Going Beyond Saliency Maps: Training Deep Models to Interpret Deep Models
GGoing Beyond Saliency Maps:Training Deep Models to Interpret Deep Models
Zixuan Liu , Ehsan Adeli , , Kilian M. Pohl , , and Qingyu Zhao Department of Electrical Engineering, Stanford University, CA 94305 Department of Psychiatry & Behavioral Sciences, Stanford University, CA 94305 Department of Computer Science, Stanford University, CA 94305 Center for Biomedical Sciences, SRI International, CA 94025
Abstract.
Interpretability is a critical factor in applying complex deeplearning models to advance the understanding of brain disorders in neu-roimaging studies. To interpret the decision process of a trained classi-fier, existing techniques typically rely on saliency maps to quantify thevoxel-wise or feature-level importance for classification through partialderivatives. Despite providing some level of localization, these maps arenot human-understandable from the neuroscience perspective as they donot inform the specific meaning of the alteration linked to the brain dis-order. Inspired by the image-to-image translation scheme, we propose totrain simulator networks that can warp a given image to inject or re-move patterns of the disease. These networks are trained such that theclassifier produces consistently increased or decreased prediction logitsfor the simulated images. Moreover, we propose to couple all the simu-lators into a unified model based on conditional convolution . We appliedour approach to interpreting classifiers trained on a synthetic datasetand two neuroimaging datasets to visualize the effect of the Alzheimer’sdisease and alcohol use disorder. Compared to the saliency maps gen-erated by baseline approaches, our simulations and visualizations basedon the Jacobian determinants of the warping field reveal meaningful andunderstandable patterns related to the diseases.
In recent years, deep learning has achieved unparalleled success in the field ofmedical image computing [1] and is increasingly used to classify patients withbrain diseases from normal controls based on their Magnetic Resonance Imaging(MRI) data [2]. These models can generally result in superior classification ac-curacy than traditional machine learning methods by training on a larger scaleof annotated data and with enhanced computational power [3]. Due to the exactsame reason, research attention has been largely directed to the methodologicaldevelopment of deep classifiers by employing more complex network architec-tures and learning strategies.The ramification of learning models being more complex is that they are lessinterpretable, which poses a serious challenge to their application to most neu-roimaging studies. When a learning model is used to aid the diagnosis by human a r X i v : . [ ee ss . I V ] F e b Liu et al. experts, one needs to understand how the model reasons about its prediction[4]. In studies where neuroimaging is not a part of the diagnosis workflow (i.e.,discovery-oriented analysis), the goal of learning image-based classifiers is solelyfor revealing the impact of the disease on the brain [5,6]. In both scenarios, modelinterpretability plays a pivotal role.Compared to the large body of literatures on model development, methods formodel interpretation (also known as model visualization) are still oversimplified.To this end, the most widely used techniques in neuroimaging applications aregradient-based methods [7,8], which aim to generate a saliency map for each MRimage. This map encodes the importance of the information contained withineach voxel (or local neighborhood). Specifically, the saliency value is quantifiedas the partial derivative of the prediction with respect to the feature value orvoxelwise intensity. However, despite the wide usage in computer vision tasks,their application to neuroimaging studies is limited as the saliency maps aregenerally noisy on the pixel level, imprecise in localization, and selective onnetwork architectures. Most importantly, the saliency maps are not interpretablefrom the neuroscientific perspective as they only inform where but not how(which aspect of) the brain structure is affected by the disease.In this work, we propose to train separate simulator networks to learn human-understandable morphological patterns within an image that can impact theclassifier’s prediction. Motivated by the image-to-image translation scheme, onesimulator can warp an image to inject the disease patterns such that the classi-fier increases its confidence in predicting the image as diseased (i.e., logit shift),and the other simulator can remove the patterns from the image. As such,subject-level visualization is enabled by visually comparing the image appear-ance between the raw and simulated image pair or by quantifying the Jacobianmap (encoding tissue expansion and shrinkage) of the warping field. To robustlylearn the simulators, we employ a cycle-consistent scheme to encourage the sim-ulators to inject and remove patterns only related to disease while preservingsubject-specific information irrelevant to the disease. Furthermore, we proposeto couple the two simulators into one coherent model by using the conditionalconvolution operation. The proposed visualization method was applied to in-tepret classifiers training on a synthetic dataset, 1344 T1-weighted MR imagesfrom the Alzheimer’s Disease Neuroimaging Initiative (ADNI), and a dataset of1225 MR images for classifying the diagnosis of alcohol use disorder. We com-pared our visualization with a number of widely used visualization techniques.Results indicate that our learning-based visualization provides a means of cap-turing high-level shape change of brain tissue associated with the disease, whichis more meaningful and stable than the feature- or voxel-level saliency derivedby traditional methods.
