Title: EXCITATION DROPOUT: ENCOURAGING PLASTICITY IN DEEP NEURAL NETWORKS

Abstract: We propose a guided dropout regularizer for deep networks based on the evidence of a network prediction: the firing of neurons in specific paths. In this work, we utilize the evidence at each neuron to determine the probability of dropout, rather than dropping out neurons uniformly at random as in standard dropout. In essence, we dropout with higher probability those neurons which contribute more to decision making at training time. This approach penalizes high saliency neurons that are most relevant for model prediction, i.e. those having stronger evidence. By dropping such high-saliency neurons, the network is forced to learn alternative paths in order to maintain loss minimization, resulting in a plasticity-like behavior, a characteristic of human brains too. We demonstrate better generalization ability, an increased utilization of network neurons, and a higher resilience to network compression using several metrics over four image/video recognition benchmarks.

1. INTRODUCTION:

Dropout [Hinton et al. (2012) ; Srivastava et al. (2014) ] is a classical regularization technique that is used in many state-of-the-art deep neural networks, typically applied to fully-connected layers. Standard Dropout selects a fraction of neurons to randomly drop out by zeroing their forward signal. In this work, we propose a scheme for biasing this selection. Our scheme utilizes the contribution of neurons to the prediction made by the network at a certain training iteration stage.

Dropout can be interpreted as model averaging technique that avoids overfitting on training data, allowing for better generalization on unseen test data. A recent variant of dropout that targets improved generalization ability is Curriculum Dropout [Morerio et al. (2017) ]. It targets adjusting the dropout rate by exponentially increasing the unit suppression rate during training, answering the question How many neurons to drop out over time? Like Standard Dropout [Hinton et al. (2012) ; Srivastava et al. (2014) ], Curriculum Dropout selects the neurons to be dropped randomly. In this work, however, we target at determining how the dropped neurons are selected, answering the question Which neurons to drop out?

Our approach is inspired by brain plasticity [Hebb (2005) ; Song et al. (2000) ; Mittal et al. (2018) ; Miconi et al. (2018) ]. We deliberately, and temporarily, paralyze/injure neurons to enforce learning alternative paths in a deep network. At training time, neurons that are more relevant to the current prediction are given a higher dropout probability. The relevance of a neuron for making a certain prediction is quantified using Excitation Backprop, a top-down saliency approach proposed by Zhang et al. (2016) . Excitation Backprop conveniently yields a probability distribution at each layer that reflects neuron saliency, or neuron contribution to the prediction being made. This is utilized in the pipeline of our approach, named Excitation Dropout, which is summarized in Fig. 1 .

In particular, we study how this approach improves generalization through utilizing more network's neurons for image classification. We report an increased recognition rate for both CNN models that are fine-tuned and trained from scratch. This improvement is validated on four image/video recognition datasets, and ranges from 1.1% -6.3% over state-of-the-art Curriculum Dropout.

Next, we examine the effect of our approach on network utilization. Mittal et al. (2018) and Ma et al. (2017) introduce metrics that measure network utilization. We show a consistent increased network utilization using Excitation Dropout on four image/video recognition datasets. For example, Step 2: Backward EB is performed until the specified dropout layer; this gives a neuron saliency map at the dropout layer in the form of a probability distribution.

Step 3: The probability distribution is used to generate a binary mask for each image of the batch based on a Bernoulli distribution determining whether each neuron will be dropped out or not. Step 4: A forward pass is performed from the specified dropout layer to the end of the network, zeroing the activations of the dropped out neurons.

Step 5: The standard backward pass is performed to update model weights.

averaged over all four benchmarks, we get 76.55% reduction in conservative filters, filters whose parameters do not change significantly during training, as compared to Standard Dropout.

Finally, we study network resilience to neuron dropping at test time. We observe that training with Excitation Dropout leads to models that are a lot more robust when layers are shrunk/compressed by removing units. We demonstrate this when dropping the most relevant neurons, the least relevant neurons, and with a random dropping selection. This can be quite desirable for compressing/distilling [Hinton et al. (2015) ] a model, e.g. for deployment on mobile devices.

In summary, by encouraging plasticity-like behavior, our contributions are threefold:

1. Better generalization on test data. 2. Higher utilization of network neurons. 3. Resilience to network compression.

2. RELATED WORK:

Dropout was first introduced by Hinton et al. (2012) and Srivastava et al. (2014) as a way to prevent neural units from co-adapting too much on the training data by randomly omitting subsets of neurons at each iteration of the training phase. Some follow-up works have explored different schemes for determining how much dropout is applied to neurons/weights. Wager et al. (2013) described the dropout mechanism in terms of an adaptive regularization, establishing a connection to the AdaGrad algorithm. Inspired by information theoretic principles, Achille & Soatto (2018) propose Information Dropout, a generalization dropout which can be automatically adapted to the data. Kingma et al. (2015) showed that a relationship between dropout and Bayesian inference can be extended when the dropout rates are directly learned from the data. Kang et al. (2017) introduces Shakeout which instead of randomly discarding units as dropout does, it randomly enhances or reverses each units contribution to the next layer. Wan et al. (2013) introduced the DropConnect framework, adding dynamic sparsity on the weights of a deep model. DropConnect generalized Standard Dropout by randomly dropping the weights rather than the neuron activations in the network. Rennie et al. (2014) proposed a time scheduling for the retaining probability for the neurons in the network. The presented adaptive regularization scheme smoothly decreased in time the number of neurons turned off during training.

Recently, Morerio et al. (2017) proposed Curriculum Dropout to adjust the dropout rate in the opposite direction, exponentially increasing unit suppression rate during training, leading to a better generalization on unseen data.

