuning, and first group of residual blocks is frozen. We then took finetuned ResNet-34 networks and used them as teachers for ResNet-18 pretrained on ImageNet, with F 2 sum attention losses on 2 last groups.

Table content: <table><tr><td>type</td><td>model</td><td colspan="2">ImageNet→CUB ImageNet→Scenes</td></tr><tr><td colspan="2">student ResNet-18</td><td>28.5</td><td>28.2</td></tr><tr><td>KD</td><td>ResNet-18</td><td>27 (-1.5)</td><td>28.1 (-0.1)</td></tr><tr><td>AT</td><td>ResNet-18</td><td>27 (-1.5)</td><td>27.1 (-1.1)</td></tr><tr><td colspan="2">teacher ResNet-34</td><td>26.5</td><td>26</td></tr></table>

Attention transfer validation error (single crop) on ImageNet. Transfer losses are added on epoch 60/100.A.2 IMPLEMENTATION DETAILSThe experiments were conducted in Torch machine learning framework. Double propagation can be implemented in a modern framework with automatic differentiation support, e.g. Torch, Theano, Tensorflow. For ImageNet experiments we used fb.resnet.torch code, and used 2 Titan X cards with data parallelizm in both teacher and student to speed up training. Code and models for our experiments are available at https://github.com/szagoruyko/attention-transfer.

Table content: <table/>

Peer review (iclr2017):
The paper presented a modified knowledge distillation framework that minimizes the difference of the sum of statistics across the a feature map between the teacher and the student network. The authors empirically demonstrated the proposed methods outperform the fitnet style distillation baseline. Pros: + The author evaluated the proposed methods on various computer vision dataset + The paper is in general well-written Cons: - The method seems to be limited to the convolutional architecture - The attention terminology is misleading in the paper. The proposed method really just try to distill the summed squared(or other statistics e.g. summed lp norm) of activations in a hidden feature map. - The gradient-based attention transfer seems out-of-place. The proposed gradient-based methods are never compared directly to nor are used jointly with the *attention-based* transfer. It seems like a parallel idea added to the paper that does not seem to add much value. - It is also not clear how the induced 2-norms in eq.(2) is computed. Q is a matrix in mathbb{R}^{H 	imes W} whose induced 2-norm is its largest singular value. It seems computationally expensive to compute such cost function. Is it possible the authors really mean the Frobenius norm? Overall, the proposed distillation method works well in practice but the paper has some organization issues and unclear notation.