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+# CUD-NET: Color Universal Design Neural Filter for the Color Weakness
+
+Anonymous Author(s)   
+Affiliation   
+Address   
+email
+
+# Abstract
+
+1 Information on images should be visually understood to anyone, including the color   
+2 weakness. However, it is not recognizable if color that seems distorted to the color   
+3 weakness meets an adjacent object. We suggest CUD-NET1 based on convolutional   
+4 deep neural network to generate color universal design (CUD) images that satisfy   
+5 both color preservation and distinguishment of color for input images. CUD-NET   
+6 regresses the node point of the piecewise linear function based on information of   
+7 input images and comprises a specific filter per image. We present the following   
+8 methods to generate CUD images for the color weakness. First, we refine the CUD   
+9 dataset on specific criteria by color experts. Second, the input image information   
+10 is expanded through the pre-processing specialized on the color weakness vision.   
+11 Third, we suggest a multi-modal feature fusion architecture that combines features   
+12 to process expanded images. Finally, we suggest a deformable loss function by the   
+13 composition of the predicted image through the model to avoid the one-to-many   
+14 problems of the dataset.
+
+# 15 1 Introduction
+
+# 16 1.1 Motivation
+
+17 The green and red color blindness are made up of $8 \%$ of males and $0 . 5 \%$ of females in Northern   
+18 European descent[Won11], which is almost up to rate of one person in 20 people. Green and red   
+19 blindness is the most common pattern, followed by blue, yellow, and total color blindness. In this   
+20 paper, we generate Color Universal Design (CUD) images, which are color weakness friendly design   
+21 forms, through deep learning around the aspect of the red color weakness (protanopia) and green   
+22 color weakness (deuteranopia) vision. Protanopia is insensitive to red color and deuteranopia is   
+23 insensitive to green color, although it varies depending on individual color weakness extent.
+
+There are studies that help color discrimination to the color weakness, including wearable devices and surgeries[VZCR20]. However, since these research require time and cost, we simply generate CUD images with an image enhancement method based on deep learning to make the corresponding color visible for the color weakness. For an example of the left-above image $I$ in Figure 1, the people who are not color weakness can distinguish the letter $\cdot 5 '$ in the image. But as a deuteranopia vision in left-below image $I ^ { d }$ , the surrounding color and the letter $\cdot 5 '$ are very analogous, making it ambiguous to distinguish the bound of adjacent object. The right-bottom target image ${ \bf \bar { \boldsymbol { T } } } ^ { d }$ , refined image by color expert designers, shows that the letter $\cdot 5 '$ appeared well at the deuteranopia vision. Here, we define the non-CUD objects as the letter $\cdot 5 '$ and surroundings invisible to deuteranopia vision in the image $I$ , and define the CUD objects as the letter $\bullet _ { 5 } ,$ and surroundings visible to deuteranopia vision in the image $T$ . In other words, CUD object means that adjacent objects are distinguishable on both the
+
+![](images/8e40a88186fe991a1f5b33f0d69f552be1b201d8e8b9ad49435e47363052c85c.jpg)  
+Figure 1: Comparisons of the non-CUD image, our CUD-NET’s predicted image, and CUD image. The above row is represented in normal vision, and below row is represented in deuteranopia vision.
+
+35 normal vision and the color weakness vision. The non-CUD object means that adjacent objects are   
+36 distinguishable on normal vision but not the color weakness vision. Consequently, we generate $\hat { I }$ that   
+37 satisfies CUD with a specific filter to the image $I$ .   
+38 We want to apply as weak filter as possible to CUD objects to preserve color, which requires a   
+39 certain level of object comprehension mechanism to do so. There are various studies from classic   
+40 PCA[WEG87] to machine learning-based object segmentation methods[TSC20, $Z \mathrm { G L } ^ { * } 2 0 ]$ to define   
+41 specific objects or areas in image. The research on semantic segmentation, which even provides labels   
+42 between objects, seems that deep learning still does not have a complete comprehension of all objects   
+43 in the real-world. The visual question answering to arbitrary questions about object’s interactions,   
+44 the most general issue on comprehension of object, does not have high transmission power to be   
+45 practical uses $[ \mathrm { A H B ^ { * } } 1 8$ , $\mathrm { K Z G ^ { * } } 1 7$ , $\mathrm { L Y L } ^ { * } 2 0 ]$ . Therefore, we expand feature of the input image around   
+46 the information of color weakness vision and define the robust neural filter. In summary, we suggest   
+47 a CUD-NET that generates an image suitable for CUD, while complying with the color preservation   
+48 for the source image.   
+49 In this paper, we suggest the Color Universal Design Network (CUD-NET) to satisfy both color   
+50 preservation and contrast of non-CUD objects (CUD suitability). We introduce 4 core contributions   
+51 of CUD-NET.
+
+• Dataset refinement criteria for CUD image We refine training data into two groups, the one with a simple color tone image based on H and $\mathrm { v }$ in the HSV color space, the other with two or more non-CUD objects that must be distinguished in publications. • Image pre-processing for CUD-NET We carry out pre-processing to expand the information of the input image. Input image $I$ is reconstructed with three expanded feature information with noise removed. Multi-modal feature fusion architecture We define a feature layer, the fusion layer, and a regression layer to handle pre-processed images. The three features from the feature extracting layer are combined into the one fusion feature, and finally a filter is constructed by regressing the node point of the piecewise linear function, or indicator of filter. • Variational loss function We suggest a deformable loss function by the composition of the predicted image through the model. Our data have a problem of one-to-many, where the specific color in input image $I$ is mapped into multiple colors in target image $T$ .
+
+# 65 1.2 Related Works
+
+66 Image-to-Image translation based on GAN GAN is used in various image translation areas,   
+67 including image generation, style transfer, and colorization[KWK21, IZZE17]. In a preliminary   
+68 experiment, Cycle-GAN[PEZZ20] has reached the best performance in maximizing the contrast of   
+69 non-CUD objects. However, our goal is to keep the color preservation of the input image as well,   
+70 so in the case of black color, which has lost all its color of the input image, it is considered the   
+71 worst case for color preservation. Enlighten-GAN[JGL $^ { * } 2 1$ ] complements those instability, enabling   
+72 them to generate more stable results on color preservation. But since most of the GAN-based image   
+73 translation fixes the size of the predicted image, reshaping a high-resolution image causes information   
+74 loss of source image. Also, it is difficult to reconstruct the complete geometry for the source image   
+75 as it generates images through the dilated convolution layer.   
+76 Image enhancement based on neural filter estimation Unlike GAN, there are researches that   
+77 scale the pixel values of images based on neural filter estimation $[ \mathrm { W } \mathrm { Z F ^ { * } } 1 9 $ , DLT18, BCPS19]. Zero  
+78 $\mathrm { D C E } [ \mathrm { G L G } ^ { * } 2 0 ]$ is a low-light image enhancement research that provides a brighter visual display   
+79 of input image. It estimates pixel-wise and high-order filter for dynamic range adjustment of input   
+80 images with lightweight deep network, DCE-Net. DeepLPF $\mathbf { M M M } ^ { * } 2 0 ]$ tried to solve the problem by   
+81 using a graduated filter, elliptical filter, and polynomial filter. The authors not only tried to visually   
+82 enhance the contrast of images but also to comprise stable filters that are easy to understand for   
+83 the spectators while keeping the color preservation. In our problem, however, the contrast factor is   
+84 almost same results as the input image in both visions, while complying the high color preservation,   
+85 resulting over-stable filter. It is assumed that the inability in comprehension of object’s interaction   
+86 leads to over-stable filter.
+
+![](images/b08f9cfa25e49147de6bd5c99c32e6d5058eeef27cd23f658d79d4db5b7758a1.jpg)  
+Figure 2: The ideal color conversion of predicted image between contrast and color preservation. Non-CUD object $a$ should increase the gap compared to the input image and preserve its original color, while the CUD object $b$ maintain both contrast and color.
+
+# 87 2 Methodology
+
+88 We define the ideal predicted image as an increase in the contrast between non-CUD objects and the   
+89 color preservation for the input image. The non-CUD object $a$ should be mapped into $\acute { a }$ and CUD   
+90 object $b$ should preserve its color and contrast like an ideal example of Figure 2. However, as our   
+91 neural filter affects the whole pixels throughout the image, we have the constraint of applying the   
+92 same filter to objects $a$ and $b$ . It is very hard to make the contrast and color of object $b$ exactly the   
+93 same as before the filter adjustment while maximizing the contrast of object $a$ . Therefore, we propose   
+94 a deep learning-based regression to comprise the specific filter per image that maximizes the contrast   
+95 of object $a$ while minimizing the adjustment of features on object $b$ .   
+96 First, we propose a solution to maximize the contrast of the $\mathrm { L }$ channel values in CIELab color   
+97 space[RG19]. We empirically confirmed that protanopia and deuteranopia, which account for the   
+98 most proportion of color weakness, can distinguish the difference by $\mathrm { L }$ channel values in common   
+99 when the non-CUD objects are adjacent to each other. To illustrate Figure 1 again, the $\mathrm { L }$ channel   
+100 value of letter $^ { \bullet } 5 ^ { \bullet }$ in image $I$ is 61 and the surrounding color is 61. The distinguishment between   
+101 the two objects is easy to normal vision, however the image $I ^ { d }$ , the deuteranopia vision, is very   
+102 ambiguous. On the contrary, the CUD target image $T$ and $T ^ { d }$ have a difference of $\mathrm { L }$ channel value 75   
+103 for the letter $\bullet _ { 5 } ,$ and 45 for the surroundings, making it easy to distinguish between the normal and   
+104 the deuteranopia vision. Due to the characteristics of these data, we refine a data pair by defining a   
+105 criterion that separates two invisible non-CUD objects by $\mathrm { L }$ channel values.   
+106 Secondly, we propose a variational loss function and multi-modal feature fusion network for color   
+107 preservation. It can be said that the increase in the contrast of $\mathrm { L }$ channel values between non-CUD   
+108 objects is quantitatively superior, but not in the case of increasing the differences in color preservation   
+109 of input images. When non-CUD objects exist, as a simple example, the most likely way to maximize   
+110 contrast is to polarize the color of the object black and white. But it is the result of complete ignorance   
+111 for color preservation, so just enabling to distinguish between non-CUD objects is not always a good   
+112 answer. A strong filter must be applied to distinguish non-CUD object, but its impact should not be   
+113 too extensive to leading the loss of information in CUD objects. In this paper, we solve this problem   
+114 by taking an appropriate trade-off of color preservation and contrast of L channel value.
+
+# 115 2.1 Dataset refinement criteria for CUD image
+
+116 The training data is refined by two groups. The one is vectorized image with two colors divided   
+117 by value $\mathrm { v }$ and hue degree H in HSV color space[HMKO19], and the other is image with two   
+118 or more objects that must be distinguished while preserving the color of non-CUD objects. The   
+119 training data is grouped about 1,600 color combinations into the same V and then simulates them   
+120 with the deuteranopia vision, converting to the adjacent color family to comply color preservation.   
+121 All conversions are scaled within only S and V in HSV color space to increase at least 15 difference   
+122 in the L channel value of selected non-CUD objects. The colors are combined with the 10 essential H   
+123 and tones, and the similar color simulated with the deuteranopia vision was converted. Consequently,   
+124 the key part of refining training data is preservation of color, allowing the models to comply with the   
+125 same approach on learning.
+
+# 2.2 Image pre-processing
+
+127 Our model regresses node points of piecewise linear function, which will be described in the model   
+128 architecture section, and the final filter is a multiplication operation for the input image. Therefore,   
+129 the multiplication operations of less than the number 1 tend to fade the color saturation. The image   
+130 without color inversion converges the white color value to 1, so if the multiplying value is in the [0,   
+131 1] range, the white color is shifted to the black. By inverting the color of input image, it ignores the   
+132 multiplication operations for white value with 0.   
+133 We generate the map image $I ^ { m }$ based on original RGB input images calculating the difference value   
+134 between the image with an aspect of normal vision and the image with an aspect of deuteranopia vision.   
+135 Recent studies have been conducted to augment the information or expanded the models’ perspective   
+136 through transformer models[JSZK16, RFB15]. In our experiment, however, the transformer model   
+137 tends to generate the predicted image ignoring the source color, which result in the polarized color to   
+138 black and white like Cycle-GAN’s.
+
+$$
+{ \cal I } ^ { m } = \vert i n v e r t ( I ^ { n } ) - i n v e r t ( I ^ { d } ) \vert
+$$
+
+$$
+{ \cal I } ~ = ~ \delta \left( c a t ^ { c h a n n e l } \left( I ^ { n } , I ^ { d } , I ^ { m } \right) \right)
+$$
+
+139 After applying color inversion from the original RGB input image $I ^ { n }$ , we generate the image $I ^ { d }$ with   
+140 an aspect of deuteranopia vision in equation 1. From these two generated images, we can get the   
+141 absolute difference value to compose the map image $I ^ { m }$ . In equation 2, the final input $I$ concatenated   
+142 with $9 \times H \times W$ dimensions passes through the model. The $\bar { \delta } ( . )$ clips output to a range of [0, 1].
+
+# 2.3 Model Architecture
+
+144 CUD-NET regresses the node points of piecewise linear filter function from the input. The value   
+145 of each node points computes the multiplication operation and generates the predicted image. The   
+146 input $I$ is compressed into 3 feature blocks matching each input through convolution layer, pooling   
+147 layer, and global pooling layer. The input with 9 channels is separated into $3 \times 3$ channels before   
+148 passing the model. The first 3 channels are literally used as the main inputs, where the multiplication   
+149 operation takes place, while the remaining 6 channels are used as features.   