Other works focus on which neurons to drop out. Dropout is usually applied to fully-connected layers of a deep network. Conversely, Wu & Gu (2015) studied the effect of dropout in convolutional and pooling layers. The selection of neurons to drop depends on the layer where they reside. In contrast, we select neurons within a layer based on their contribution. Wang & Manning (2013) demonstrate that sampling neurons from a Gaussian approximation gave an order of magnitude speedup and more stability during training. Li et al. (2016) proposed to use multinomial sampling for dropout, i.e. keeping neurons according to a multinomial distribution with specific probabilities for different neurons. Ba & Frey (2013) jointly trained a binary belief network with a neural network to regularize its hidden units by selectively setting activations to zero accordingly to their magnitude. While this takes into consideration the magnitude of the forward activations, it does not take into consideration the relationship of these activations to the ground-truth. In contrast, we drop neurons based on how they contribute to a network's decision.

We compare our results against Morerio et al. (2017) . To the best of our knowledge, we are the first to probabilistically select neurons to dropout based on their task-relevance.

3. METHOD:

3.1 BACKGROUND Saliency maps that quantize the importance of class-specific neurons for an input image are instrumental to our proposed scheme. Popular approaches include Class Activation Maps (CAM) [Zhou et al. (2016) ], Gradient-weighted Class Activation Mapping (Grad-CAM) [Selvaraju et al. (2017) ], and Excitation Backprop (EB) [Zhang et al. (2017) ]. A thorough analysis of all saliency methods is out of the scope of this work, and the saliency problem in general is far from solved. We choose to use EB since it produces a valid probability distribution for each network layer. The saliency maps obtained using this approach are evaluated for spatial localization of objects and demonstrate the ability of pointing to the right region of an image [Zhang et al. (2017) ].

In a standard CNN, the forward activation of neuron a j is computed by a j = φ( i w ij a i + b i ), where a i is the activation coming from the previous layer, φ is a nonlinear activation function, w ij and b i are the weight from neuron i to neuron j and the added bias at layer i, respectively. EB devises a backpropagation formulation able to reconstruct the evidence used by a deep model to make decisions. It computes the probability of each neuron recursively using conditional probabilities P (a i |a j ) in a top-down order starting from a probability distribution over the output units, as follows:

EQUATION

where P i is the parent node set of a i . EB passes top-down signals through excitatory connections having non-negative activations, excluding from the competition inhibitory ones. EB is designed with an assumption of non-negative activations. Most modern CNNs use ReLU activation functions, which satisfy this assumption. Therefore, negative weights can be assumed to not positively contribute to the final prediction. Assuming C j the child node set of a j , for each a i ∈ C j , the conditional winning probability P (a i |a j ) is defined as

EQUATION

where Z j is a normalization factor such that ai∈Cj P (a i |a j ) = 1. Recursively propagating the top-down signal and preserving the sum of backpropagated probabilities, it is possible to highlight the salient neurons in each layer using Eqn. 1, i.e. neurons that mostly contribute to a specific task. We will refer to the distribution of P (a i ) as p EB (a i ). This plot was created using N = 10 and a base retaining probability P = 0.5. In this case, when the saliency of neurons is uniform, i.e. p EB = 0.1, then p = P as marked in the figure.

3.2. EXCITATION DROPOUT:

In the standard formulation of dropout [Hinton et al. (2012) ; Srivastava et al. (2014) ], the suppression of a neuron in a given layer is modeled by a Bernoulli random variable 0 < p ≤ 1 where p is defined as the probability of retaining a neuron. Given a specific layer where dropout is applied, during the training phase, each neuron is turned off with a probability 1 -p.

We argue for a different approach that is guided in the way it selects neurons to be dropped. In a training iteration, certain paths have high excitation contributing to the resulting classification, while other regions of the network have low response. We encourage learning alternative paths (plasticity) through the temporary damaging of the currently highly excited path. We re-define the probability of retaining a neuron as a function of its contribution in the currently highly excited path

EQUATION

where p EB is the probability backpropagated through the EB formulation (Eqn. 1) in layer l, P is the base probability of retaining a neuron when all neurons are equally contributing to the prediction and N is the number of neurons in a fully-connected layer l or the number of filters in a convolutional layer l. The retaining probability defined in Eqn. 3 drops neurons which contribute the most to the recognition of a specific class, with higher probability. Dropping out highly relevant neurons, we retain less relevant ones and thus encourage them to awaken. We also study how this compares to dropping the least relevant neurons (Adaptive Dropout by Ba & Frey (2013) ) in the Appendix.

Fig. 2 shows p as a function of p EB . To gain some intuition for Eqn. 3, we can look more closely at the graph: 1) If neuron a i has p EB (a i ) = 1: This results in a retaining probability of p = 0. We do not want to keep a neuron which has a high contribution to the correct label. 2) If neuron a i has p EB (a i ) = 0: This results in a retaining probability of p = 1. We want to keep a neuron which has not contributed to the correct classification of an image. 3) If neuron a i has p EB (a i ) = 1/N , i.e. p EB is a uniform probability distribution: This results in a retaining probability p = P . We want to keep a neuron with base probability P since all neurons contribute equally.

Eqn. 3 provides a dropout probability for each neuron, which is then used as the parameter of a Bernoulli distribution giving a binary dropout mask. During training, each image in a batch leads to different excitatory connections in the network and therefore has a different p EB distribution, consequently leading to a different dropout mask. Fig. 1 presents the pipeline of Excitation Dropout at training time, and a run-time analysis is presented in the Appendix.