Most existing methods for model interpretation provide visualization throughfeature-level or voxel-level saliency scores quantified by partial derivatives [7,8]; eep Visualization 3
Disease Simulator P 𝑿 "𝑿 P 𝑝 ̂𝑝 > 𝑝 + 𝛿 (𝑿 G Control Simulator G Disease Simulator P 𝒀 "𝒀 P 𝑝 ̂𝑝 < 𝑝 − 𝛿 (𝒀 Cycle-consistent loss Cycle-consistent lossLogit shift loss Logit shift loss
Control Simulator G Disease Simulator G Fig. 1.
To interpret a trained classifier ( P ), the proposed framework trains two sepa-rate simulator networks to learn the morphological change that defines the separationbetween control and diseased cohorts. The disease simulator ( G ) injects the diseasepattern into an image X such that the prediction logit ˆ p for the simulated image ˆ X increases by a pre-dined threshold δ . The control simulator removes the pattern froman image. The two simulators are trained in a cycle-consistent fashion. i.e., how a small change in feature or voxel values can influence the final predic-tion. These derivatives can be efficiently computed by back-propagation. How-ever, the voxelwise derivatives are generally noisy and non-informative as thevariation in a voxel is more related to low-level features rather than the finalprediction. On the other hand, Grad-CAM [8] can generate smooth and robustvisualization based on deriving feature-level importance, but the method cannotaccurately locate object boundaries and is only applicable to a narrow range ofnetwork types. Other than using partial derivatives, occlusion-based methods [9]quantify the importance of a local image neighborhood for prediction by firstmasking the regional information in the images (zero-out, blur, shuffle, deforma-tion, etc) and then evaluating the impact on the classifier’s prediction accuracy.However, the resulting model interpretation is confined to the group level. Re-cently, Ghorbani [10] has proposed a concept-based interpretation, which aims todirectly identify critical image segments that drive the model decision. However,when applied to neuroimaging applications, all the above methods can only pro-vide localization but do not explain the alteration of brain structures associatedwith a disease.Recently, image-to-image translation frameworks have achieved marked suc-cess in medical applications including denoising, multi-modal image registration,and super-resolution reconstruction [11,12]. The goal of such frameworks is tolearn a bijective mapping between two distributions from different image do-mains. In this work, we formulate the two domains as images of healthy anddiseased cohorts and learn how an image of a healthy subject will be altered ifthe subject is affected by the disease (and vice versa). Let X and Y be the MR datasets of a control cohort and a diseased cohort. Weassume a deep classifier P has been trained on the datasets such that p = P ( X ) Liu et al. is the logit (value before sigmoid ) encoding the confidence in labeling image X as diseased; i.e., X is from a diseased subject if p > P to understand what themorphological information in X can impact the final prediction p . To do so, wepropose to train two simulator networks G and G , where ˆ X = G ( X ) addsthe ‘disease pattern’, i.e., changes in image appearance induced by the disease,to an input control image X ∈ X , and ˆ Y = G ( Y ) removes the pattern from adiseased input Y ∈ Y .Traditional methods suggest to use adversarial training [13] to learn G and G in such image translation tasks; i.e., to fool the classifier such that P ( ˆ X ) > P ( ˆ Y ) <