+150 First of all, we use multi-modal fusion architecture for three separate inputs to extract expanded   
+151 features. The three inputs converted to the HSV color space pass through a weights-sharing convolu  
+152 tion layer to extract a feature block corresponding to the inputs. Each convolution layer consists of   
+153 kernel size $^ { = 3 }$ , stride $^ { : = 1 }$ , and padding=1, reducing dimension through average pooling. We empirically   
+154 noticed that the most values of output feature have distribution within the range of [-1, 1] with valid   
+155 values for constructing the node points, so we use hyperbolic tan for activation function. Since we   
+156 use inputs with unstructured image size, the last global pooling block holds the size of the feature   
+157 instead of the average pooling block[LCY14].   
+158 The three feature blocks are combined through the multi-modal compact bilinear pooling gate   
+159 $( \mathbf { M C B } ) [ \mathbf { F P Y ^ { * } } 1 6 ]$ , following the fusion process shown in Figure 3. The MCB gate allows both   
+160 features to interact in a multiplicative way with low memory consumption and computation   
+161 times. The fusion features are complemented to enhanced feature through the split attention   
+162 mechanism $[ Z \mathrm { W } Z ^ { \ast } 2 0 ]$ . At the beginning of the experiment, we have applied the convolutional   
+163 block attention mechanism[WPLK18] of each MCB gate, but we found that it does not make sense   
+164 of understanding the feature itself, so we apply only one attention block to the last fusion feature.   
+165 The enhanced feature pass through the fully-connected regression layer. We picked the 64 points   
+166 to be regressed to compose the piecewise linear function, which is empirically confirmed to the   
+167 optimized number of points in this research. The first half of the values construct the node points of   
+168 the S channel and the other half comprise the $\mathrm { v }$ channel in HSV color space. Finally, node points   
+169 become the scaling factors to generate predicted image in equation 3[MMS19].
+
+![](images/6fe42bfba41420f38aecf4a17ab1e4d9b4816d2107844d698cd5beb3f6b072ab.jpg)  
+Figure 3: Overview structure of CUD image generation
+
+$$
+S \left( I _ { i } ^ { s , v } \right) = k _ { 0 } + \sum _ { m = 0 } ^ { M - 1 } \left( k _ { m + 1 } - k _ { m } \right) \delta \left( M I _ { i } ^ { s , v } - m \right)
+$$
+
+170 The total number of node point $M$ , each pixel values of S, V channel in input image $I _ { i } ^ { s , v }$ are   
+171 multiplicated with the slope of actual regressed value $k _ { m }$ , the $m - t h$ generated node point. The   
+172 specific node points $M$ is scaled through a multiplication operation to pixel value of the input image   
+173 according to each node point.
+
+# 174 2.4 Loss function
+
+175 Our dataset has one-to-many problems between input and target data. In dataset pair   
+176 $( I _ { 1 } , T _ { 1 } )$ , $( I _ { 2 } , T _ { 2 } )$ , . . . , $( I _ { n } , T _ { n } )$ , for example, the red color in $I _ { 1 }$ can be targeted to purple color in   
+177 $T _ { 1 }$ , and the red color in $I _ { 2 }$ can be targeted to orange color in $T _ { 2 }$ . With these one-to-many dataset   
+178 structures, we design the loss function $\mathcal { L }$ that expresses the potential and the diversity of predicted   
+179 image in equation 4.
+
+$$
+\mathcal { L } = \sum _ { i = 1 } ^ { N } L a b _ { l o s s } \left( V \left( \Phi \left( \hat { I } _ { i } \right) \right) \right) + H _ { l o s s } \left( \Phi \left( \hat { I } _ { i } \right) \right)
+$$
+
+180 Stencil Masking As explained in the dataset refining criteria, we do not proceed with color   
+181 conversion for all areas in the target images, but only for areas with color combinations that are   
+182 invisible to the deuteranopia (non-CUD object). For this reason, the input image has color regions of   
+183 converting color and unconverting color, which also can be referred to as non-CUD object and CUD   
+184 object. To imply the color bound to model, the stencil masking method is introduced.
+
+$$
+\Phi \left( { \hat { I } } _ { i } \right) = { \hat { I } } _ { i j } \parallel ( I _ { i j } \cdot T _ { i j } )
+$$
+
+185 We consist a stencil maps through the logical and operations ’·’ of each pixel value $I _ { i j }$ , $T _ { i j }$ . Stencil   
+186 map can specify the non-CUD area and be computed with predicted image $\hat { I } _ { i j }$ of logical or operation   
+187 ’ $| |$ ’in equation 5. Consequently, CUD object of the image adjusted with a stencil mask does not carry   
+188 out the neural filter computation, such as the same way we refine the target image. This refined image   
+189 is calculated on the loss function.   
+190 CIELab Loss We use the CIELab channel loss function to maximize the contrast of color on   
+191 deuteranopia vision. To stabilize the contrast and brightness of the predicted image, we calculate the   
+192 MS· SSIM(multi-scale structural similarity[WSB03]) of $\mathrm { L }$ channel.
+
+$$
+L a b _ { l o s s } = \left\| L a b \left( \hat { I } _ { i } ^ { r g b } \right) - L a b \left( T _ { i } ^ { r g b } \right) \right\| _ { 1 } + M S \cdot S S I M \left( L a b \left( \hat { I } _ { i } ^ { L } \right) , L a b \left( T _ { i } ^ { L } \right) \right)
+$$
+
+193 The $L a b \left( . \right)$ expression in equation 6 returns the CIELab channel corresponding to the RGB channel,   
+194 and all calculations are made only on the L channel.   
+195 Histogram Loss We use the histogram loss function to comply with the color preservation of the   
+196 image. The RGB channel is used to preserve its color, contrary to using only the $\mathrm { L }$ channel in other   
+197 loss functions. Handling the RGB channel as a loss function rather than using Lab’s ab channels has   
+198 shown better results on color preservation.
+
+$$
+H _ { l o s s } = - { \omega _ { h i s t } } \int N \left( \hat { I } _ { i } ^ { r g b } ; \sigma \right) - { \cal N } \left( T _ { i } ^ { r g b } ; \sigma \right)
+$$
+
+199 When simply designing a loss function with the L1 distance of the RGB channel pixel values, it was   
+200 very sensitive to certain values and the gradients are diverged, resulting in an untrainable experiment.   
+201 Therefore, we used a gaussian expansion method $[ S \mathbf { A } C ^ { * } 1 7 ]$ denoted by $N ( . )$ to infer a differentiable   
+202 histogram loss function in equation 7. We compute the difference of the RGB channel of the   
+203 differentiable histogram function, which can be altered to mean squared error or cosine similarity.   
+204 The scaler $\omega _ { h i s t }$ is determined in inverse proportion to the size of the input image. By maintaining   
+205 the RGB similarity between the predicted image and the target image, we can comply with the color   
+206 preservation.   
+207 Variational Prediction There are various ways to maximize difference of the L channel in the   
+208 image. And the target image is converted at least two colors compared to the input image. However,   
+209 the predicted image of the model is generated by the neural filter, so it is unpredictable which area   
+210 of color is modified. Therefore, if the color in predicted image is over-shifted or in the color value   
+211 of opposite shifts to the target, the loss will rather increase. In addition to one-to-many problem   
+212 that the data pair itself does not matches one-to-one in a particular color, it is necessary to generate   
+213 alternative predicted image with the same aspect of the data pair. We calculate the loss function with   
+214 a variational prediction based on the predicted image for potential color shifts.   
+215 The first potential is the case of excessive shifts. Assume that $I _ { i } ^ { L } = \{ 7 4 , 4 1 , 7 9 \}$ , $\hat { I } _ { i } ^ { L } = \{ 9 7 , 1 0 , 7 0 \}$ ,   
+216 $T _ { i } ^ { L } \ = \ \{ 5 0 , 4 1 , 8 0 \}$ in L channel value. The first and third components of each image is non-CUD   
+217 objects, and second component is CUD object. Therefore, we refined data paired with a difference of   
+218 15 on L channel. Here, we clip the excessive $\mathrm { L }$ channel value in $\hat { I } _ { i } ^ { L }$ by equation 8. Up to this point,   
+219 no calculation is made as no value is exceeded in this example. The second potential is the case of   
+220 opposite shifts. It can be said that a complete neural filter has been proceeded for value 97, 10, 70   
+221 where $\mathrm { L }$ channel difference is 27. However, if we actually calculate the mean square error between   
+222 $\hat { I } _ { i } ^ { L }$ and $T _ { i } ^ { L }$ , it will be an large value over 1k. Here we can generate alternative predicted image from   
+223 equation 9 and 10.
+
+$$
+c l i p \left( \hat { I } _ { i j } \right) \ = \ \left\{ { m a x } { \left( \hat { I } _ { i j } , { T } _ { i j } \right) } , \qquad I _ { i j } \ > T _ { i j } \right.
+$$
+
+$$
+R _ { 1 } = \ 2 I _ { i j } - \ \hat { I } _ { i j } , R _ { 2 } = \ \hat { I } _ { i j }
+$$
+
+$$
+V \left( { \hat { I } } _ { i j } \right) = a r g m i n \left( \left\| c l i p \left( R _ { 1 , 2 } \right) - T _ { i j } \right\| _ { 2 } \right)
+$$
+
+224 As mentioned above, we define thresholds by the maximum and minimum value of each corresponding   
+225 pixel position of $\hat { I } _ { i } ^ { L }$ and $T _ { i } ^ { L }$ . By computing a difference of residual map and the input image, we   
+226 induce the alternative two images $R _ { 1 }$ , $R _ { 2 }$ . As a result, $\hat { I } _ { i } ^ { L }$ with a smaller L2 distance is selected to   
+227 alternative predicted image in equation 10, and it is finally computed with loss function compared to   
+228 the $T _ { i } ^ { L }$ . The above equation establishes $V \left( \Phi \left( \hat { I } _ { i } \right) \right) = \{ \stackrel { \cdot } { 5 4 } , 4 1 , \stackrel { \cdot } { 8 0 } \}$ and the mean square error to the   
+229 target image is approximately 5, which is agreeable loss value respect to $\hat { I } _ { i } ^ { L }$ itself.   
+230 Identity Loss[ZPIE17, TPW16] We use $\mathcal { L } _ { i d e n t i t y } \left( T _ { i } \right)$ to apprehend the CUD object to the model.   
+231 In the case of target image that already satisfy the CUD, the filter should be relatively weakly applied   
+232 than input image. The input of identity loss is target image $T _ { i j }$ instead of input image $I _ { i j }$ , and the   
+233 reference of the loss function is also target image $T _ { i j }$ to maintain the value itself. In computing   
+234 identity loss, we do not require variational prediction as we cannot judge the potential region by   
+235 equation 10.
+
+# 236 3 Experiments
+
+237 The experiment was performed with Tesla V100 SXM2 and Intel Xeon Gold 5120 and the computation   
+238 speed was about 40 images per minutes. We refined a dataset with Adobe Photoshop to maximize   
+239 contrast in the L channel by adjusting saturation and brightness for areas that require color conversion   
+240 based on deuteranopia vision simulation. Color experts has refined about 1,500 vectorized image for   
+241 the training data and 300 publication images for the validation data. All the comparative experimental   
+242 models used the same train, test, validation data in this paper. We used the inference data in   
+243 publications, which is almost composed of vectorized images, as colors often appear distorted in a   
+244 gradation-rich image. The Figure 4 is arranged in descending order of the number of combinations in   
+245 colors from the top image.   
+246 Both structure similarity (SSIM)[ZBSS04] and peak signal to noise ratio (PSNR) in Table 1 can   
+247 indicate whether the image is suitable for CUD or not. As a notable aspect, the result has shown that   
+248 comparative models with lower metrics are sensitive to high-gradation input images, which generated   
+249 color-heterogeneous image. SSIM and PSNR itself can determine the increase in contrast compared   
+250 to the target image but do not determine whether the color preservation complied. Therefore, we   
+251 evaluated SSIM and PSNR with three references, inputs images $I$ , predicted images $\hat { I }$ , and target   
+252 images $T$ . The higher the estimation of the $\hat { I }$ and $I$ , the more color preservation factor worked.   
+253 The higher the estimation of the $\hat { I }$ and $T$ , the more increase in contrast can be considered. We also   
+254 define SSIM mean absolute error, PSNR mean absolute error to measure the extent of the conversion   
+255 between the $F : I  T$ and $F : \dot { I }  \hat { I }$ in equation 11 and 12, respectively. The $N$ is total number   
+256 of inference data.
+
+$$
+S S I M \cdot M A E =  \frac { 1 } { N } \sum _ { i = 1 } ^ { N } | S S I M ( \hat { I } _ { i } , \mathcal { T } _ { i } ) - S S I M ( I _ { i } , T _ { i } ) |
+$$
+
+$$
+P S N R \cdot M A E =  \frac { 1 } { N } \sum _ { i = 1 } ^ { N } | P S N R ( \hat { I } _ { i } , \mathcal { T } _ { i } ) - P S N R ( I _ { i } , T _ { i } ) |
+$$
+
+![](images/ee74ef15b1c4bf5acba45467aa3b157cb56fa3118986b351ff3cd98fe81ae34d.jpg)  
+Figure 4: Comparisons of predicted images in deuteranopia vision. The color experts selected the validation data that do not satisfy the CUD in publications.
+
+Table 1: Evaluation table of comparison experiment. The CUD-NET with a low bottle-neck feature achieves better results in the experiment of the deuteranopia and the protanopia subjects(Figure 5), although the evaluation metrics are lower than that of CUD-NET.   