4. EXPERIMENTS:

In this section, we present how Excitation Dropout improves the generalization ability on four image/video recognition datasets in fully connected layers of different architectures. We then present an analysis of how Excitation Dropout affects the utilization of network neurons on the same datasets. Finally, we examine the resilience of a model trained using Excitation Dropout to network compression. We present results on four architectures. Relatively shallow architectures are trained from scratch, and deeper popular architectures are fine-tuned after being pre-trained on ImageNet [Deng et al. (2009) ]. Models trained from scratch: We train the CNN-2 architecture used in Morerio et al. (2017) , the state-of-the-art dropout variant, for comparison purposes. This architecture consists of three convolutional and two fully-connected layers (see Appendix). We train this network from scratch for 100K iterations on the datasets: Cifar-10, Cifar-100 and Caltech-256. We use minibatches of 100 images and fix the learning rate to be 10 -3 , decreasing to 10 -4 after 25K iterations. Fine-tuned models: We fine-tune the commonly used architectures: AlexNet [Krizhevsky et al. (2012) ], VGG16 and VGG19 [Simonyan & Zisserman (2014) ] pre-trained on ImageNet. We finetune the models for a frame by frame action recognition task on UCF101. The learning rate is fixed to 10 -3 for all the processes. We fine-tune AlexNet for 5K while VGG16 and VGG19 for 30K iterations. We use a batch size of 128 and 50 images for AlexNet and VGG16/19, respectively. Results presented here are averaged over five trained models for each of the datasets: Cifar10, Cifar100, Caltech256 and UCF101 (σ in brackets). Excitation Dropout consistently produces more neurons with non-zero activations, has a more spread saliency map leading to a lower saliency peak, has a higher entropy of both activations and saliency, and has a lower number of conservative filters; all reflecting an improved utilization of the network neurons using Excitation Dropout.

4.2. SETUP AND RESULTS: GENERALIZATION:

In this section we compare the performance of Excitation Dropout to that of No Dropout, Standard Dropout, and Curriculum Dropout [Morerio et al. (2017) ]. We train a CNN-2 model from scratch on the datasets: Cifar10, Cifar100, Caltech256. Fig. 3 depicts the test accuracies over training iterations for the three datasets averaged over five trained models. After convergence, Excitation Dropout demonstrates a significant improvement in performance compared to other methods. We hypothesize that Excitation Dropout takes longer to converge due to the additional loop (Steps 2-4 in Fig. 1 ) introduced in the learning process, and due to the learning of the alternative paths. We note that Excitation Dropout, during training, uses a different binary mask for each image in a minibatch, while in Standard Dropout, one random mask is employed per minibatch. To prove that it is precisely the fact that masks reflective of the particular input give rise to a boost in accuracy, and not the fact that different masks are used for different images, we add a comparison with Standard Dropout having a different random mask for each image. We refer to this accuracy as 'Standard Dropout + Mask/Img' in the plots. As expected, the latter approach is comparable to Standard Dropout in performance. Excitation Dropout shows more robustness when more neurons are switched off. This is demonstrated through its ability to recover more of the saliency map even when a high percentage of the most salient neurons is dropped-out. This ability reflects the alternative learnt paths. Histograms of the leftmost and rightmost saliency maps are presented to demonstrate that Excitation Dropout has a wider range of saliency values.

Excitation Dropout:

Curriculum Dropout Standard Dropout No Dropout

Next, we evaluate the effectiveness of Excitation Dropout on popular network architectures that employ dropout layers: AlexNet, VGG16, VGG19. This is done by fine-tuning on the video recognition dataset UCF101. Fig. 3 shows superior Excitation Dropout performance on AlexNet fine-tuned on UCF101. Table 1 presents more comparative results on other deep architectures by reporting the accuracy after convergence. Again, Excitation Dropout demonstrates higher generalizability on the test data for all architectures.

For fair comparison, we set p = 0.5 for Standard Dropout and P = 0.5 for the base retaining probability of Excitation Dropout in all experiments1 . We perform dropout in the first fully-connected layer of the networks (fc1 for CNN-2 and fc6 for AlexNet and VGGs) for Standard, Curriculum, and Excitation Dropout. For Curriculum Dropout we fix the parameter γ to 5 * 10 -4 as in Morerio et al. (2017) .

4.3. SETUP AND RESULTS: UTILIZATION OF NETWORK NEURONS:

In this section we examine how Excitation Dropout expands the network's utilization of neurons through the learnt alternative paths for a certain task. Mittal et al. (2018) introduced scoring functions to rank the filters in specific network layers including the average percentage of zero activations, a metric to count how many neurons have zero activations, and the entropy of activations, a metric to measure how much information is contained in the neurons of a layer. We analogously compute the Neurons ON which is the average number of non-zero activations, the entropy of p EB which is higher when the probability distribution is spread out over more neurons in a layer. We also compute the peak p EB which is expected to be lower on a more spread distribution. Moreover, Ma et al. (2017) introduced conservative filters: filters whose parameters do not change significantly during training. Conservative filters reduce the effective number of parameters in a CNN and may limit the CNNs modeling capacity for the target task. A conservative filter is a filter k in layer n whose weights have changed by ∆ k n = ŵk n -w k n , where ∆ k n is less than a threshold ∆ (empirically set). We evaluate the presented metrics for Excitation Dropout and compare against Standard and Curriculum Dropout in Table 2 . This is done on the same datasets and architectures considered in Sec. 4.2. All metrics are computed for the first fully-connected layer of the CNN-2 and VGG16 nets consisting of 2048 and 4096 neurons, respectively. We compute each metric over the test set of each dataset. Excitation Dropout consistently outperforms Standard and Curriculum Dropout in all the metrics over all datasets. Excitation Dropout shows a higher number of active neurons, a higher entropy over activations, a probability distribution p EB that is more spread (higher entropy over p EB ) among the neurons of the layer, leading to a lower peak probability of p EB and therefore less specialized neurons. Averaging models having less specialized neurons results in higher robustness to information loss. We also observe a significantly smaller number of conservative filters when using Excitation Dropout. Fewer filters remain unchanged, i.e. do not sufficiently learn anything far from the random initialization. These results show that the models trained with Excitation Dropout were trained to be more informative, i.e. the contribution for the final classification task is provided by a higher number of neurons in the network, reflecting the alternative learnt paths. An analysis of such metrics over the training iterations is presented in the Appendix.