0. However, the neurological condition linked to a brain disordermay lie in a continuous spectrum as encoded in the predicted logit p . E.g., theseverity of cognitive impairment can be highly heterogeneous in the AD cohort,resulting in some AD patients having larger logits and others having logits closerto 0. As such, the above binary adversarial objective may implicitly reweigh theimportance across subjects during training. To ensure an impartial training,we enforce the simulators to produce a logit shift greater than a pre-definedthreshold δ for each subject; i.e., P ( ˆ X ) − P ( X ) > δ and P ( ˆ Y ) − P ( Y ) < − δ . Thislogit shift loss is then formulated as E logit = E X ∼X [max( P ( X ) − P ( ˆ X ) , − δ )] + E Y ∼Y [max( P ( ˆ Y ) − P ( Y ) , − δ )] . (1)As commonly explored in the literature, we also incorporate the cycle-consistent loss to ensure that the simulators can recover the original input from a simulatedimage. This guarantees that subject-specific information in the image irrelevantto the disease is not perturbed during the simulation. E cycle = E X ∼X [ || G ( G ( X )) − X ) || ] + E Y ∼Y [ || G ( G ( Y )) − Y ) || ] . (2) A drawback of traditional cycle-consistent learning is that the two simulators G and G are designed as independent networks albeit the two simulation tasksare extremely coupled (injecting vs removing disease patterns). In other words,the network parameters between G and G should be highly dependent, andeach convolutional kernel at a certain layer should perform related functions.Here, we propose to combine the two simulators into a coherent model whosebehavior can be adjusted based on the specific simulation task. We do so by using conditional convolution (CondConv) [14] as the fundamental building blocksof the network (Fig. 2). Let f and f (cid:48) be the input and output features of aconvolutional operation with activation σ . As opposed to the static convolutionalkernel, the CondConv kernel W is conditionally parameterized as a mixture ofexperts f (cid:48) = σ ( α · W (cid:126) f + ... + α K · W K (cid:126) f ) , (3)where W is a linear combination of k sub-kernels with weights { α k | k = 1 , ..., K } determined via a routing function r k ( · ). With t being the task label, we design eep Visualization 5 CondConvCondConvCondConv CondConvCondConvCondConv
Task ⨁ Joint Simulator
𝑿
Fig. 2.
Two simulators are coupled into one single model by using Conditional Convo-lution (CondConv), whose parameters are dependent on the specific simulation task.The output of the joint simulator is a warping field φ that is applied to the input X to derived the simulated ˆ X . the following routing function α k = r k ( f, t ) = sigmoid ([ GlobalAvgPool ( f ) , t ] ∗ R k ) , (4)where R k are the learnable parameters to be multiplied with the concatenation ofthe pooled feature and the task label. In doing so, the behavior of the convolutioncan adapt to subject-specific brain appearance as encoded in f and to the specifictask ( G or G ). In principle, the two simulators can generate any patterns that separate thehealthy and diseased cohorts (intensity difference, shape change, etc). However,unlike image modalities like CT, the voxel intensities in MRI are only mean-ingful within a neighborhood but variant across different images due to factorssuch as scanner types, imaging protocol difference, and intensity inhomogeneity.Therefore, we enforce the simulators to only learn the shape patterns that dif-ferentiate cohorts. To do so, we let the output of the simulators be 3D warpingfields φ = G ( X ) and φ = G ( X ), which are then applied to the input imagesto derived the warped images ˆ X = X ◦ φ , ˆ Y = Y ◦ φ . The warping layer isimplemented the same as in [15], which uses linear interpolation to compute theintensity of a sub-voxel defined at non-integer locations. As also adopted in [15],a diffusion regularizer is added to warping field φ to preserve the smoothness of φ . Let V be the voxels in the image space. The smoothness loss is E φ = λ φ (cid:88) v ∈ V ||∇ φ ( v ) || , where ∇ φ ( v ) = ( ∂φ ( v ) ∂x , ∂φ ( v ) ∂y , ∂φ ( v ) ∂z ) . (5) To showcase the concept of our cycle-consistent image simulation, we first evalu-ated the method on a synthetic dataset by omitting the warping field component,
Liu et al.