+
+<table><tr><td rowspan=1 colspan=1>Architecture</td><td rowspan=1 colspan=1>sSIM(i,1)</td><td rowspan=1 colspan=1>SSIM(i,T)</td><td rowspan=1 colspan=1>PSNR(i,1)</td><td rowspan=1 colspan=1>PSNR(i,T)</td><td rowspan=1 colspan=1>SSIM-MAE</td><td rowspan=1 colspan=1>PSNR·MAE</td></tr><tr><td rowspan=2 colspan=1>Cycle-GANZero-DCE</td><td rowspan=1 colspan=1>0.630</td><td rowspan=1 colspan=1>0.634</td><td rowspan=1 colspan=1>13.28</td><td rowspan=1 colspan=1>13.83</td><td rowspan=1 colspan=1>0.3191</td><td rowspan=1 colspan=1>8.4430</td></tr><tr><td rowspan=1 colspan=1>0.924</td><td rowspan=1 colspan=1>0.888</td><td rowspan=1 colspan=1>21.95</td><td rowspan=1 colspan=1>18.67</td><td rowspan=1 colspan=1>0.0661</td><td rowspan=1 colspan=1>3.7300</td></tr><tr><td rowspan=2 colspan=1>DeepLPFEnlighten-GAN</td><td rowspan=1 colspan=1>0.850</td><td rowspan=1 colspan=1>0.831</td><td rowspan=1 colspan=1>26.31</td><td rowspan=1 colspan=1>20.34</td><td rowspan=1 colspan=1>0.1220</td><td rowspan=1 colspan=1>2.0566</td></tr><tr><td rowspan=1 colspan=1>0.820</td><td rowspan=1 colspan=1>0.808</td><td rowspan=1 colspan=1>21.85</td><td rowspan=1 colspan=1>19.58</td><td rowspan=1 colspan=1>0.1470</td><td rowspan=1 colspan=1>3.9983</td></tr><tr><td rowspan=1 colspan=1>Enlighten-GAN(scaled)</td><td rowspan=1 colspan=1>0.966</td><td rowspan=1 colspan=1>0.921</td><td rowspan=1 colspan=1>24.86</td><td rowspan=1 colspan=1>21.36</td><td rowspan=1 colspan=1>0.0392</td><td rowspan=1 colspan=1>3.4937</td></tr><tr><td rowspan=2 colspan=1>CUD-NET(low bottle-neck feature)CUD-NET</td><td rowspan=1 colspan=1>0.897</td><td rowspan=1 colspan=1>0.866</td><td rowspan=1 colspan=1>27.77</td><td rowspan=1 colspan=1>21.01</td><td rowspan=1 colspan=1>0.0901</td><td rowspan=1 colspan=1>2.0826</td></tr><tr><td rowspan=1 colspan=1>0.962</td><td rowspan=1 colspan=1>0.924</td><td rowspan=1 colspan=1>29.54</td><td rowspan=1 colspan=1>21.19</td><td rowspan=1 colspan=1>0.0312</td><td rowspan=1 colspan=1>1.4760</td></tr></table>
+
+257 Cycle-GAN and Zero-DCE showed worse result than others. Cycle-GAN model had difficulty   
+258 reconstructing a geometry of a particular object, and overall color had low saturation and brightness,   
+259 resulting in color conversion into an almost grey scale image. Zero-DCE is faded in color, and the   
+260 contrast was not much different from the input image. The overall image lost its color preservation,   
+261 which we focused to solve in this paper.   
+262 DeepLPF meets both the color preservation and contrast that we deal with for. However, DeepLPF   
+263 tends to color be over-stably filtered for the images with fewer color combinations. Although the   
+264 color preservation has complied better than other experiments, there were many failed results from   
+265 the perspective of contrast, which the over-stable filter leads to by DeepLPF.   
+266 Remarkably, predicted images of Enlighten-GAN showed reasonable results. However, simple color   
+267 combinations or the images with already satisfying the CUD often showed results degenerated with   
+268 low CUD suitability. Enlighten-GAN was able to generate the results we targeted, but its deviation of   
+269 filter is so high that it sometimes failed to satisfy the contrast even on simple images or decreased   
+270 the contrast. As the problem of GAN-based method including Enlighten-GAN, moreover, model   
+271 fixes the width and height of the predicted image. If width and height of $T$ and $I$ down-scaled
+
+to size of Enlighten-GAN 272 $\hat { I }$ (approximately 25K pixels in this experiment), the $S S I M \left( \hat { I } , I \right)$ and $P S N R \left( \hat { I } , T \right)$ showed higher estimation in some metrics than CUD-NET. In the opposite case of $\hat { I }$ up-scaled to size of $T$ and $I$ , the significantly low estimation was recorded due to the information loss of up-scaling problem.
+
+CUD-NET showed stable and robust predicted images in both color preservation and increase in the contrast compared to other experiments. In comparing the values in the same region of $I$ and $\hat { I }$ , the model scaled two $\mathrm { L }$ channel values with opposite side in the most of case, the one goes up and the other goes down. When we reduced the number of bottle-neck feature of model, it tends to record relatively high deviation of filter scales according to the number of combinations of colors. In summary, the CUD-NET showed the highest estimations for 4 evaluation metrics. Moreover, as our model adopted a neural filter unlike generation models, there is no loss of information regarding the scaling of predicted images.
+
+![](images/9a2ce8b4db1667e120d3e391edc4e605f10711786bdbd70de95e46dfcb47ad39.jpg)  
+Figure 5: The box bar is ordered to the left side, input image $I$ , Enlighten-GAN, DeepLPF, CUDNET. The y position of box bar represents a mean and length of the box bar represents a deviation of each experiment. The lower the graph is, the higher the rank is.
+
+284 The figure 5 shows the evaluation of the deuteranopia and the protanopia. The evaluation metrics   
+285 consist of object distinguishability and color harmony in order of input image I, predicted image   
+286 of Enlighten GAN, DeepLPF, and CUD-NET. User study has tested upon the total of 6 subjects, 4   
+287 deuteranomaly and 2 protanomaly. The subjects were asked to list the ranks of object distinguishability   
+288 and color harmony of 4-paired-image for each model-blinded item. As the experimental results,   
+289 the deuteranopia subject ranked the 1-st in the object distinguishability of CUD-NET at an average   
+290 rank of 1.821, followed by Enlighten-GAN at an average rank of 2.512. Similarly, the protanopia   
+291 subject also ranked the 1-st in CUD, followed by Enlighten-GAN, DeepLPF, and input images. The   
+292 evaluation of color harmony showed that the subjects tend to assume that the image with a good   
+293 object distinguishability has good color harmony preferentially. For a total of six subjects, the five   
+294 subjects chose the CUD-NET, with the exception of one who ranked Enlighten-GAN by a subtle gap
+
+# 295 4 Conclusion
+
+296 In this paper, we proposed deep network to generate CUD images from non-CUD input images. The   
+297 pre-processing and multi-modal fusion layer could comprehend the information for color weakness,   
+298 and the variational loss function makes the model further adapt to CUD dataset. Compared to other   
+299 research, we are able to maintain high-resolution images and both stable color preservation and   
+300 contrast with neural filter per images.   
+301 Our current research shows a robust filter for a single color, such as vectorized images, but it is   
+302 difficult to expect stable results in the case of a real-world image with high gradation in hues. We   
+303 consider the same limitation of our work when the certain pixel values react sensitively, making noise   
+304 appear more prominent in the predicted image. In the future, we plan to create additional datasets   
+305 with gradation on the vectorized image and focus on the fusion layer to improve performance of the   
+306 model.   
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+
+# 403 Checklist
+
+1. For all authors...
+
+(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes]   
+(b) Did you describe the limitations of your work? [Yes] See on conclusion section   
+(c) Did you discuss any potential negative societal impacts of your work? [N/A] This work is for positive societal impacts   
+(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
+
+2. If you ran experiments...
+
+(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] See on github: https://github.com/Anonymous68864576/CUD-NET-anonymous
+
+(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] on github repository   
+(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] See on section 2.3   
+(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See on Experiment section
+
+3. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...
+
+(a) If your work uses existing assets, did you cite the creators? [Yes] Cooperated with Co-author   
+(b) Did you mention the license of the assets? [Yes] on github repository   
+(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] on github repository   
+(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [Yes] on github repository   
+(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]

parse/train/3g5KdPD8LIL/3g5KdPD8LIL_content_list.json

@@ -0,0 +1,1021 @@
+[
+    {
+        "type": "text",
+        "text": "CUD-NET: Color Universal Design Neural Filter for the Color Weakness ",
+        "text_level": 1,
+        "bbox": [
+            181,
+            122,
+            816,
+            171
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous Author(s)   \nAffiliation   \nAddress   \nemail ",
+        "bbox": [
+            423,
+            222,
+            578,
+            276
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
+        "bbox": [
+            462,
+            313,
+            535,
+            329
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 Information on images should be visually understood to anyone, including the color   \n2 weakness. However, it is not recognizable if color that seems distorted to the color   \n3 weakness meets an adjacent object. We suggest CUD-NET1 based on convolutional   \n4 deep neural network to generate color universal design (CUD) images that satisfy   \n5 both color preservation and distinguishment of color for input images. CUD-NET   \n6 regresses the node point of the piecewise linear function based on information of   \n7 input images and comprises a specific filter per image. We present the following   \n8 methods to generate CUD images for the color weakness. First, we refine the CUD   \n9 dataset on specific criteria by color experts. Second, the input image information   \n10 is expanded through the pre-processing specialized on the color weakness vision.   \n11 Third, we suggest a multi-modal feature fusion architecture that combines features   \n12 to process expanded images. Finally, we suggest a deformable loss function by the   \n13 composition of the predicted image through the model to avoid the one-to-many   \n14 problems of the dataset. ",
+        "bbox": [
+            148,
+            344,
+            766,
+            539
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "15 1 Introduction ",
+        "text_level": 1,
+        "bbox": [
+            148,
+            564,
+            312,
+            580
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "16 1.1 Motivation ",
+        "text_level": 1,
+        "bbox": [
+            153,
+            594,
+            289,
+            609
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "17 The green and red color blindness are made up of $8 \\%$ of males and $0 . 5 \\%$ of females in Northern   \n18 European descent[Won11], which is almost up to rate of one person in 20 people. Green and red   \n19 blindness is the most common pattern, followed by blue, yellow, and total color blindness. In this   \n20 paper, we generate Color Universal Design (CUD) images, which are color weakness friendly design   \n21 forms, through deep learning around the aspect of the red color weakness (protanopia) and green   \n22 color weakness (deuteranopia) vision. Protanopia is insensitive to red color and deuteranopia is   \n23 insensitive to green color, although it varies depending on individual color weakness extent. ",
+        "bbox": [
+            147,
+            621,
+            825,
+            718
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "There are studies that help color discrimination to the color weakness, including wearable devices and surgeries[VZCR20]. However, since these research require time and cost, we simply generate CUD images with an image enhancement method based on deep learning to make the corresponding color visible for the color weakness. For an example of the left-above image $I$ in Figure 1, the people who are not color weakness can distinguish the letter $\\cdot 5 '$ in the image. But as a deuteranopia vision in left-below image $I ^ { d }$ , the surrounding color and the letter $\\cdot 5 '$ are very analogous, making it ambiguous to distinguish the bound of adjacent object. The right-bottom target image ${ \\bf \\bar { \\boldsymbol { T } } } ^ { d }$ , refined image by color expert designers, shows that the letter $\\cdot 5 '$ appeared well at the deuteranopia vision. Here, we define the non-CUD objects as the letter $\\cdot 5 '$ and surroundings invisible to deuteranopia vision in the image $I$ , and define the CUD objects as the letter $\\bullet _ { 5 } ,$ and surroundings visible to deuteranopia vision in the image $T$ . In other words, CUD object means that adjacent objects are distinguishable on both the ",
+        "bbox": [
+            168,
+            723,
+            825,
+            876
+        ],
+        "page_idx": 0
+    },
+    {
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+        "image_caption": [
+            "Figure 1: Comparisons of the non-CUD image, our CUD-NET’s predicted image, and CUD image. The above row is represented in normal vision, and below row is represented in deuteranopia vision. "
+        ],
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+        "text": "35 normal vision and the color weakness vision. The non-CUD object means that adjacent objects are   \n36 distinguishable on normal vision but not the color weakness vision. Consequently, we generate $\\hat { I }$ that   \n37 satisfies CUD with a specific filter to the image $I$ .   \n38 We want to apply as weak filter as possible to CUD objects to preserve color, which requires a   \n39 certain level of object comprehension mechanism to do so. There are various studies from classic   \n40 PCA[WEG87] to machine learning-based object segmentation methods[TSC20, $Z \\mathrm { G L } ^ { * } 2 0 ]$ to define   \n41 specific objects or areas in image. The research on semantic segmentation, which even provides labels   \n42 between objects, seems that deep learning still does not have a complete comprehension of all objects   \n43 in the real-world. The visual question answering to arbitrary questions about object’s interactions,   \n44 the most general issue on comprehension of object, does not have high transmission power to be   \n45 practical uses $[ \\mathrm { A H B ^ { * } } 1 8$ , $\\mathrm { K Z G ^ { * } } 1 7$ , $\\mathrm { L Y L } ^ { * } 2 0 ]$ . Therefore, we expand feature of the input image around   \n46 the information of color weakness vision and define the robust neural filter. In summary, we suggest   \n47 a CUD-NET that generates an image suitable for CUD, while complying with the color preservation   \n48 for the source image.   \n49 In this paper, we suggest the Color Universal Design Network (CUD-NET) to satisfy both color   \n50 preservation and contrast of non-CUD objects (CUD suitability). We introduce 4 core contributions   \n51 of CUD-NET. ",