4.4. SETUP AND RESULTS: RESILIENCE TO COMPRESSION:

In this section, we simulate 'Brain Damage' by dropping out neurons at test time. Fig. 4 demonstrates how a network utilizes the learnt alternative paths to capture the evidence of the class HorseRiding in a video frame of the UCF101 dataset. Given a VGG16 model fine-tuned with Excitation, Curriculum, Standard, and No Dropout at the f c6 layer, we show the excitation saliency map obtained at the conv5-1 layer as we drop out a fixed number of the most relevant neurons from the same layer dropout is performed upon during training. A neuron is considered to be more relevant if it has a higher p EB . In the first column of frames of Fig. 4 , the original saliency maps for the different models are shown. As already highlighted in Table 2 , the original saliency map obtained from the model trained with Excitation Dropout is more spread as compared to that of the other schemes, which present more pronounced red peaks. In the following columns of Fig. 4 , we present the saliency maps the model is able to restore when the 100, 200, 300, 400, 500 most relevant neurons are dropped-out. Despite the increasing number of relevant neurons being dropped-out, Excitation Dropout is capable of restoring more of the saliency map contributing to HorseRiding. This means that the network with Excitation Dropout was trained to find alternative paths which belong to the same HorseRiding-relevant cues of the image. Despite the fact that we are considering the worst-case scenario, where we are switching off the most relevant neurons at test time, Excitation Dropout shows most robustness. More examples are presented in the Appendix. While Fig. 4 visualizes one example qualitatively, Fig. 5 presents a complete quantitative analysis on the entire test set after training is complete. We study how the predicted ground-truth (GT) probability changes as more neurons are dropped-out at test time. On the left we present the worst case when the neurons dropped are the most relevant to the prediction. The horizontal axis in the graph represents p c , where 0 ≤ p c ≤ 1 is the cumulative sum of p EB of neurons which will be switched off starting from the most 'important'. The analysis is performed for p c = {0, 0.05, . . . , 0.90, 0.95}. In the center, we present an analogous analysis starting to drop from the 'least' relevant neurons. On the right, we present the random case (more realistic) when k neurons (k = 0, 128, 256, . . . , 4096) are randomly switched off. As we drop more neurons, Excitation Dropout (purple curves) is capable of maintaining a much less steep decline of GT probability, indicating more robustness against network compression. Cifar10, Cifar100, and Caltech256 show similar behavior (see analogous plots in the Appendix).

5. CONCLUSION:

We propose a new regularization scheme that encourages the learning of alternative paths in a neural network by deliberately paralyzing high-saliency neurons that contribute more to a network's prediction during training. In experiments on four image/video recognition datasets, and on different architectures, we demonstrate that our approach yields better generalization on unseen data, higher utilization of network neurons, and higher resilience to network compression.

APPENDIX:

CNN-2 architecture. Table 3 shows the details of the CNN-2 architecture adopted for Cifar10, Cifar100, and Caltech256 experiments. The size of the softmax layer depends upon the number of classes for each dataset. Caffe python layer on a GTX Titan X GPU and Intel(R) Xeon(R) CPU E5-2650 v3 @ 2.30GHz. In parenthesis is the percentage increase with respect to SD.

Layer:

Sensitivity analysis. In this section we present a sensitivity analysis over the dropout rate hyperparameter. In our work, we implement Excitation Dropout with a base retaining probability P , and we compare that to standard dropout with a retaining probability p, where P = p. If Excitation Dropout produced a uniform probability distribution over the desired layer, then every node would have a retain probability equal to the base probability P . For completeness, we add a sensitivity analysis of the parameters p and P in Table 6 . Additional Visualizations. In this section, we present more visualizations similar to that of Fig. 4 in the main manuscript. Visualizations for a VGG16 network fine-tuned on UCF101 for the actions: PlayingFlute, PlayingSitar, and GolfSwing are presented in Fig.s 6,7,8, respectively. Every column displays the saliency map over the same video frame of an action while incrementally switching off the most k relevant neurons (k = 0, 100, 200, . . . , 500). Excitation Dropout is more robust over higher number of switched off neurons. This is demonstrated through its ability to recover the saliency map even when a high percentage of the most salient neurons is dropped-out. This is done through the alternative learnt paths, which are reflected in the higher number of non-zero activations that remain after dropout compared to other dropout strategies. Additional Plots. In this section we present the f c compression results for three additional datasets: Cifar10, Cifar100, and Caltech256 (Fig. 9 ), using CNN-2. We study how the predicted ground-truth (GT) probability changes as more neurons are dropped-out at test time. On the left we present the worst case when the neurons dropped are the most relevant to the prediction. The horizontal axis in the graph represents p c , where 0 ≤ p c ≤ 1 is the cumulative sum of p EB of neurons which will be switched off starting from the most 'important'. The analysis is performed for p c = {0, 0.05, . . . , 0.90, 0.95}. In the center, we present an analogous analysis starting to drop from the 'least' relevant neurons. On the right, we present the random case (more realistic) when k neurons (k = 0, 128, 256, . . . , 2048) are randomly switched off. As we drop more neurons, Excitation Dropout (purple curves) is capable of maintaining a much less steep decline of GT probability.