Back propagation Guided Back-propagation Grad-CAM Guided Grad-CAM Ours (Conv)
Ours (CondConv)
Ground Truth(b) Raw Group 2 (c) Simulated Group 1 (d) Cycle-back Group 2 O u r s ( C ond C on v ) G r ad - C A M O u r s ( C on v ) G u i ded B a ck - p r opaga t i on B a ck - p r opaga t i on G u i ded G r ad - C A M V i s ua li z a t i on s NCC (a) (e)(f) (g) (h)Raw Group 1 Simulated Group 2 Cycle-back Group 1 𝐺 ! 𝐺 " 𝐺 " 𝐺 ! Fig. 3. (a) The group-separating pattern was the magnitude of two off-diagonal Gaus-sians. (b,c,d) The learned simulators could reduce and increase the intensity of off-diagonal Gaussians of a given image in a cycle-consistent fashion; (e) Normalizedcross-correlation (NCC) between the ground-truth pattern and the pattern derivedby different approaches. Bottom: visualizations of the group-separating patterns. so the method could learn generic patterns that influenced the prediction of thetrained classifier. We then incorporated the warping-field learning (Section 3.3)to explicitly investigate the shape change linked to two brain disorders on tworeal neuroimaging datasets.
We generated a synthetic dataset comprised of two groups of data, eachcontaining 512 images of resolution 32 ×
32 pixels. Each image was generatedby 4 Gaussians, whose locations randomly varied within each of the 4 blocks(Fig. 3b). We assume the magnitude of the two off-diagonal Gaussians definedthe differential pattern between the two cohorts. Specifically, the magnitudewas sampled from a uniform distribution U (1 ,
5) for each image from Group 1and from U (4 ,
8) (with stronger intensities) for Group 2 (Fig. 3a). On the otherhand, the magnitude of the two diagonal Gaussians was sampled from U (1 ,
6) andregarded as subject-specific information impartial to group assignment. Gaussiannoise was added to the images with standard deviation 0 . Implementation.
We first trained a classifier to distinguish the two groupson 80% of the data. The classifier network ( P ) comprised of 3 stacks of 2D con-volution (feature dimension = { , , } ), ReLU, and max-pooling layers. Theresulting 128 features were fed to a multi-layer perceptron with one hidden layerof dimension 16 and ReLU activation. Training the classifier resulted in a clas-sification accuracy of 87.5% on the remaining 20% testing images. eep Visualization 7 Our goal here was to train the simulators of Fig. 1 to visualize the group-separating pattern learned by the classifier. To do so, we designed the simula-tor as a U-net structure with skip connections. The encoder was 4 stacks of 2DCondConv (feature dimension = { , , , } ), BatchNorm, LeakyReLu, and max-pooling layers. Each CondConv operation used 3 experts ( K = 3) as adoptedin the original implementation of [14]. The resulting 64 features were fed into afully connected layer of dimension 64 and ReLU activation. The decoder had aninverse structure of the encoder by replacing the pooling layers with up-samplinglayers. The warping field was not used in this experiment, so the networks di-rectly generated simulated images. The logit shift threshold was set to δ = 5. Metrics and Baselines.
For each test image, we aimed to generate a visu-alization defining the pattern that drove the prediction of the classifier. Basedon the construction of the synthetic data, we generated the ground-truth pat-tern as the magnitude difference associated with the two off-diagonal Gaussians(Fig. 3h). For our model, we generated the visualization as the intensity differ-ence between the input test image ( X ) and the simulated image ( ˆ X ) producedby the model. We also generated visualizations through 4 baseline approaches:back-propagation (BP), guided BP [7], Grad-CAM, and guided Grad-CAM [8].To show the importance of using conditional convolution for our model, we alsogenerated the pattern using our model trained with two separate encoders usingconventional convolution. As the results of different approaches had differentscales, each estimated pattern was compared with the ground-truth using nor-malized cross-correlation (NCC). Results.