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+        "text": "• Dataset refinement criteria for CUD image We refine training data into two groups, the one with a simple color tone image based on H and $\\mathrm { v }$ in the HSV color space, the other with two or more non-CUD objects that must be distinguished in publications. • Image pre-processing for CUD-NET We carry out pre-processing to expand the information of the input image. Input image $I$ is reconstructed with three expanded feature information with noise removed. Multi-modal feature fusion architecture We define a feature layer, the fusion layer, and a regression layer to handle pre-processed images. The three features from the feature extracting layer are combined into the one fusion feature, and finally a filter is constructed by regressing the node point of the piecewise linear function, or indicator of filter. • Variational loss function We suggest a deformable loss function by the composition of the predicted image through the model. Our data have a problem of one-to-many, where the specific color in input image $I$ is mapped into multiple colors in target image $T$ . ",
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+        "type": "text",
+        "text": "65 1.2 Related Works ",
+        "text_level": 1,
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+        "text": "66 Image-to-Image translation based on GAN GAN is used in various image translation areas,   \n67 including image generation, style transfer, and colorization[KWK21, IZZE17]. In a preliminary   \n68 experiment, Cycle-GAN[PEZZ20] has reached the best performance in maximizing the contrast of   \n69 non-CUD objects. However, our goal is to keep the color preservation of the input image as well,   \n70 so in the case of black color, which has lost all its color of the input image, it is considered the   \n71 worst case for color preservation. Enlighten-GAN[JGL $^ { * } 2 1$ ] complements those instability, enabling   \n72 them to generate more stable results on color preservation. But since most of the GAN-based image   \n73 translation fixes the size of the predicted image, reshaping a high-resolution image causes information   \n74 loss of source image. Also, it is difficult to reconstruct the complete geometry for the source image   \n75 as it generates images through the dilated convolution layer.   \n76 Image enhancement based on neural filter estimation Unlike GAN, there are researches that   \n77 scale the pixel values of images based on neural filter estimation $[ \\mathrm { W } \\mathrm { Z F ^ { * } } 1 9 $ , DLT18, BCPS19]. Zero  \n78 $\\mathrm { D C E } [ \\mathrm { G L G } ^ { * } 2 0 ]$ is a low-light image enhancement research that provides a brighter visual display   \n79 of input image. It estimates pixel-wise and high-order filter for dynamic range adjustment of input   \n80 images with lightweight deep network, DCE-Net. DeepLPF $\\mathbf { M M M } ^ { * } 2 0 ]$ tried to solve the problem by   \n81 using a graduated filter, elliptical filter, and polynomial filter. The authors not only tried to visually   \n82 enhance the contrast of images but also to comprise stable filters that are easy to understand for   \n83 the spectators while keeping the color preservation. In our problem, however, the contrast factor is   \n84 almost same results as the input image in both visions, while complying the high color preservation,   \n85 resulting over-stable filter. It is assumed that the inability in comprehension of object’s interaction   \n86 leads to over-stable filter. ",
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+        "image_caption": [
+            "Figure 2: The ideal color conversion of predicted image between contrast and color preservation. Non-CUD object $a$ should increase the gap compared to the input image and preserve its original color, while the CUD object $b$ maintain both contrast and color. "
+        ],
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+        "text": "87 2 Methodology ",
+        "text_level": 1,
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+        "text": "88 We define the ideal predicted image as an increase in the contrast between non-CUD objects and the   \n89 color preservation for the input image. The non-CUD object $a$ should be mapped into $\\acute { a }$ and CUD   \n90 object $b$ should preserve its color and contrast like an ideal example of Figure 2. However, as our   \n91 neural filter affects the whole pixels throughout the image, we have the constraint of applying the   \n92 same filter to objects $a$ and $b$ . It is very hard to make the contrast and color of object $b$ exactly the   \n93 same as before the filter adjustment while maximizing the contrast of object $a$ . Therefore, we propose   \n94 a deep learning-based regression to comprise the specific filter per image that maximizes the contrast   \n95 of object $a$ while minimizing the adjustment of features on object $b$ .   \n96 First, we propose a solution to maximize the contrast of the $\\mathrm { L }$ channel values in CIELab color   \n97 space[RG19]. We empirically confirmed that protanopia and deuteranopia, which account for the   \n98 most proportion of color weakness, can distinguish the difference by $\\mathrm { L }$ channel values in common   \n99 when the non-CUD objects are adjacent to each other. To illustrate Figure 1 again, the $\\mathrm { L }$ channel   \n100 value of letter $^ { \\bullet } 5 ^ { \\bullet }$ in image $I$ is 61 and the surrounding color is 61. The distinguishment between   \n101 the two objects is easy to normal vision, however the image $I ^ { d }$ , the deuteranopia vision, is very   \n102 ambiguous. On the contrary, the CUD target image $T$ and $T ^ { d }$ have a difference of $\\mathrm { L }$ channel value 75   \n103 for the letter $\\bullet _ { 5 } ,$ and 45 for the surroundings, making it easy to distinguish between the normal and   \n104 the deuteranopia vision. Due to the characteristics of these data, we refine a data pair by defining a   \n105 criterion that separates two invisible non-CUD objects by $\\mathrm { L }$ channel values.   \n106 Secondly, we propose a variational loss function and multi-modal feature fusion network for color   \n107 preservation. It can be said that the increase in the contrast of $\\mathrm { L }$ channel values between non-CUD   \n108 objects is quantitatively superior, but not in the case of increasing the differences in color preservation   \n109 of input images. When non-CUD objects exist, as a simple example, the most likely way to maximize   \n110 contrast is to polarize the color of the object black and white. But it is the result of complete ignorance   \n111 for color preservation, so just enabling to distinguish between non-CUD objects is not always a good   \n112 answer. A strong filter must be applied to distinguish non-CUD object, but its impact should not be   \n113 too extensive to leading the loss of information in CUD objects. In this paper, we solve this problem   \n114 by taking an appropriate trade-off of color preservation and contrast of L channel value. ",
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+        "type": "text",
+        "text": "115 2.1 Dataset refinement criteria for CUD image ",
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+        "text": "116 The training data is refined by two groups. The one is vectorized image with two colors divided   \n117 by value $\\mathrm { v }$ and hue degree H in HSV color space[HMKO19], and the other is image with two   \n118 or more objects that must be distinguished while preserving the color of non-CUD objects. The   \n119 training data is grouped about 1,600 color combinations into the same V and then simulates them   \n120 with the deuteranopia vision, converting to the adjacent color family to comply color preservation.   \n121 All conversions are scaled within only S and V in HSV color space to increase at least 15 difference   \n122 in the L channel value of selected non-CUD objects. The colors are combined with the 10 essential H   \n123 and tones, and the similar color simulated with the deuteranopia vision was converted. Consequently,   \n124 the key part of refining training data is preservation of color, allowing the models to comply with the   \n125 same approach on learning. ",
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+        "type": "text",
+        "text": "2.2 Image pre-processing ",
+        "text_level": 1,
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+        "text": "127 Our model regresses node points of piecewise linear function, which will be described in the model   \n128 architecture section, and the final filter is a multiplication operation for the input image. Therefore,   \n129 the multiplication operations of less than the number 1 tend to fade the color saturation. The image   \n130 without color inversion converges the white color value to 1, so if the multiplying value is in the [0,   \n131 1] range, the white color is shifted to the black. By inverting the color of input image, it ignores the   \n132 multiplication operations for white value with 0.   \n133 We generate the map image $I ^ { m }$ based on original RGB input images calculating the difference value   \n134 between the image with an aspect of normal vision and the image with an aspect of deuteranopia vision.   \n135 Recent studies have been conducted to augment the information or expanded the models’ perspective   \n136 through transformer models[JSZK16, RFB15]. In our experiment, however, the transformer model   \n137 tends to generate the predicted image ignoring the source color, which result in the polarized color to   \n138 black and white like Cycle-GAN’s. ",
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+        "type": "equation",
+        "img_path": "images/2145ab9b3bc8178553796fba897c230aa364a9743d0b54f31a575a34b3004279.jpg",
+        "text": "$$\n{ \\cal I } ^ { m } = \\vert i n v e r t ( I ^ { n } ) - i n v e r t ( I ^ { d } ) \\vert\n$$",
+        "text_format": "latex",
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+        "type": "equation",
+        "img_path": "images/112dfe3d49a6bf56b784a4733b751cf0a34de8798cb4de036bc65b74280c3606.jpg",
+        "text": "$$\n{ \\cal I } ~ = ~ \\delta \\left( c a t ^ { c h a n n e l } \\left( I ^ { n } , I ^ { d } , I ^ { m } \\right) \\right)\n$$",
+        "text_format": "latex",
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+        "text": "139 After applying color inversion from the original RGB input image $I ^ { n }$ , we generate the image $I ^ { d }$ with   \n140 an aspect of deuteranopia vision in equation 1. From these two generated images, we can get the   \n141 absolute difference value to compose the map image $I ^ { m }$ . In equation 2, the final input $I$ concatenated   \n142 with $9 \\times H \\times W$ dimensions passes through the model. The $\\bar { \\delta } ( . )$ clips output to a range of [0, 1]. ",
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+        "text": "2.3 Model Architecture ",
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+        "text": "144 CUD-NET regresses the node points of piecewise linear filter function from the input. The value   \n145 of each node points computes the multiplication operation and generates the predicted image. The   \n146 input $I$ is compressed into 3 feature blocks matching each input through convolution layer, pooling   \n147 layer, and global pooling layer. The input with 9 channels is separated into $3 \\times 3$ channels before   \n148 passing the model. The first 3 channels are literally used as the main inputs, where the multiplication   \n149 operation takes place, while the remaining 6 channels are used as features.   \n150 First of all, we use multi-modal fusion architecture for three separate inputs to extract expanded   \n151 features. The three inputs converted to the HSV color space pass through a weights-sharing convolu  \n152 tion layer to extract a feature block corresponding to the inputs. Each convolution layer consists of   \n153 kernel size $^ { = 3 }$ , stride $^ { : = 1 }$ , and padding=1, reducing dimension through average pooling. We empirically   \n154 noticed that the most values of output feature have distribution within the range of [-1, 1] with valid   \n155 values for constructing the node points, so we use hyperbolic tan for activation function. Since we   \n156 use inputs with unstructured image size, the last global pooling block holds the size of the feature   \n157 instead of the average pooling block[LCY14].   \n158 The three feature blocks are combined through the multi-modal compact bilinear pooling gate   \n159 $( \\mathbf { M C B } ) [ \\mathbf { F P Y ^ { * } } 1 6 ]$ , following the fusion process shown in Figure 3. The MCB gate allows both   \n160 features to interact in a multiplicative way with low memory consumption and computation   \n161 times. The fusion features are complemented to enhanced feature through the split attention   \n162 mechanism $[ Z \\mathrm { W } Z ^ { \\ast } 2 0 ]$ . At the beginning of the experiment, we have applied the convolutional   \n163 block attention mechanism[WPLK18] of each MCB gate, but we found that it does not make sense   \n164 of understanding the feature itself, so we apply only one attention block to the last fusion feature.   \n165 The enhanced feature pass through the fully-connected regression layer. We picked the 64 points   \n166 to be regressed to compose the piecewise linear function, which is empirically confirmed to the   \n167 optimized number of points in this research. The first half of the values construct the node points of   \n168 the S channel and the other half comprise the $\\mathrm { v }$ channel in HSV color space. Finally, node points   \n169 become the scaling factors to generate predicted image in equation 3[MMS19]. ",
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+        "image_caption": [
+            "Figure 3: Overview structure of CUD image generation "
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+        "img_path": "images/0cf2ca09adb19d88f99a939c9cae489ced9b2a5be9f1843f20a31b298dbe24b6.jpg",
+        "text": "$$\nS \\left( I _ { i } ^ { s , v } \\right) = k _ { 0 } + \\sum _ { m = 0 } ^ { M - 1 } \\left( k _ { m + 1 } - k _ { m } \\right) \\delta \\left( M I _ { i } ^ { s , v } - m \\right)\n$$",
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+        "text": "170 The total number of node point $M$ , each pixel values of S, V channel in input image $I _ { i } ^ { s , v }$ are   \n171 multiplicated with the slope of actual regressed value $k _ { m }$ , the $m - t h$ generated node point. The   \n172 specific node points $M$ is scaled through a multiplication operation to pixel value of the input image   \n173 according to each node point. ",
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+        "text": "174 2.4 Loss function ",
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+        "text": "175 Our dataset has one-to-many problems between input and target data. In dataset pair   \n176 $( I _ { 1 } , T _ { 1 } )$ , $( I _ { 2 } , T _ { 2 } )$ , . . . , $( I _ { n } , T _ { n } )$ , for example, the red color in $I _ { 1 }$ can be targeted to purple color in   \n177 $T _ { 1 }$ , and the red color in $I _ { 2 }$ can be targeted to orange color in $T _ { 2 }$ . With these one-to-many dataset   \n178 structures, we design the loss function $\\mathcal { L }$ that expresses the potential and the diversity of predicted   \n179 image in equation 4. ",