Dataset:

Metric Analysis During Training. In this section we report an extended analysis of the metrics: # Neurons ON, Peak p EB , Entropy of Activations, and Entropy of p EB during training. Excitation Dropout shows a higher number of active neurons, a higher entropy over activations, a probability distribution p EB that is more spread (higher entropy over p EB ) among the neurons of the layer, leading to a lower peak probability of p EB and therefore less specialized neurons. These results are observed to have consistent trends over all training iterations for all datasets considered (see 

:

We also present a hyper-parameter sensitivity analysis for the dropout rate in the Appendix.

Figures and Tables:

Figure 1: Training pipeline of Excitation Dropout. Step 1: A minibatch goes through the standard forward pass.Step 2: Backward EB is performed until the specified dropout layer; this gives a neuron saliency map at the dropout layer in the form of a probability distribution.Step 3: The probability distribution is used to generate a binary mask for each image of the batch based on a Bernoulli distribution determining whether each neuron will be dropped out or not. Step 4: A forward pass is performed from the specified dropout layer to the end of the network, zeroing the activations of the dropped out neurons.Step 5: The standard backward pass is performed to update model weights.

Figure 2: The retaining probability, p, as a function of the Excitation Backprop probability p EB . This plot was created using N = 10 and a base retaining probability P = 0.5. In this case, when the saliency of neurons is uniform, i.e. p EB = 0.1, then p = P as marked in the figure.

Figure 3: We compare the test accuracy of different dropout training strategies on four image/video recognition datasets: Cifar10, Cifar100, Caltech256, UCF101. Results presented here are averaged over five trained models and the standard deviation is depicted around the mean curve using a lighter shade. Excitation Dropout performs best after convergence compared to the other strategies.

Figure 4: Visualizations for a VGG16 network fine-tuned on UCF101. The middle columns display the saliency map over the same video frame of the action HorseRiding while incrementally switching off the most k relevant/salient neurons (k = 0, 100, 200, . . . , 500) in the fc6 layer at test time.Excitation Dropout shows more robustness when more neurons are switched off. This is demonstrated through its ability to recover more of the saliency map even when a high percentage of the most salient neurons is dropped-out. This ability reflects the alternative learnt paths. Histograms of the leftmost and rightmost saliency maps are presented to demonstrate that Excitation Dropout has a wider range of saliency values.

Figure 5: Robustness of predicted ground-truth class probabilities as more neurons are droppedout for UCF101 test images. We fine-tune VGG16 with Excitation, Curriculum, Standard, and No Dropout at the f c6 layer, averaging results over five trained models. The standard deviation is depicted around the mean curve using a lighter shade. At test time, we switch off starting from the most relevant neurons with respect to p c (left), from the least relevant neurons with respect to p c (center), and k random neurons (right). In all scenarios, Excitation Dropout shows more robustness to network compression (dropping f c neurons ≡ removing filters).

Figure 6: Despite the increasing number of relevant neurons being dropped out at test time, Excitation Dropout is capable of restoring more of the saliency map contributing to the specific class: PlayingFlute

Figure 9: Robustness of predicted ground-truth class probabilities as more neurons are dropped out for each dataset's test images. We train CNN-2 from scratch with Excitation, Curriculum, Standard, and No Dropout at the f c1 layer, averaging results over five trained models. The standard deviation is depicted around the mean curve using a lighter shade. Left: the most relevant neurons with respect to the p c threshold are switched off. Center: the least relevant neurons with respect to the p c threshold are switched off. Right: k neurons are randomly switched off. In all scenarios, Excitation Dropout shows more robustness to network compression (dropping f c neurons ≡ removing filters).

Test accuracy comparison between No, Standard, Curriculum and Excitation Dropout in the f c6 layer of three architectures: AlexNet, VGG16 and VGG19, fine-tuned for the action recognition task on UCF101. The numbers reported are the final test accuracies together with the improvements (in parenthesis) with respect to No Dropout, averaged over five trained models.

Table content: <table><tr><td colspan="2">Architecture</td><td>No Dropout (%)</td><td/><td>Standard Dropout (%)</td><td>Curriculum Dropout (%)</td><td>Excitation Dropout (%)</td></tr><tr><td colspan="2">VGG16</td><td>69.37</td><td colspan="3">71.93 (+2.56%) 72.14 (+2.77%) 73.23 (+3.86%)</td></tr><tr><td colspan="2">VGG19</td><td>71.32</td><td colspan="3">72.52 (+1.29%) 73.18 (+1.86%) 74.34 (+3.02%)</td></tr><tr><td colspan="2">AlexNet</td><td>62.89</td><td colspan="3">64.50 (+1.61%) 64.55 (+1.66%) 67.56 (+4.67%)</td></tr><tr><td>Dataset</td><td/><td>Metric</td><td/><td>Standard Dropout</td><td>Curriculum Dropout</td><td>Excitation Dropout</td></tr><tr><td/><td colspan="2"># Neurons ON</td><td/><td>1194 (±153)</td><td>1169 (±61)</td><td>1325 (±61)</td></tr><tr><td>Cifar10</td><td colspan="2">Peak p EB Entropy of Activations Entropy of p EB</td><td/><td>0.011 (±0.004) 3.55 (±0.72) 3.28 (±0.56)</td><td>0.009 (±0.001) 0.003 (±0.0002) 3.50 (±0.12) 4.29 (±0.28) 3.32 (±0.13) 4.26 (±0.26)</td></tr><tr><td/><td colspan="3">Conservative Filters ∆=0.25</td><td>1204 (±37)</td><td>959 (±34)</td><td>124 (±22)</td></tr><tr><td>Cifar100</td><td colspan="3"># Neurons ON Peak p EB Entropy of Activations Entropy of p EB Conservative Filters ∆=0.30</td><td colspan="2">453 (±183) 0.011 (±0.0004) 0.012 (±0.0004) 0.005 (±0.0005) 460 (±75) 943 (±131) 1.67 (±0.31) 1.70 (±0.29) 3.21 (±0.44) 1.64 (±0.27) 1.67 (±0.26) 3.17 (±0.41) 2048 (±51) 2038 (±44) 14 (±13)</td></tr><tr><td>Caltech256</td><td colspan="3"># Neurons ON Peak p EB Entropy of Activations Entropy of p EB Conservative Filters ∆=1.25</td><td colspan="2">412 (±126) 0.014 (±0.0007) 0.013 (±0.0006) 0.007 (±0.0003) 471 (±146) 702 (±171) 1.63 (±0.32) 1.84 (±0.35) 2.63 (±0.23) 1.58 (±0.29) 1.77 (±0.31) 2.59 (±0.22) 2048 (±46) 2048 (±49) 1671 (±31)</td></tr><tr><td>UCF101</td><td colspan="2"># Neurons ON Peak p EB Entropy of Activations Entropy of p EB</td><td/><td colspan="2">1120 (±25) 0.007 (±0.0002) 0.007 (±0.0002) 0.004 (±0.0002) 1143 (±22) 1404 (±37) 2.04 (±0.23) 2.08 (±0.21) 2.51 (±0.18) 1.92 (±0.22) 1.95 (±0.20) 2.42 (±0.18)</td></tr><tr><td/><td colspan="3">Conservative Filters ∆=0.15</td><td>3599 (±66)</td><td>3859 (±53)</td><td>44 (±36)</td></tr></table>