Fig. 3 shows two examples of the learned simulation. For a trainingimage from Group 2 (Fig. 3b), the simulator reduced the intensity of off-diagonalGaussians, indicating that the model successfully captured the group-separatingpatterns (Fig. 3c). Meanwhile, the model preserved subject-specific informationincluding the location and magnitude of the two diagonal Gaussians. Throughcycle-consistent simulation, the model also accurately recovered the input image(Fig. 3d). In line with the visual comparison, the pattern generated by our model(Fig. 3g) only focused on the off-diagonal Gaussians and closely resembled theground-truth (Fig. 3h). Note, when replacing the CondConv with conventionalconvolution, the pattern became less robust (Fig. 3f). On the other hand, thevisualizations derived by BP, guided BP and guided Grad-CAM were noisy asthe saliency values frequently switched signs. This behavior was inconsistent withour data construction, where the magnitude change of the Gaussians had thesame sign at each voxel. The pattern associated with Grad-CAM was too smoothand could not accurately locate the object of interest. Lastly, this qualitativeanalysis was supported by the NCC metric (Fig. 3e), which indicates our modelwith CondConv was the most accurate approach for defining the pattern.
We then evaluated the proposed model on 1344 T1-weighted MRIsfrom the Alzheimer’s Disease Neuroimaging Initiative (ADNI1). The datasetconsisted of images from 229 Normal Control (NC) subjects (age: 76 ± Liu et al. and 185 subjects with Alzheimer’s Disease (75.3 ± × ×
64 volume, and transforming image intensities within the brainmask to z-scores. This dataset was randomly split into 80% training and 20%testing on the subject level (images of the same subject either belonged to thetraining or testing set).
Implementation.
We first trained a classifier P containing 4 stacks of 3 × × { , , , } ), ReLU, and max-pooling layers. The resulting 512 features were fed into a multi-layer perceptronwith one hidden layer of dimension 64 and ReLU activation. Based on this ar-chitecture, the classifier achieved 88% NC/AD classification accuracy (balancedaccuracy) on the testing set. Note, as the goal of our work was to visualize atrained classifier as opposed to optimizing the classification accuracy on a par-ticular dataset, we did not consider the dependency of longitudinal scans forsimplicity. To interpret this trained classifier, we adopted a similar simulator ar-chitecture as in the synthetic experiment while using 5 convolutional stacks with3D CondConv (feature dimension = { , , , , } ), a fully connected layerof dimension 512, and a 3-channel output (warping field φ ). We set λ φ = 0 . δ = 12 .
5. The simulators were trained on all theNC and AD subjects by an Adam optimizer for 45 epochs with a learning rateof 1e-4.
Results.
We first show the impact of the logit shift loss on the cycle-consistency of the simulation. Fig. 4a displays the logit values of all raw testingimages predicted by the classifier P (blue curve). After removing and injectingdisease patterns through the cycle-consistent simulators, the logit values consis-tently decreased and increased while preserving their relative positions. However,if we replaced the logit shift loss by the adversarial loss based on binary cross-entropy [13] (BCE, Fig. 4b), the logit values of the simulated and cycle-back P r ed i c t ed Log i t b y t he C l a ss i f i e r P r ed i c t ed Log i t b y t he C l a ss i f i e r Images Images 𝐺 ! 𝐺 " (a) Logit Shift Loss (b) Binary Adversarial Loss (BCE) Fig. 4.
Predicted logic values by the classifier of all raw AD images (blue) in the test set,simulated images after removing disease patterns (orange), and cycle-back simulations(green). Images are re-ordered based on the raw logic values. The simulator is learnedbased on (a) the proposed logit loss or (b) the binary adversarial loss .eep Visualization 9 (a) raw NC image (b) simulated image (c) Jacobian mapGrad-CAM Guided Grad-CAM BP Guided BP0.5-0.5 E x p a n s i o n S h r i n k a g e (d) raw AD image (e) simulated image (f) Jacobian map 0.5-0.5 E x p a n s i o n S h r i n k a g e Injecting Disease Patterns Removing Disease Patterns O u r s B a s e li ne Grad-CAM Guided Grad-CAM BP Guided BP 𝐺 ! 𝐺 " Fig. 5.