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+        "text": "$$\n\\mathcal { L } = \\sum _ { i = 1 } ^ { N } L a b _ { l o s s } \\left( V \\left( \\Phi \\left( \\hat { I } _ { i } \\right) \\right) \\right) + H _ { l o s s } \\left( \\Phi \\left( \\hat { I } _ { i } \\right) \\right)\n$$",
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+        "text": "180 Stencil Masking As explained in the dataset refining criteria, we do not proceed with color   \n181 conversion for all areas in the target images, but only for areas with color combinations that are   \n182 invisible to the deuteranopia (non-CUD object). For this reason, the input image has color regions of   \n183 converting color and unconverting color, which also can be referred to as non-CUD object and CUD   \n184 object. To imply the color bound to model, the stencil masking method is introduced. ",
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+        "text": "$$\n\\Phi \\left( { \\hat { I } } _ { i } \\right) = { \\hat { I } } _ { i j } \\parallel ( I _ { i j } \\cdot T _ { i j } )\n$$",
+        "text_format": "latex",
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+        "text": "185 We consist a stencil maps through the logical and operations ’·’ of each pixel value $I _ { i j }$ , $T _ { i j }$ . Stencil   \n186 map can specify the non-CUD area and be computed with predicted image $\\hat { I } _ { i j }$ of logical or operation   \n187 ’ $| |$ ’in equation 5. Consequently, CUD object of the image adjusted with a stencil mask does not carry   \n188 out the neural filter computation, such as the same way we refine the target image. This refined image   \n189 is calculated on the loss function.   \n190 CIELab Loss We use the CIELab channel loss function to maximize the contrast of color on   \n191 deuteranopia vision. To stabilize the contrast and brightness of the predicted image, we calculate the   \n192 MS· SSIM(multi-scale structural similarity[WSB03]) of $\\mathrm { L }$ channel. ",
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+        "text": "$$\nL a b _ { l o s s } = \\left\\| L a b \\left( \\hat { I } _ { i } ^ { r g b } \\right) - L a b \\left( T _ { i } ^ { r g b } \\right) \\right\\| _ { 1 } + M S \\cdot S S I M \\left( L a b \\left( \\hat { I } _ { i } ^ { L } \\right) , L a b \\left( T _ { i } ^ { L } \\right) \\right)\n$$",
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+        "text": "193 The $L a b \\left( . \\right)$ expression in equation 6 returns the CIELab channel corresponding to the RGB channel,   \n194 and all calculations are made only on the L channel.   \n195 Histogram Loss We use the histogram loss function to comply with the color preservation of the   \n196 image. The RGB channel is used to preserve its color, contrary to using only the $\\mathrm { L }$ channel in other   \n197 loss functions. Handling the RGB channel as a loss function rather than using Lab’s ab channels has   \n198 shown better results on color preservation. ",
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+        "type": "equation",
+        "img_path": "images/03e0b4da2dd1716cbf0f48130a0e3e9d6b152fda36171fe2a70ef2ee68884792.jpg",
+        "text": "$$\nH _ { l o s s } = - { \\omega _ { h i s t } } \\int N \\left( \\hat { I } _ { i } ^ { r g b } ; \\sigma \\right) - { \\cal N } \\left( T _ { i } ^ { r g b } ; \\sigma \\right)\n$$",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "199 When simply designing a loss function with the L1 distance of the RGB channel pixel values, it was   \n200 very sensitive to certain values and the gradients are diverged, resulting in an untrainable experiment.   \n201 Therefore, we used a gaussian expansion method $[ S \\mathbf { A } C ^ { * } 1 7 ]$ denoted by $N ( . )$ to infer a differentiable   \n202 histogram loss function in equation 7. We compute the difference of the RGB channel of the   \n203 differentiable histogram function, which can be altered to mean squared error or cosine similarity.   \n204 The scaler $\\omega _ { h i s t }$ is determined in inverse proportion to the size of the input image. By maintaining   \n205 the RGB similarity between the predicted image and the target image, we can comply with the color   \n206 preservation.   \n207 Variational Prediction There are various ways to maximize difference of the L channel in the   \n208 image. And the target image is converted at least two colors compared to the input image. However,   \n209 the predicted image of the model is generated by the neural filter, so it is unpredictable which area   \n210 of color is modified. Therefore, if the color in predicted image is over-shifted or in the color value   \n211 of opposite shifts to the target, the loss will rather increase. In addition to one-to-many problem   \n212 that the data pair itself does not matches one-to-one in a particular color, it is necessary to generate   \n213 alternative predicted image with the same aspect of the data pair. We calculate the loss function with   \n214 a variational prediction based on the predicted image for potential color shifts.   \n215 The first potential is the case of excessive shifts. Assume that $I _ { i } ^ { L } = \\{ 7 4 , 4 1 , 7 9 \\}$ , $\\hat { I } _ { i } ^ { L } = \\{ 9 7 , 1 0 , 7 0 \\}$ ,   \n216 $T _ { i } ^ { L } \\ = \\ \\{ 5 0 , 4 1 , 8 0 \\}$ in L channel value. The first and third components of each image is non-CUD   \n217 objects, and second component is CUD object. Therefore, we refined data paired with a difference of   \n218 15 on L channel. Here, we clip the excessive $\\mathrm { L }$ channel value in $\\hat { I } _ { i } ^ { L }$ by equation 8. Up to this point,   \n219 no calculation is made as no value is exceeded in this example. The second potential is the case of   \n220 opposite shifts. It can be said that a complete neural filter has been proceeded for value 97, 10, 70   \n221 where $\\mathrm { L }$ channel difference is 27. However, if we actually calculate the mean square error between   \n222 $\\hat { I } _ { i } ^ { L }$ and $T _ { i } ^ { L }$ , it will be an large value over 1k. Here we can generate alternative predicted image from   \n223 equation 9 and 10. ",
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+        "img_path": "images/689434e91b4dde1ece15a75047f8b53515cfedbab3ace44521bfc1117625af75.jpg",
+        "text": "$$\nc l i p \\left( \\hat { I } _ { i j } \\right) \\ = \\ \\left\\{ { m a x } { \\left( \\hat { I } _ { i j } , { T } _ { i j } \\right) } , \\qquad I _ { i j } \\ > T _ { i j } \\right.\n$$",
+        "text_format": "latex",
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+        "img_path": "images/9b2597f442abd0c904edd84c873c006247936ef70233e08802bcb5c81bd995f5.jpg",
+        "text": "$$\nR _ { 1 } = \\ 2 I _ { i j } - \\ \\hat { I } _ { i j } , R _ { 2 } = \\ \\hat { I } _ { i j }\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/c3a32688718fc2498034dc1d8c73a0871eedd77b075fe8697acaf10411eb48b5.jpg",
+        "text": "$$\nV \\left( { \\hat { I } } _ { i j } \\right) = a r g m i n \\left( \\left\\| c l i p \\left( R _ { 1 , 2 } \\right) - T _ { i j } \\right\\| _ { 2 } \\right)\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "224 As mentioned above, we define thresholds by the maximum and minimum value of each corresponding   \n225 pixel position of $\\hat { I } _ { i } ^ { L }$ and $T _ { i } ^ { L }$ . By computing a difference of residual map and the input image, we   \n226 induce the alternative two images $R _ { 1 }$ , $R _ { 2 }$ . As a result, $\\hat { I } _ { i } ^ { L }$ with a smaller L2 distance is selected to   \n227 alternative predicted image in equation 10, and it is finally computed with loss function compared to   \n228 the $T _ { i } ^ { L }$ . The above equation establishes $V \\left( \\Phi \\left( \\hat { I } _ { i } \\right) \\right) = \\{ \\stackrel { \\cdot } { 5 4 } , 4 1 , \\stackrel { \\cdot } { 8 0 } \\}$ and the mean square error to the   \n229 target image is approximately 5, which is agreeable loss value respect to $\\hat { I } _ { i } ^ { L }$ itself.   \n230 Identity Loss[ZPIE17, TPW16] We use $\\mathcal { L } _ { i d e n t i t y } \\left( T _ { i } \\right)$ to apprehend the CUD object to the model.   \n231 In the case of target image that already satisfy the CUD, the filter should be relatively weakly applied   \n232 than input image. The input of identity loss is target image $T _ { i j }$ instead of input image $I _ { i j }$ , and the   \n233 reference of the loss function is also target image $T _ { i j }$ to maintain the value itself. In computing   \n234 identity loss, we do not require variational prediction as we cannot judge the potential region by   \n235 equation 10. ",
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+    {
+        "type": "text",
+        "text": "236 3 Experiments ",
+        "text_level": 1,
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+    },
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+        "type": "text",
+        "text": "237 The experiment was performed with Tesla V100 SXM2 and Intel Xeon Gold 5120 and the computation   \n238 speed was about 40 images per minutes. We refined a dataset with Adobe Photoshop to maximize   \n239 contrast in the L channel by adjusting saturation and brightness for areas that require color conversion   \n240 based on deuteranopia vision simulation. Color experts has refined about 1,500 vectorized image for   \n241 the training data and 300 publication images for the validation data. All the comparative experimental   \n242 models used the same train, test, validation data in this paper. We used the inference data in   \n243 publications, which is almost composed of vectorized images, as colors often appear distorted in a   \n244 gradation-rich image. The Figure 4 is arranged in descending order of the number of combinations in   \n245 colors from the top image.   \n246 Both structure similarity (SSIM)[ZBSS04] and peak signal to noise ratio (PSNR) in Table 1 can   \n247 indicate whether the image is suitable for CUD or not. As a notable aspect, the result has shown that   \n248 comparative models with lower metrics are sensitive to high-gradation input images, which generated   \n249 color-heterogeneous image. SSIM and PSNR itself can determine the increase in contrast compared   \n250 to the target image but do not determine whether the color preservation complied. Therefore, we   \n251 evaluated SSIM and PSNR with three references, inputs images $I$ , predicted images $\\hat { I }$ , and target   \n252 images $T$ . The higher the estimation of the $\\hat { I }$ and $I$ , the more color preservation factor worked.   \n253 The higher the estimation of the $\\hat { I }$ and $T$ , the more increase in contrast can be considered. We also   \n254 define SSIM mean absolute error, PSNR mean absolute error to measure the extent of the conversion   \n255 between the $F : I  T$ and $F : \\dot { I }  \\hat { I }$ in equation 11 and 12, respectively. The $N$ is total number   \n256 of inference data. ",
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+        "img_path": "images/b5c3ae0112d4775e1d17c9295e5537664ae043d2a3d125584282c129b55680db.jpg",
+        "text": "$$\nS S I M \\cdot M A E =  \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } | S S I M ( \\hat { I } _ { i } , \\mathcal { T } _ { i } ) - S S I M ( I _ { i } , T _ { i } ) |\n$$",
+        "text_format": "latex",
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+    {
+        "type": "equation",
+        "img_path": "images/ab9235c819339abb3bd3d756dfaf8257af88464cf4bb5c06397fd49952b333df.jpg",
+        "text": "$$\nP S N R \\cdot M A E =  \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } | P S N R ( \\hat { I } _ { i } , \\mathcal { T } _ { i } ) - P S N R ( I _ { i } , T _ { i } ) |\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/ee74ef15b1c4bf5acba45467aa3b157cb56fa3118986b351ff3cd98fe81ae34d.jpg",
+        "image_caption": [
+            "Figure 4: Comparisons of predicted images in deuteranopia vision. The color experts selected the validation data that do not satisfy the CUD in publications. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/54f033e20437b2470146b6ad167747c161c7dea49907ec6e1075a5ad9b5bc028.jpg",
+        "table_caption": [
+            "Table 1: Evaluation table of comparison experiment. The CUD-NET with a low bottle-neck feature achieves better results in the experiment of the deuteranopia and the protanopia subjects(Figure 5), although the evaluation metrics are lower than that of CUD-NET. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1>Architecture</td><td rowspan=1 colspan=1>sSIM(i,1)</td><td rowspan=1 colspan=1>SSIM(i,T)</td><td rowspan=1 colspan=1>PSNR(i,1)</td><td rowspan=1 colspan=1>PSNR(i,T)</td><td rowspan=1 colspan=1>SSIM-MAE</td><td rowspan=1 colspan=1>PSNR·MAE</td></tr><tr><td rowspan=2 colspan=1>Cycle-GANZero-DCE</td><td rowspan=1 colspan=1>0.630</td><td rowspan=1 colspan=1>0.634</td><td rowspan=1 colspan=1>13.28</td><td rowspan=1 colspan=1>13.83</td><td rowspan=1 colspan=1>0.3191</td><td rowspan=1 colspan=1>8.4430</td></tr><tr><td rowspan=1 colspan=1>0.924</td><td rowspan=1 colspan=1>0.888</td><td rowspan=1 colspan=1>21.95</td><td rowspan=1 colspan=1>18.67</td><td rowspan=1 colspan=1>0.0661</td><td rowspan=1 colspan=1>3.7300</td></tr><tr><td rowspan=2 colspan=1>DeepLPFEnlighten-GAN</td><td rowspan=1 colspan=1>0.850</td><td rowspan=1 colspan=1>0.831</td><td rowspan=1 colspan=1>26.31</td><td rowspan=1 colspan=1>20.34</td><td rowspan=1 colspan=1>0.1220</td><td rowspan=1 colspan=1>2.0566</td></tr><tr><td rowspan=1 colspan=1>0.820</td><td rowspan=1 colspan=1>0.808</td><td rowspan=1 colspan=1>21.85</td><td rowspan=1 colspan=1>19.58</td><td rowspan=1 colspan=1>0.1470</td><td rowspan=1 colspan=1>3.9983</td></tr><tr><td rowspan=1 colspan=1>Enlighten-GAN(scaled)</td><td rowspan=1 colspan=1>0.966</td><td rowspan=1 colspan=1>0.921</td><td rowspan=1 colspan=1>24.86</td><td rowspan=1 colspan=1>21.36</td><td rowspan=1 colspan=1>0.0392</td><td rowspan=1 colspan=1>3.4937</td></tr><tr><td rowspan=2 colspan=1>CUD-NET(low bottle-neck feature)CUD-NET</td><td rowspan=1 colspan=1>0.897</td><td rowspan=1 colspan=1>0.866</td><td rowspan=1 colspan=1>27.77</td><td rowspan=1 colspan=1>21.01</td><td rowspan=1 colspan=1>0.0901</td><td rowspan=1 colspan=1>2.0826</td></tr><tr><td rowspan=1 colspan=1>0.962</td><td rowspan=1 colspan=1>0.924</td><td rowspan=1 colspan=1>29.54</td><td rowspan=1 colspan=1>21.19</td><td rowspan=1 colspan=1>0.0312</td><td rowspan=1 colspan=1>1.4760</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "257 Cycle-GAN and Zero-DCE showed worse result than others. Cycle-GAN model had difficulty   \n258 reconstructing a geometry of a particular object, and overall color had low saturation and brightness,   \n259 resulting in color conversion into an almost grey scale image. Zero-DCE is faded in color, and the   \n260 contrast was not much different from the input image. The overall image lost its color preservation,   \n261 which we focused to solve in this paper.   \n262 DeepLPF meets both the color preservation and contrast that we deal with for. However, DeepLPF   \n263 tends to color be over-stably filtered for the images with fewer color combinations. Although the   \n264 color preservation has complied better than other experiments, there were many failed results from   \n265 the perspective of contrast, which the over-stable filter leads to by DeepLPF.   \n266 Remarkably, predicted images of Enlighten-GAN showed reasonable results. However, simple color   \n267 combinations or the images with already satisfying the CUD often showed results degenerated with   \n268 low CUD suitability. Enlighten-GAN was able to generate the results we targeted, but its deviation of   \n269 filter is so high that it sometimes failed to satisfy the contrast even on simple images or decreased   \n270 the contrast. As the problem of GAN-based method including Enlighten-GAN, moreover, model   \n271 fixes the width and height of the predicted image. If width and height of $T$ and $I$ down-scaled ",