Different metrics to reflect the usage of network capacity in the first fully-connected layer of the CNN-2 architecture consisting of 2048 neurons and the VGG16 consisting of 4096 neurons.

Table content: <table/>

Details of the CNN-2 architecture used for experiments on the Cifar10, Cifar100, and Caltech-256 datasets.Least vs. most relevant neurons. Popular dropout methods (e.g. Adaptive DropoutBa & Frey (2013)) drop useless neurons with low activations during training. In this work we motivate and demonstrate that dropping neurons based on their Excitation Backprop (EB) probability has added benefits. Please note that we are not simply considering neuron activation. We demonstrate the performance of Excitation Dropout compared to the variant Adaptive Dropout[Ba & Frey (2013)] in Table4. In essence, Adaptive and Excitation Dropout are opposites by dropping the least and most important neurons, respectively.

Table content: <table><tr><td colspan="4">Type Layer Size Filter Size Padding/Stride</td></tr><tr><td>conv</td><td>96 filters</td><td>5x5</td><td>2/1</td></tr><tr><td>max pool</td><td/><td>3x3</td><td>0/2</td></tr><tr><td>conv</td><td>128 filters</td><td>5x5</td><td>2/1</td></tr><tr><td>max pool</td><td/><td>3x3</td><td>0/2</td></tr><tr><td>conv</td><td>256 filters</td><td>5x5</td><td>2/1</td></tr><tr><td>max pool</td><td/><td>3x3</td><td>0/2</td></tr><tr><td>fc</td><td>2048 units</td><td/><td/></tr><tr><td>fc</td><td>2048 units</td><td/><td/></tr><tr><td>softmax</td><td># classes</td><td/><td/></tr><tr><td>Dataset</td><td colspan="3">Adaptive Dropout Excitation Dropout</td></tr><tr><td>Cifar10</td><td>76.82%</td><td/><td>81.94%</td></tr><tr><td>Cifar100</td><td>44.55%</td><td/><td>52.04%</td></tr><tr><td>Caltech256</td><td>23.32%</td><td/><td>35.77%</td></tr><tr><td>UCF101</td><td>71.76%</td><td/><td>73.23%</td></tr></table>

Accuracy comparison between Adaptive Dropout and Excitation Dropout. The numbers reported in this table are the average test set accuracy over five trained models for each dataset.Model complexity. Excitation Dropout consistently outperforms Standard Dropout (SD), with zero increase in test-time computational complexity. In training, there is a moderate increase in computation: in the worst case, Excitation Dropout will take double (same O-notation complexity) the training time of SD. This will happen when the utilized Excitation Dropout maps are at the first layer of the network. If a middle layer map is used, Excitation Dropout requires an additional partial forward-backward pass. We use maps of fc layers close to the end of the network to reduce this overhead. Table5presents a run-time analysis for the two main architectures used in this work and compares it to that of Standard Dropout.

Table content: <table><tr><td/><td/><td>Standard Dropout</td><td>Excitation Dropout</td></tr><tr><td>Run-time</td><td>CNN-2 (1 iter) VGG16 (1 iter)</td><td>0.1532 ± 0.0064 2.2928 ± 0.0297</td><td>0.1885 ± 0.0070 (+23%) 2.8202 ± 0.0312 (+23%)</td></tr></table>

Run-time comparison: Average time of 100 iterations (in seconds, batch size=50) for a