Example visualization of our proposed approach and the baselines. Color scaleswere omitted for baseline approaches as they are arbitrary across models and subjects.All the computation was performed in the down-sampled space and resized to theoriginal resolution for easy visualization. images became all uniform. This was undesirable as the goal of the simulatorwas to uncover the pattern that correlated with the severity of the brain dis-order, which was encoded by the magnitude of the logit values. Using binaryadversarial loss simply ‘fooled’ the classifier but lost this important information.Fig. 5b shows an simulated image after injecting the AD pattern into the rawimage of a control subject. By directly comparing the two gray scale images, weobserve enlargement of the ventricles and cerebrospinal fluid (CSF) and atrophyof brain tissue. This pattern comported with the effects of AD reported in priorliterature [16]. Moreover, the morphological change captured by the simulatorcan be quantitatively measured by the log of Jacobian determinant of the warp-ing field φ (Fig. 5c). We used this Jacobian map as the visualization producedby our method, which was then compared with the visualization of the samesubject produced by the baseline approaches. In line with the synthetic experi-ment, the Grad-CAM saliency map was smooth and did not locate meaningfulregions with respect to the AD effect. Other saliency maps by BP, guided BP,and guided Grad-CAM were noisy and contained frequent sign change in thesaliency values.As a second example, we also visualize the simulated image (Fig. 5e) af-ter removing the disease pattern from an AD subject and the correspondingJacobian map (Fig. 5f). The patterns were similar to Fig. 5c except for thechange of direction (regions with shrinkage now showed expansion), indicatingthe cycle-consistent nature of the two coupled simulators. Beyond the subject-level visualization, we also produced the Jacobian visualization on the grouplevel by non-rigidly registering the structural maps of all control subjects to atemplate and computing the average Jacobian map in the template space. Thisprocedure was also used to produce the group-level visualization of baseline ap- Ours
OcclusionBack-propagation Guided back-propagationGuided Grad-CAMGrad-CAM
Fig. 6.
Group-level visualization for the ADNI dataset. proaches. We also generated a group-level visualization based on the occlusionmethod (this method cannot be applied to generate subject-level visualization),which first used a sliding window of 8 × × The dataset was comprised of 1225 T1-weighted MRIs of 274 NC subjects (age:47 . ± .
6) and 329 patients diagnosed with alcohol use disorder (age: 49 . ± . eep Visualization 11 Jacobian-0.5 -0.25
Fig. 7.
Left: Jacobian visualization of the AUD effect; Right: gray matter volume of 4brain regions from the orbitofrontal lobe measured for all control and AUD subjects.The volumes scores were corrected for age and sex. the simulators on all images, we computed the group-level Jacobian visualizationfor all the control subjects in the testing set. Results indicate that the CSFexpansion and tissue atrophy were less pronounced compared with the AD effect.Fig. 7 indicates that regions with the most severe tissue shrinkage located in theorbitofrontal lobe. This converge with recent studies that frequently suggestedthe disruption in the structural and functional properties of the orbitofrontalcortex associated with alcohol dependence [17].To confirm this finding, we used a traditional group test to assess the volu-metric measures of 4 regions of interest for each subject: the superior and medicalfronto-orbital gyri, the rectus, and the olfactory gyrus. Only the baseline MR ofeach subject was used in this analysis. The volumetric measures were extractedby segmenting the brain tissue into gray matter, white matter, and CSF via At-ropos and parcellating the regions by the SRI24 atlas. With age and gender beingthe covariates, a general linear model tested the group difference between thecontrol and AUD subjects in the gray matter volume of the 4 regions. All testsresulted in significant group difference based on two-tailed t-statistics ( p < . In this work, we have proposed a novel interpretation/visualization techniquebased on the image-to-image translation scheme. By learning simulators thatcould inject and remove disease patterns from a given image, our approach per-mitted human-understandable and robust visualization on both the subject leveland group level. While we used Jacobian maps as the primary way of visualizingvolume change, the simulation allows the quantification of other morphologicalchanges (e.g., using Laplacian maps for curvature analysis of the cortical sur-face) and can be readily combined with a priori regional analysis (e.g., Fig. 7).Our method also has great generalizability as it is independent on the classi-fier’s architecture. In summary, our work marks an important step towards theapplication of deep learning in neuroimaging studies.
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