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+    {
+        "type": "text",
+        "text": "to size of Enlighten-GAN 272 $\\hat { I }$ (approximately 25K pixels in this experiment), the $S S I M \\left( \\hat { I } , I \\right)$ and $P S N R \\left( \\hat { I } , T \\right)$ showed higher estimation in some metrics than CUD-NET. In the opposite case of $\\hat { I }$ up-scaled to size of $T$ and $I$ , the significantly low estimation was recorded due to the information loss of up-scaling problem. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "CUD-NET showed stable and robust predicted images in both color preservation and increase in the contrast compared to other experiments. In comparing the values in the same region of $I$ and $\\hat { I }$ , the model scaled two $\\mathrm { L }$ channel values with opposite side in the most of case, the one goes up and the other goes down. When we reduced the number of bottle-neck feature of model, it tends to record relatively high deviation of filter scales according to the number of combinations of colors. In summary, the CUD-NET showed the highest estimations for 4 evaluation metrics. Moreover, as our model adopted a neural filter unlike generation models, there is no loss of information regarding the scaling of predicted images. ",
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/9a2ce8b4db1667e120d3e391edc4e605f10711786bdbd70de95e46dfcb47ad39.jpg",
+        "image_caption": [
+            "Figure 5: The box bar is ordered to the left side, input image $I$ , Enlighten-GAN, DeepLPF, CUDNET. The y position of box bar represents a mean and length of the box bar represents a deviation of each experiment. The lower the graph is, the higher the rank is. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "284 The figure 5 shows the evaluation of the deuteranopia and the protanopia. The evaluation metrics   \n285 consist of object distinguishability and color harmony in order of input image I, predicted image   \n286 of Enlighten GAN, DeepLPF, and CUD-NET. User study has tested upon the total of 6 subjects, 4   \n287 deuteranomaly and 2 protanomaly. The subjects were asked to list the ranks of object distinguishability   \n288 and color harmony of 4-paired-image for each model-blinded item. As the experimental results,   \n289 the deuteranopia subject ranked the 1-st in the object distinguishability of CUD-NET at an average   \n290 rank of 1.821, followed by Enlighten-GAN at an average rank of 2.512. Similarly, the protanopia   \n291 subject also ranked the 1-st in CUD, followed by Enlighten-GAN, DeepLPF, and input images. The   \n292 evaluation of color harmony showed that the subjects tend to assume that the image with a good   \n293 object distinguishability has good color harmony preferentially. For a total of six subjects, the five   \n294 subjects chose the CUD-NET, with the exception of one who ranked Enlighten-GAN by a subtle gap ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "295 4 Conclusion ",
+        "text_level": 1,
+        "bbox": [
+            142,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "296 In this paper, we proposed deep network to generate CUD images from non-CUD input images. The   \n297 pre-processing and multi-modal fusion layer could comprehend the information for color weakness,   \n298 and the variational loss function makes the model further adapt to CUD dataset. Compared to other   \n299 research, we are able to maintain high-resolution images and both stable color preservation and   \n300 contrast with neural filter per images.   \n301 Our current research shows a robust filter for a single color, such as vectorized images, but it is   \n302 difficult to expect stable results in the case of a real-world image with high gradation in hues. We   \n303 consider the same limitation of our work when the certain pixel values react sensitively, making noise   \n304 appear more prominent in the predicted image. In the future, we plan to create additional datasets   \n305 with gradation on the vectorized image and focus on the fusion layer to improve performance of the   \n306 model.   \n307 References   \n308 [AHB∗18] ANDERSON P., HE X., BUEHLER C., TENEY D., JOHNSON M., GOULD S., ZHANG L.: Bottom  \n309 up and top-down attention for image captioning and visual question answering. In Proceedings of   \n310 the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (June 2018).   \n311 [BCPS19] BIANCO S., CUSANO C., PICCOLI F., SCHETTINI R.: Content-preserving tone adjustment for   \n312 image enhancement. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern   \n313 Recognition (CVPR) Workshops (June 2019).   \n314 [DLT18] DENG Y., LOY C. C., TANG X.: Aesthetic-driven image enhancement by adversarial learning.   \n315 In Proceedings of the 26th ACM International Conference on Multimedia (New York, NY, USA,   \n316 2018), MM ’18, Association for Computing Machinery, p. 870–878. URL: https://doi.org/   \n317 10.1145/3240508.3240531, doi:10.1145/3240508.3240531.   \n318 $\\mathrm { [ F P Y ^ { * } 1 6 ] }$ FUKUI A., PARK D. H., YANG D., ROHRBACH A., DARRELL T., ROHRBACH M.: Multimodal   \n319 compact bilinear pooling for visual question answering and visual grounding, 2016. arXiv:   \n320 1606.01847.   \n321 [GLG∗20] GUO C., LI C., GUO J., LOY C. C., HOU J., KWONG S., CONG R.: Zero-reference deep curve   \n322 estimation for low-light image enhancement. 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+# CONDITIONAL GENERATION OF MOLECULES FROM DISENTANGLED REPRESENTATIONS
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Though machine learning approaches have shown great success in estimating properties of small molecules, the inverse problem of generating molecules with desired properties remains challenging. This difficulty is in part because the set of molecules which have a given property is structurally very diverse. Treating this inverse problem as a conditional distribution estimation task, we draw upon work in learning disentangled representations to learn a conditional distribution over molecules given a desired property, where the molecular structure is encoded in a continuous latent random variable. By including property information as an input factor independent from the structure representation, one can perform conditional molecule generation via a “style transfer” process, in which we explicitly set the property to a desired value at generation time. In contrast to existing approaches, we disentangle the latent factors from the property factors using a regularization term which constrains the generated molecules to have the property provided to the generation network, no matter how the latent factor changes.
+
+# 1 INTRODUCTION
+
+Conditional molecule generation is far from being solved. The main challenge is the enormous and discrete nature of the molecules space and the fact that molecule properties are highly sensitive to molecular structure (Kirkpatrick & Ellis, 2004). Approaches to conditional generation are typically two-step, either using a model or genetic algorithm to generate candidates which are later filtered, or learning a continuous embedding of the discrete molecules and optimizing in a real-valued representation space. The former is computationally expensive, the latter performs conditional generation only very obliquely.
+
+We propose a conditional generative model that produces candidate molecules which targeting a desired property in a single step. This approach builds on work in structured deep generative models (Kingma et al., 2014; Siddharth et al., 2017), which aim to learn a disentangled representation that factors into observed properties we want to control for, and latent factors that account for the remaining features which are either hard to annotate or irrelevant to the properties we wish to optimize.
+
+We derive a regularizer for supervised variational autoencoders which exploits property information that we provide as supervision, ensuring that produced molecules adhere to target properties they are conditioned on. We demonstrate the ability of our model to perform accurate conditional molecule generation and a sort of “style transfer” on molecules, where a latent representation for a single molecule can have its target properties perturbed independently of its learnt structural characteristics, allowing direct and efficient generation of candidates for local optimization of molecules.
+
+# 2 BACKGROUND
+
+Molecule discovery tasks come in two flavors. Global optimization seeks to find molecules that have a particular target property. Local optimization starts from some initial molecule and searches for molecules which have a desired property while not straying too far from the prototype. There is some overlap in methods used in the two approaches.
+
+# 2.1 DEEP GENERATIVE MODELS FOR MOLECULES
+
+Virtual screening methods start from a large database of possible molecules and retain the promising ones (Eckert & Bajorath, 2007), as measured by some quality function $f ( \cdot )$ . Machine learning approaches expand on this by dynamically generating additional candidate molecules; Segler et al. (2017) uses a stacked LSTM to produce large numbers of novel molecules which have similar characteristics to an existing database.
+
+For properties which are expensive to evaluate, generating large sets of candidate molecules is not particularly useful. More sample-efficient global search can be achieved using Bayesian optimization methods, which use a generative model with a latent space that functions as a continuous representation of molecules (Gomez-Bombarelli et al., 2016; Kusner et al., 2017). Optimization is then ´ carried out over this continuous representation space to find candidates which are expected to have the desired property. Local gradient-based search can also be applied on continuous latent spaces to optimize the latent representation with respect to a target property (Jin et al., 2018; Liu et al., 2018).
+
+A challenge for these latent variable models is to reliably produce valid molecules. Character variational autoencoders (CVAEs) (Gomez-Bombarelli et al., 2016) generate molecules one character ´ at a time, and are prone to syntactic and semantic errors; the grammar-based variational autoencoder (GVAE) (Kusner et al., 2017) and syntax-directed variational autoencoder (SD-VAE) (Dai et al., 2018) instead operate in the space of context-free and attribute grammars, respectively, to ensure syntactic validity. Other work generative models that operates on graph representations (Simonovsky & Komodakis, 2018; De Cao & Kipf, 2018; Jin et al., 2018; You et al., 2018; Liu et al., 2018), largely improving the ability to generate valid molecules.
+
+Suppose we are given a training set of pairs $\mathcal { D } = \{ ( \mathbf { x } _ { i } , \mathbf { y } _ { i } ) \} , i = 1 , \ldots , N .$ , where x corresponds to molecules and y represents a value of some properties of the molecule $\mathbf { x }$ . Assume the molecules represent an i.i.d. sample from some unknown distribution $\tilde { p } ( { \bf x } )$ , which assigns high probability to molecules believed to be useful for a given task. Aside from Segler et al. (2017), which has no latent space and thus directly trains via maximum likelihood, these latent variable models are trained by optimizing a standard ELBO objective for variational autoencoders (?). This entails learning a stochastic encoder $q _ { \phi } ( { \bf z } | { \bf x } )$ which maps molecules into a latent space, and a stochastic decoder $p _ { \boldsymbol { \theta } } ( \mathbf { x } | \mathbf { z } )$ for reconstructing molecules, by maximizing
+
+$$
+\mathcal { L } ( \boldsymbol { \theta } , \boldsymbol { \phi } ) = \sum _ { i = 1 } ^ { N } \bigg \{ \mathbb { E } _ { q _ { \boldsymbol { \phi } } ( \mathbf { z } _ { i } | \mathbf { x } _ { i } ) } [ \log p _ { \boldsymbol { \theta } } ( \mathbf { x } _ { i } | \mathbf { z } _ { i } ) ] - D _ { K L } ( q _ { \boldsymbol { \phi } } ( \mathbf { z } _ { i } | \mathbf { x } _ { i } ) | | p ( \mathbf { z } _ { i } ) ) \bigg \} .
+$$
+
+Notably, the objective is not a function of y: most existing generative models with latent variables do not perform direct conditional generation, and approaches for targeted molecule discovery are bolted on to the learnt model. Some, e.g. Kusner et al. (2017), are trained in an “unsupervised” manner, agnostic to any property which later may need to be optimized. Others, e.g. Gomez-Bombarelli ´ et al. (2016); Liu et al. (2018), train the autoencoder jointly alongside a function to predict y from z, hoping to guide the latent space to be also good for predicting the desired property. A recent exception is Assouel et al. (2018), which learns a deterministic autoencoder where the decoder takes the latent code and the desired property as input, using a mutual information term in training to steer the model towards generating molecules whose target properties match the input. Guimaraes et al. (2017); De Cao & Kipf (2018); You et al. (2018) instead learn generation models optimized towards specific metrics, such as drug-likeliness and solubility; the major downside is that these models must be retrained each time for a new property. In contrast, the autoencoder-based methods can be re-used to optimize towards any particular value of the property.
+
+# 2.2 STYLE TRANSFER WITH SUPERVISED VAES
+
+While the latent representations learned through standard VAE models perform well on the task of molecule reconstruction they do not necessarily provide interpretable factorised representations. A disentangled representation gives us additional control on the molecule generation process, allowing us to modify a single property leaving the remaining unaffected (Bengio et al., 2013a). In many cases important variation in the data is easy to annotate. For example in the case of molecule datasets we have access to different functional descriptors of the molecules obtained by chemoinformatics software such as RDKit (Landrum). Particularly useful to us here are supervised methods for learning disentangled representations (Kingma et al., 2014; Siddharth et al., 2017). These are distinct from unsupervised disentangling approaches such as InfoGAN (Chen et al., 2016) or $\beta$ -VAE (Higgins et al., 2017), which encourages the latent factor to learn a disentangled representation by modifying the objective to promote component independence.