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Hyper-parameter sensitivity analysis for the Standard Dropout probability, and the Excitation Dropout base dropout probability. The accuracy is reported on the test set of each dataset. The retaining probability p or P is one minus the dropout rate.Excitation Dropout in Convolutional Layers. Excitation Dropout is a generic formulation that can be applied to any neural network layer. For a convolutional layer, a generic convolutional activation map is in the form of [w, h, N ], where N is the number of feature maps while w and h are the spatial dimensions. To apply Excitation Dropout to a convolutional layer, first p EB is computed for each feature map N as the sum of p EB across spatial locations w and h. Specific 2D feature maps are then dropped-out following Eqn. 3. We test Excitation Dropout at conv3 of the CNN-2 architecture and obtain the following accuracy results for Cifar10: No Dropout 76.91%; Excitation Dropout at conv3 78.01%; Excitation Dropout at f c1 81.94%. Again, we observe an improvement respect to No Dropout, but consistent with the literature[Hinton et al. (2012);Srivastava et al. (2014)], the improvement is not as large as using dropout in fully connected layers.Validation on Multiple Architectures. In this section we report additional results for Caltech256 and Cifar10 datasets considering different architectures. Table7reports the results of fine-tuning the deep architectures AlexNet, VGG16 and VGG19 on Caltech256 for the task of image classification. Finally, we adopt the WideResNet (WRN-28-10) architecture, a ResNet style architecture which combines batch normalization and dropout regularization techniques. WideResNet is used to obtain state-of-the-art results on Cifar10. We replace the Standard Dropout layer in the network with Excitation Dropout obtaining 3.88% test error on Cifar10 (vs. 4.17% Zagoruyko et al.s published result, BMVC16). Therefore, Excitation Dropout gives state-of-the-art result on Cifar10.

Table content: <table><tr><td/><td>Dropout Scheme</td><td>0.25 Dropout</td><td>0.5 Dropout</td><td>0.75 Dropout</td></tr><tr><td>Cifar10</td><td>Standard Excitation</td><td>79.16% 81.38%</td><td>80.13% 81.94%</td><td>81.19% 81.55%</td></tr><tr><td>Cifar100</td><td>Standard Excitation</td><td>48.44% 53.23%</td><td>50.36% 52.04%</td><td>51.64% 51.87%</td></tr><tr><td>Caltech256</td><td>Standard Excitation</td><td>26.23% 33.60%</td><td>28.73% 35.77%</td><td>32.51% 36.81%</td></tr><tr><td>UCF101</td><td>Standard Excitation</td><td>71.01% 73.56%</td><td>71.93% 73.23%</td><td>72.92% 73.06%</td></tr></table>

Test accuracy comparison between No, Standard, Curriculum, and Excitation Dropout in the f c6 layer of three architectures: AlexNet, VGG16 and VGG19, fine-tuned for the image recognition task on Caltech256. The numbers reported are the final test accuracies together with the improvements (in parenthesis) with respect to No Dropout, averaged over five trained models.