+
+We will learn representations that specifically disentangle molecular properties of interest which we may later want to modify. Kingma et al. (2014) demonstrates how disentangling can be used to take two MNIST images of different digits, written in different styles, and independently change the digit while holding the style constant. An analogous operation on molecules would involve holding the physical structure of a molecule (its “style”) relatively fixed while modifying a salient property. Unlike (say) the style transfer example for the MNIST digits, the conditional distribution of molecules with a particular value of properties might be very diverse; for example, the QED score attempts to measure the drug-likeness of a molecule, and the set of molecules generated at high values of this score would hopefully have high probability on a large, varied set of molecules. An essential challenge here is that the property only provides a very weak signal as to the overall structure of the molecule. To account for this diversity, we model the conditional distribution with a latent variable $\mathbf { z }$ , such that $\begin{array} { r } { p _ { \theta } ( \mathbf { x } | \mathbf { y } ) = \int p _ { \theta } ( \mathbf { x } | \mathbf { z } , \mathbf { y } ) p ( \mathbf { \bar { z } } ) d \mathbf { z } } \end{array}$ .
+
+Disentangling the latent code $\mathbf { z }$ from the property y enables style transfer. This is done by taking an initial $\mathbf { x }$ , computing the posterior over the latent variable $\mathbf { z }$ , and then generating a new $\mathbf { x } ^ { \prime }$ with the property modified to have a target value $\mathbf { y } ^ { \prime }$ , with $p _ { \theta } ( \mathbf { x } ^ { \prime } | \mathbf { y } ^ { \prime } , \mathbf { x } ) =$ $\begin{array} { r } { \int p _ { \theta } ( \mathbf { x } ^ { \prime } | \mathbf { y } ^ { \prime } , \mathbf { z } ) p _ { \theta } ( \mathbf { z } | \mathbf { x } ) d \mathbf { z } } \end{array}$ .
+
+![](images/d6fdd5f7e997772d80bd45c81d2d6a587e1202c9b2e03df60b1f8ea2b7c46b4e.jpg)  
+Figure 1: A demonstration of style transfer
+
+Concretely, this involves fitting a joint generative model of the form $p _ { \boldsymbol { \theta } } ( \mathbf { x } , \mathbf { y } , \mathbf { z } ) = p _ { \boldsymbol { \theta } } ( \mathbf { x } | \mathbf { y } , \mathbf { z } ) p ( \mathbf { y } ) \bar { p ( \mathbf { z } ) }$ , in which $\mathbf { y }$ and $\mathbf { z }$ are independent under the prior, and we assume a unit multivariate normal prior $p ( \mathbf { z } )$ . To infer the latent variable $\mathbf { z }$ we will use a variational distribution $q _ { \phi } ( { \bf z } | { \bf x } )$ , which takes the form of a multivariate normal distribution with parameters a nonlinear function of $\mathbf { x }$ , to approximate the true posterior $p _ { \theta } ( \mathbf { z } | \mathbf { x } , \mathbf { y } )$ . This objective function
+
+$$
+\mathcal { L } _ { E L B O } ( \theta , \phi ) = \sum _ { i = 1 } ^ { N } \left\{ \mathbb { E } _ { q _ { \phi } ( \mathbf { z } _ { i } | \mathbf { x } _ { i } ) } [ \log p _ { \theta } ( \mathbf { x } _ { i } | \mathbf { y } _ { i } , \mathbf { z } _ { i } ) ] - D _ { K L } ( q _ { \phi } ( \mathbf { z } _ { i } | \mathbf { x } _ { i } ) | | p ( \mathbf { z } _ { i } ) ) \right\}
+$$
+
+corresponds to learning a supervised VAE (Kingma et al., 2014), and represents a fairly na¨ıve approach to modeling a conditional distribution.
+
+# 3 CONDITIONAL GENERATION BY DISENTANGLING
+
+Maximizing this conditional ELBO in Eq (2) will likely yield good reconstructions of molecules from an embedding $\mathbf { z }$ (alongside the true property y), but for properties which only weakly inform the generative model there is nothing to enforce that the variable $\mathbf { y }$ actually directly has an effect on the generative process. Since the value $\mathbf { y }$ is something we know is a derived property of the molecule $\mathbf { x }$ , it is completely possible for all information about y to also be encoded in the representation $\mathbf { z }$ , in which case there is no guarantee that the learnt likelihood $p _ { \theta } ( \mathbf { x } | \mathbf { y } , \mathbf { z } )$ actually takes into account the value of $\mathbf { y }$ — in fact, we know it is possible to fit variational autoencoders where the decoder simply has the form $p _ { \boldsymbol { \theta } } ( \mathbf { x } | \mathbf { z } )$ — and we are relying on the utility of $\mathbf { y }$ in reconstructions to see any sort of disentangling effect.
+
+# 3.1 CONSTRAINED ELBO
+
+In the case of conditional generation of molecules, we often have access to some oracle function $f$ (possibly non-differentiable) which for any given $\mathbf { x }$ outputs a property estimate $\mathbf { y }$ , for instance, the chemoinformatics software RDKit (Landrum). Since for conditional generation our ultimate goal is to generate a molecule $\mathbf { x }$ for any given target property $\mathbf { y } _ { 0 }$ , which then actually has $f ( \mathbf { x } ) = \bar { \mathbf { y } } _ { 0 }$ , we can reframe the problem by introducing hard constraints on the generated values, i.e. if restricting to values of $\mathbf { y }$ in the training set,
+
+$$
+\begin{array} { r l } & { \underset { \theta , \phi } { \operatorname* { m a x } } \mathcal { L } _ { E L B O } ( \theta , \phi ) } \\ & { \mathrm { s u b j e c t ~ t o ~ } \mathbb { E } _ { \mathbf { x } \sim p ( \mathbf { x } \mid \mathbf { y } _ { i } ) } [ \mathbb { I } [ f ( \mathbf { x } ) = \mathbf { y } _ { i } ] ] = 1 } \end{array}
+$$
+
+![](images/11c4f6bc728cef0a1f7156261ab4dd96723193136e4805467ad1b99711c5ae7c.jpg)  
+Figure 2: Setting and modeling pipeline for conditional generation of molecules, with supervision provided via an external property prediction oracle. Red lines correspond to non-differentiable components, including both a potentially complex sampling process and the property prediction itself. The blue dashed line corresponds to the approximate property predictor, which aims to predict the expected value of the property from a continuous relaxation, marginalized over the sampling process.
+
+for all $i = 1 , \ldots , N$ . This is an unreasonably hard constraint, unlikely to be satisfied by any distribution other than one which simply places a point mass on the single training $\mathbf { x } _ { i }$ associated with $\mathbf { y } _ { i }$ , but we can relax it by considering that (unlike the molecular space $\mathbf { x }$ ) the property space $\mathbf { y }$ is typically smooth, as many properties are continuous-valued and correspond to a human-interpretable scale. Following Ma et al. (2018) and Hu et al. (2017), we reframe the constraint as a soft penalty on the ELBO,
+
+$$
+\mathcal { L } ( \theta , \phi ) = \mathcal { L } _ { E L B O } ( \theta , \phi ) - \frac { \lambda _ { 1 } } { 2 } \sum _ { i = 1 } ^ { N } \mathbb { E } _ { \hat { \mathbf { x } } \sim p _ { \theta } ( \mathbf { x } | \mathbf { y } _ { i } ) } \Vert f ( \hat { \mathbf { x } } ) - \mathbf { y } _ { i } \Vert ^ { 2 }
+$$
+
+so that they are consistent with the property prediction, i.e., as we have an oracle function $f$ which enable us to access the property of any generated data, we can explicitly add a soft constraint to our loss function to provide explicit guidance for the generative model such that $f ( \hat { \mathbf x } ) = \mathbf y$ . This constraint is expected to hold for any pair $\displaystyle ( \mathbf { x } , \mathbf { y } )$ we may happen to come across, not just those in the training data. We also show optimizing the relaxed constraint is equivalent to maximizing mutual information with the target $\mathbf { y } _ { i }$ and generated molecule $\hat { \bf x }$ ; for details see appendix Section 6.1.
+
+# 3.2 APPROXIMATING THE PROPERTY PREDICTOR
+
+Introducing the regularizer as in Eq. (3) implicitly guides the reconstruction to take into account the property information, such that the reconstructed data should exhibit properties which match the input properties it is conditioned on. However, existing implementations of $f$ are often non-differentiable or CPU-bound, and $\hat { \bf x }$ are discrete samples from a categorical distribution, all of which means the gradient of the regularizer can’t flow back to the generator. This is outlined in Figure 2. To enable the gradient based methods on GPUs during training and avoid discrete sampling, one approach would be to first fit a differentiable approximation to $f$ , and then use either a Gumbel-softmax relaxation (Jang et al., 2016) or tricks like a “straight-through” estimator (Bengio et al., 2013b) as a continuous approximation for the discrete samples. Instead, we propose bypassing the discrete sampling step entirely and learning a function $f _ { \omega }$ that can map from a learned representation of the molecules directly to molecules property (Hu et al., 2017).
+
+To do this, we take as input the last hidden layer of the decoder network which parameterizes $p _ { \theta } ( \mathbf { x } | \mathbf { z } , \mathbf { y } )$ , denoting this deterministic transformation as $g _ { \boldsymbol { \theta } } ( \mathbf { z } , \mathbf { y } )$ . For the grammar VAE and the syntax-directed VAE, this last layer $\mathbf { h } = g _ { \boldsymbol { \theta } } ( \mathbf { z } , \mathbf { y } )$ is the output of a recurrent layer that generates logits corresponding to unmasked and unnormalized log probabilities for each character at each position in the string; see Kusner et al. (2017) and Dai et al. (2018) for details on the implementation of the somewhat complex sampling process in the decoder. Ideally, $f _ { \omega }$ would estimate the property distribution obtained by marginalizing out the discrete sampling step, with
+
+$$
+f _ { \omega } ( \mathbf { h } \equiv g _ { \theta } ( \mathbf { z } , \mathbf { y } _ { 0 } ) ) \approx \mathbb { E } _ { p _ { \theta } ( \mathbf { x } | \mathbf { z } , \mathbf { y } _ { 0 } ) } [ f ( \mathbf { x } ) ] ,
+$$
+
+where we condition on $\mathbf { z }$ , and $\mathbf { y } _ { 0 }$ refers to an arbitrary input target property.
+
+Assuming the approximation in Eq. (4), we have
+
+$$
+\begin{array} { r } { \mathbb { E } _ { p _ { \theta } ( \hat { \mathbf { x } } | \mathbf { y } _ { i } ) } \| f ( \hat { \mathbf { x } } ) - \mathbf { y } _ { i } \| ^ { 2 } = \mathbb { E } _ { p ( \mathbf { z } ) } \left[ \mathbb { E } _ { p _ { \theta } ( \hat { \mathbf { x } } | \mathbf { y } _ { i } , \mathbf { z } ) } \| f ( \hat { \mathbf { x } } ) - \mathbf { y } _ { i } \| ^ { 2 } \right] \approx \mathbb { E } _ { p ( \mathbf { z } ) } \| f _ { \omega } ( g _ { \theta } ( \mathbf { z } , \mathbf { y } _ { i } ) ) - \mathbf { y } _ { i } \| ^ { 2 } , } \end{array}
+$$
+
+an expectation over a real-valued variable which does not depend on any of the parameters we are estimating, meaning we can use a simple path estimate of the gradient with respect to $\theta , \omega$ by exchanging the gradient with the expectation. We thus define a regularization term
+
+$$
+\mathcal { L } _ { d i s e n t } ( \theta , \omega ) = \frac { \lambda _ { 1 } } { 2 } \sum _ { i = 1 } ^ { N } \mathbb { E } _ { p ( \mathbf { z } ) } \| f _ { \omega } \big ( g _ { \theta } ( \mathbf { z } , \mathbf { y } _ { i } ) \big ) - \mathbf { y } _ { i } \| ^ { 2 }
+$$
+
+which can be used as a drop-in replacement for the non-differentiable penalty term in Eq. (3), yielding a candidate objective function
+
+$$
+\mathcal { L } ( \theta , \phi ) \approx \hat { \mathcal { L } } _ { \omega } ( \theta , \phi ) = \mathcal { L } _ { E L B O } ( \theta , \phi ) - \mathcal { L } _ { d i s e n t } ( \theta , \omega )
+$$
+
+3.3 LEARNING THE PROPERTY ESTIMATOR JOINTLY WITH GENERATIVE MODEL
+
+While one could imagine attempting to learn $f _ { \omega }$ jointly with $\phi , \theta$ by direct optimization of Eq. (6), in practice this is very unstable, as values of $g _ { \boldsymbol { \theta } } ( \mathbf { z } , \mathbf { y } _ { i } )$ early in training may correspond to very poor generated molecules $\hat { \mathbf { x } } _ { i }$ which may not have properties at all similar to $\mathbf { y } _ { i }$ . This can be sidestepped by training the property estimator jointly as part of an extended generative model on [x, y].