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Peer review (iclr2019):
 The authors propose a data-dependent dropout variant that produces dropout candidates based on their predictive saliency / relevance. Results are reported for 4 datasets (Cifar10, Cifar100, Caltech256 and UCF101) and 4 different models (CNN-2, AlexNet, VGG16 and VGG19), and suggest an increase in generalization performance over other dropout approaches (curriculum dropout, standard dropout, no dropout), as well as increase in the network*s plasticity as measured by some existing metrics from the literature. The authors conclude that Excitation Dropout results in better network utilization and offers advantages for network compression (in the sense of neuron pruning). Overall I find the idea to be interesting and fairly novel, and commend the authors for the fluid writing style. However, I find key issues with the testing and experiments. Specifically, the lack of confidence bounds for individual results makes it impossible to determine whether the reported incremental improvements are actually significant over those of existing approaches. Likewise, I criticize the choice of methods the authors have chosen to compare against, as several other data-dependent dropout approaches (e.g. Information Dropout) exist that may be conceptually closer (and therefore more comparable) to the proposed approach. I also question the choice of tested network architectures and the placement of the dropout layer. The paper could be of high significance if all claims in the paper could be backed up by experiments that show the advantage of Excitation Dropout to be not a random effect. I will therefore give a lower score for the paper in its current form, but am willing to revise my rating the major points below are properly addressed. Pros: + novel mechanism to improve dropout, results seemingly superior over other methods + achieves better utilization of network resources and achieves robustness to dropping out neurons at test time Cons: - results without error bars, unclear if advantage is significant - did not compare against most relevant competing methods MAJOR POINTS Section 2 - The comparison to Moreiro et al. is not entirely clear. A fairer comparison would be with some of the other methods listed which also focus on answering the question of which neurons to dropout, or approaches which determine the dropout policy based on information gained from the data, such as Information Dropout (Achille & Soatto). The authors state that Morerio et al are the state-of-the-art in dropout techniques, however based on the results presented here (Figure 3) it seems to perform just as well as standard dropout. Perhaps there are architecture-specific or data-specific issues? In any case this example undermines the confidence of the claims. Section 3.2, equation 3 - is there some theoretical underpinning as to how this equation was modelled, or was it chosen simply because it covers the expected corner cases described in paragraph 4 of this section? Also, given the intuition in this paragraph (e.g. p_EB = 1 / N), it is correct to assume this equation models the dropout probability but only for fully connected layers? What about dropout in convolutional layers? Though some previous statements do point to the usage of dropout predominantly for fully connected layers, I feel that this context is missing here and should be explicitly addressed. The caption to e.g. Table 1 seems to imply the authors add a single dropout layer in one of the fully connected layers, however this begs the question as to why this positioning was chosen - why only one dropout layer, and why precisely at that location? The scope of the claims should be adapted accordingly. Section 4.2 - "After convergence, ED demonstrates a significant improvement in performance compared to other methods". If five trained models were used, then some sense of measure of uncertainty should be given throughout. For example, in the Cifar10 results for Figure 3, it is difficult to say whether the marginal improvement from about 80% (standard dropout and curriculum dropout) to about 82% (excitation dropout) is significant or not. Perhaps this would be less of an issue if the authors had worked with e.g. ImageNet, but for these smaller datasets it would definitely be worth to be on the safe side. I highly suspect that statistically speaking (perhaps with the exception of the results on Caltech256), the effects of all of these dropout variants are indistinguishable from each other. I urge the authors to include a measure of the standard deviation / 95% confidence interval across the models that were tested. The results presented sub-section 4.3 do not justify the claim that the models trained with Excitation Dropout tend to be more informative. Perhaps the definition of "informative" should be expanded upon in length. Can the authors show that the alternative paths learned by the models augmented with Excitation Dropout indeed carry complimentary information and not just redundant information? Figure 5 shows interesting results, but once again begs the question of whether there is any significant difference between standard dropout and curriculum dropout. I encourage the authors to include confidence bounds for each trace. Likewise, there is an inherent bias in the results, in that the leftmost figure compares EB and CD in the context in which EB was trained, i.e. dropping of "most salient" neurons. The comparison is one-sided, however, as no results are reported from the context in which CD was trained, i.e. dropping neurons more frequently as training progresses. Comparing these results would bring to light whether the performance boost see in Figure 5 is a function of "overfitting" to the training manner or not. Also, I believe the results for the second column (dropping out least relevant neurons) are misleading. To the best of my understanding, as p_c increases, at some point neurons start to be dropped that actually have high relevance. This could explain why all curves start out similarly and EB slowly begins to stick out - at this point the EB models once again start to be used in the context within which they were trained, in contrast to the other approaches. The authors should perhaps also explicity clarify why this second column gives any more information than the first. MINOR POINTS The authors propose Excitation Dropout as a guided regularization technique. Batch normalization is another standard regularization technique which is often compared with dropout. In particular, for deep CNNs, batch normalization is known to work very well, often better than the standard dropout. In the experiments here, to what extent was batch normalization and / or any other widely utilized network regularizers used? Is it possible that the regularizing effect found here actually comes from one of these? I.e. were the models that were not trained from scratch trained with batch normalization? It would be good if more data could be provided for EB vs. other regularizing techniques, if the claim is that EB is a novel regularizer. Section 3.1 - "We choose to use EB since it produces a valid probability distribution for each network layer". Though this is a nice property, were there any other considerations for choosing the saliency method? Recent work (Adebayo et al, "Sanity Checks for Saliency Maps") has shown that even some well established saliency techniques are actually independent from both the model and data. As this approach relies heavily on the correctness of EB, I feel that a further justification should be given to validate its use for this scenario other than just based on the type of output it produces. Section 3.1, equation 2 - more detail and reasoning should be given as to why connections with negative weights are excluded from the computation of the conditional probability, if possible without referring the reader to the EB paper. Why is this justified? Is this probability modelled for a specific activation function? The authors do not provide the details of the CNN-2 architecture (even in the appendix) and simply refer to another article. If the majority of the results presented in the paper are based on this network (including a reference made to a specific layer of the network in subsection 4.2) – which is not commonly known – why not to detail the network architecture and save additional effort for the reader? How are the class-wise training and test images chosen for Caltech256 dataset? The authors test the CNN-2 architecture on Cifar10 and Cifar100, and AlexNet, VGG16, and VGG19 on UCF101. I feel that at least a couple architectures should be validated with more than a single dataset, or the authors should justify the current matching between architectures and datasets. Table 2 is unclear regarding what models were used for what datasets (caption could be interpreted to mean that VGG16 was also used for Cifar and Caltech, however other statements seem to say otherwise). "To prove that the actual boost in accuracy with ED is not provided by the choice of specific masks,..." I suggest that the authors rephrase or explain this sentence in more detail. To the best of my understanding, it is precisely the fact that different masks are used, each reflective of the particular input used to generate the forward activations, that gives boost in performance over "standard" dropout methods by identifying salient paths in the network. Although it is a very important experimental detail, only in the end of sub-section 4.2, it becomes clear in which layers Excitation Dropout was applied. Y-axis labels are missing for the left panels in Figure 3. The authors randomly choose to abbreviate Excitation Dropout as ED in some paragraphs, while write the full form in others. Table 2 - It is not clear that the "Neurons ON" metric refers to the "average percentage of zero activations" explained below. Table 2 - How is peak p_EB measured? Is this an average over a set of test images after convergence? If so, I similarly suggest for confidence bounds to be introduced. It would be interesting to compare this to intermediate values (e.g. after every epoch) during training. Same question for entropy of activations and entropy of pEB. This information would be useful for reproducibility. Table 2 - Where do the delta values in Table 2 come from? If empirically determined, it should be stated explicitly. Table 2 - In general, because the metrics provided in Table 2 are averages (second paragraph of this Section 4.3), both (to the best of my understanding) across input subsets (e.g. averging results over many test inputs) and models (caption to Table 1), I feel Table 2 in its current form raises confusion given the lack of confidence bounds. I recommend the authors to clarify what type of averaging was done and to introduce e.g. standard deviations across all reported scores. The authors should refrain from using the term "significantly" while describing results if no statistical testing was done, or explicitly clarify their usage of this term. Table 2 - In general, Table 2 reports results on selected metrics which, if the authors* hypothesis is correct, should have a clear trend as training progresses. An interesting idea to explore would be to include an analysis (in the appendix) of how these factors change over the course of the training procedure. Intuitively, it seems plasticity is something that should be learned slowly over time, so if these plots were to reveal something different, it would be indicative that something else is going on. Figure 4 - Judging heatmaps is difficult as it depends on the visual perception of the reader. Thus, it is difficult to judge whether, as the authors claim, ED is indeed less "peaky" than the other alternatives. I suggest that the authors use a perceptually uniform heatmap, and to acompany these figures with e.g. the histogram of the heatmap values. Likewise, it is unclear how the multi-model aspect of the testing plays a role in generating these results. From the 5 originally trained models, how was the model selected that generated these results? Was there averaging of any kind? Figure 5: the text is too small to be readble Is "re-wiring" the most appropriate term to use to describe what is happening at inference time? Although different paths may be used, the network connections themselves are fixed and thus this is a potential source for confusion. What do numbers in Table-4 in the appendix represent? Test accuracy?