+
+We note that the property estimator $f _ { \omega }$ parameterizes a probability distribution $p _ { \omega } ( f ( \mathbf { x } ) | \mathbf { z } , \mathbf { y } _ { 0 } )$ , where $\mathbf { x } \sim p _ { \theta } ( \mathbf { x } | \mathbf { z } , \mathbf { y } _ { 0 } )$ and f is the oracle function that $f ( \mathbf { x } ) = \mathbf { y }$ . With a Gaussian distribution over the error, we can consider
+
+$$
+p _ { \omega } ( f ( \mathbf { x } ) \vert \mathbf { z } , \mathbf { y } _ { 0 } ) = \mathcal { N } ( f ( \mathbf { x } ) \vert f _ { \omega } ( g _ { \theta } ( \mathbf { z } , \mathbf { y } _ { 0 } ) ) , \lambda _ { 2 } ^ { - 1 } \mathbf { I } )
+$$
+
+for small, fixed $\lambda _ { 2 }$ . Therefore, we propose defining a new ELBO based on a joint autoencoder for $\{ f ( \mathbf { x } _ { i } ) , \mathbf { y } _ { i } ) \}$ , albeit with a factorization such that the input $\mathbf { y } _ { i }$ bypasses the encoder and is passed directly into the decoder, with a joint likelihood
+
+$$
+p _ { \{ \theta , \omega \} } ( \mathbf { x } _ { i } , f ( \mathbf { x } _ { i } ) | \mathbf { z } _ { i } , \mathbf { y } _ { i } ) = p _ { \omega } ( f ( \mathbf { x } _ { i } ) | \mathbf { z } _ { i } , \mathbf { y } _ { i } ) p _ { \theta } ( \mathbf { x } _ { i } | \mathbf { z } _ { i } , \mathbf { y } _ { i } ) .
+$$
+
+This yields a joint ELBO for the training set of
+
+$$
+\mathcal { L } _ { E L B O } ( \omega , \theta , \phi ) = \sum _ { i = 1 } ^ { N } \mathbb { E } _ { q _ { \phi } ( \mathbf { z } | \mathbf { x } _ { i } ) } \left[ \log \frac { p _ { \omega } ( f ( \mathbf { x } _ { i } ) | \mathbf { z } , \mathbf { y } _ { i } ) p _ { \theta } ( \mathbf { x } _ { i } | \mathbf { z } , \mathbf { y } _ { i } ) p ( \mathbf { z } ) } { q _ { \phi } ( \mathbf { z } | \mathbf { x } _ { i } ) } \right] .
+$$
+
+Note that we can rewrite this ELBO as a function of the previous one, with
+
+$$
+\mathcal { L } _ { E L B O } ( \boldsymbol { \omega } , \boldsymbol { \theta } , \boldsymbol { \phi } ) = \mathcal { L } _ { E L B O } ( \boldsymbol { \theta } , \boldsymbol { \phi } ) - \frac { \lambda _ { 2 } } { 2 } \sum _ { i = 1 } ^ { N } \mathbb { E } _ { \boldsymbol { q } _ { \boldsymbol { \phi } } ( \mathbf { z } | \mathbf { x } _ { i } ) } \| f _ { \boldsymbol { \omega } } \big ( g _ { \boldsymbol { \theta } } ( \mathbf { z } , \mathbf { y } _ { i } ) \big ) - \mathbf { y } _ { i } \| _ { 2 } ^ { 2 } ,
+$$
+
+where we also see that $\mathcal { L } _ { E L B O } ( \omega , \theta , \phi ) \leq \mathcal { L } _ { E L B O } ( \theta , \phi )$ , allowing us to define an objective
+
+$$
+\hat { \mathcal { L } } ( \omega , \theta , \phi ) = \mathcal { L } _ { E L B O } ( \omega , \theta , \phi ) - \mathcal { L } _ { d i s e n t } ( \theta , \omega ) ,
+$$
+
+which is a lower bound on Eq. (6). Notice the two terms we have added to the original ELBO are quite similar, differing only in choice of distribution: for learning $f _ { \omega }$ , we wish to use values of $\mathbf { z }$ simulated form the approximate posterior $q _ { \phi } ( { \bf z } | { \bf x } )$ , whereas for enforcing a constraint across all possible generations we simulate $\mathbf { z }$ from the prior $p ( \mathbf { z } )$ .
+
+# 3.4 GRADIENT ESTIMATION
+
+As the regularizer $\mathcal { L } _ { d i s e n t } ( \theta , \omega )$ encourages disentangling by constraining the molecules generated from $\mathbf { y } _ { i }$ to have property $\mathbf { y } _ { i }$ no matter what value $\mathbf { z }$ takes, we found that it does not necessarily evaluate at meaningful values of $\mathbf { z }$ when sampled randomly from $p ( \mathbf { z } )$ . This roughly corresponds to the notion that not all combinations of “style” and property are physically attainable; ideally for style transfer we would like the generated molecule to stay “close” in structure to the original molecule that we intended to modify. When estimating (gradients of) the soft constraint term $\mathcal { L } _ { d i s e n t } ( \theta , \omega )$ , we found it advantageous to use samples of $\mathbf { z }$ which correspond to encodings of actual data points, as opposed to random samples from the prior. We approximate expectations with respect to $p ( \mathbf { x } )$ by looking at the so-called marginal posterior; we note that
+
+Table 1: Reconstruction performance and generation quality (Valid, Unique, Novel).   
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">QM9</td><td colspan="5">ZINC</td></tr><tr><td>Reconstruction %</td><td>Valid%</td><td>Unique %</td><td>Novel %</td><td>Reconstruction %</td><td>Valid%</td><td>Unique %</td><td>Novel %</td></tr><tr><td>CVAE Gómez-Bombarelli et al. (2016)</td><td>3.61</td><td>10.30</td><td>=</td><td>90.0</td><td>44.6</td><td>0.70</td><td>·</td><td>100</td></tr><tr><td>GVAE Kusner et al. (2017)</td><td>96.00</td><td>60.20</td><td>=</td><td>80.90</td><td>53.70</td><td>7.20</td><td>=</td><td>100</td></tr><tr><td>SD-VAE Dai et al.(2018)</td><td>97.84</td><td>98.40</td><td>99.28</td><td>91.97</td><td>76.20</td><td>43.50</td><td>-</td><td>-</td></tr><tr><td>Sup-VAE-1-GRU</td><td>97.53</td><td>93.66</td><td>91.30</td><td>92.05</td><td>74.12</td><td>32.84</td><td>94.61</td><td>100</td></tr><tr><td>CGD-VAE-1-GRU</td><td>99.27</td><td>95.61</td><td>93.65</td><td>87.87</td><td>88.64</td><td>29.00</td><td>99.24</td><td>100</td></tr><tr><td>Sup-VAE-3-GRU</td><td>97.81</td><td>97.90</td><td>95.09</td><td>89.47</td><td>82.40</td><td>36.16</td><td>86.26</td><td>100</td></tr><tr><td>CGD-VAE-3-GRU</td><td>99.31</td><td>97,80</td><td>98.77</td><td>96.21</td><td>81.80</td><td>37.78</td><td>98.75</td><td>100</td></tr></table>
+
+$$
+p ( \mathbf { z } ) = \int p _ { \theta } ( \mathbf { z } | \mathbf { x } ) p _ { \theta } ( \mathbf { x } ) d \mathbf { x } \approx \frac { 1 } { N } \sum _ { j } p _ { \theta } ( \mathbf { z } | \mathbf { x } _ { j } ) \approx \frac { 1 } { N } \sum _ { j } q _ { \phi } ( \mathbf { z } | \mathbf { x } _ { j } ) ,
+$$
+
+where the first approximation uses the empirical data distribution as an approximation to the model marginal $p _ { \theta } ( \mathbf { x } )$ , and the second uses our variational posterior approximation $q _ { \phi } ( { \bf z } | { \bf x } )$ . We define this quantity as $\begin{array} { r } { q ( \mathbf { z } ) = \frac { 1 } { N } \sum _ { j } q _ { \phi } ( \mathbf { z } | \mathbf { x } _ { j } ) } \end{array}$ , a mixture of Gaussians, which we can sample from by drawing random values from our dataset and then drawing from their encoding distributions.
+
+When we use this in estimating gradients of the soft constraint, we can use samples from the same minibatch, exactly corresponding to a property transfer task. That is, for any particular $y _ { i }$ in the dataset, we can estimate
+
+$$
+\begin{array} { r } { \mathbb { E } _ { p ( \mathbf { z } ) } \nabla _ { \theta , \omega } \| f _ { \omega } \big ( g _ { \theta } ( \mathbf { z } , \mathbf { y } _ { i } ) \big ) - \mathbf { y } _ { i } \| ^ { 2 } \approx \mathbb { E } _ { q ( \mathbf { z } _ { j } | \mathbf { x } _ { j } ) } \nabla _ { \theta , \omega } \| f _ { \omega } \big ( g _ { \theta } ( \mathbf { z } , \mathbf { y } _ { i } ) \big ) - \mathbf { y } _ { i } \| ^ { 2 } . } \end{array}
+$$
+
+for any uniformly randomly sampled $j \neq i$ . By sampling $\mathbf { z } _ { j }$ from $q ( \mathbf { z } _ { j } | \mathbf { x } _ { j } )$ where $j \neq i$ , we make sure that all the label information decoder is receiving comes from the actual $\mathbf { y } _ { i }$ that is feed to the decoder and $\mathbf { z } _ { j }$ does not include any information about label. This can be evaluated easily by simply evaluating the penalty term of Eq. (10) twice per minibatch; once as in Eq. (10), and once to approximate $\mathcal { L } _ { d i s e n t } ( \theta , \omega )$ by permuting the properties in the minibatch to be assigned to incorrect molecules. We detail the training algorithm in Section 6.2 of the appendix.
+
+# 4 EXPERIMENTS
+
+We experiment with the QM9 dataset (Ramakrishnan et al., 2014), that contains $1 3 4 \mathbf { k }$ molecules with up to 9 heavy atoms, and the ZINC dataset (Sterling & Irwin, 2015) containing $2 5 0 \mathrm { k }$ druglike molecules. Our goal here is two-fold: we would like to understand (1) whether a supervised variational autoencoder is capable of learning suitable conditional distributions over molecules, and (2) to what extent this task is assisted by the additional regularization term corresponding to the soft constraint.
+
+We represent molecules using the one-hot encoding of their SMILES production rules (Kusner et al., 2017) and add a semantic constraint (Dai et al., 2018) on the decoder network to avoid generating syntactically correct but semantically invalid molecules. We use 80 production rules to describe molecules and set the maximum SMILES sequence length to 100 for the QM9 dataset and 278 for the Zinc dataset. We experiment with the logP property of the molecules (Wildman & Crippen, 1999). We use the same encoder and decoder network structure as Dai et al. (2018) with the only difference that our decoder takes as input the concatenation of $\mathbf { y } , \mathbf { z }$ . We give the details of the architecture in the appendix section 6.2.
+
+We evaluate the reconstruction accuracy and the quality of the molecules generated by our method, which we denote by CGD-VAE (conditional generation with disentangling) and compare against CVAE (Gomez-Bombarelli et al., 2016), GVAE (Kusner et al., 2017), and SD-VAE (Dai et al., 2018). ´ We explore its conditional generation performance in two settings: controlling only the property value and controlling both the property value and the molecule structure to what can be seen as property transfer. We took the results of CVAE, GVAE from the literature. For SD-VAE we used the authors code with the default values to generate results for QM9 since these were not available for QM9. We also implemented supervised VAE versions of SD-VAE which we denote Sup-VAE-X-GRU $\mathrm { ( X \in \{ 1 , 3 \} }$ , denotes GRU layers) and which can do conditional generation.
+
+![](images/d83af7d84ad5e4b1f43f6ce0ea2358c91c263cc5eae0206da718a5bc7d37f5ab.jpg)  
+Figure 3: Conditional generation given the desired $\mathrm { l o g P { = } { - } 0 . 5 7 5 9 }$ , row molecules have a logP within a $15 \%$ range of the desired one.
+
+![](images/e0f8c116c2f73cfe17b82b2094f1aeb8977e80722189f751d7235bfe6e3e375d.jpg)  
+Figure 4: Property transfer
+
+Before proceeding with the experiments we will give some additional details on how we do conditional generation from $p _ { \theta } ( \mathbf { x } | \mathbf { y } _ { 0 } )$ given the target property $\mathbf { y } _ { 0 }$ . Instead of marginalizing over the prior marginal inference distribution mass of the dataset is in the late $p ( z )$ , we mirror the approach taken during training and integrate over an approximation to the $\begin{array} { r } { q _ { \phi } ( \mathbf { z } ) = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } q _ { \phi } ( \mathbf { z } | \mathbf { x } _ { i } ) } \end{array}$ which better characterizes where the large and we do not wish to keep the $N$ entire dataset available at test time, we approximate $q _ { \phi } ( \mathbf { z } )$ with an isotropic Gaussian distribution $\hat { q } _ { \sigma } ( \mathbf { z } ) = \mathcal { N } ( \mathbf { z } | \mathbf { 0 } , \sigma ^ { 2 } \mathbf { I } )$ . We estimate $\sigma$ for each model by Monte Carlo samples from $q _ { \phi } ( \mathbf { z } )$ . For the supervised VAE without the soft constraint regularizer this yields 0.053 for QM9 and 0.118 for ZINC. For our model with the soft constraint we get 0.0354 for QM9 and 0.096 for ZINC. We do conditional generation of $\mathbf { x }$ given $\mathbf { y } _ { 0 }$ by sampling from $\begin{array} { r } { p _ { \theta } ( \mathbf { x } | \mathbf { y } _ { 0 } ) = \int \hat { q } _ { \sigma } ( \mathbf { z } ) p _ { \theta } ( \mathbf { x } | \mathbf { z } , \mathbf { y } _ { 0 } ) d \mathbf { z } } \end{array}$ .
+
+We evaluate reconstruction performance in terms of the correctly reconstructed molecules on test sets of size 10k for QM9 and $5 \mathrm { k }$ for ZINC, for the latter we used the default test set. We evaluate the generated molecules’ quality by the percentage of valid, unique (i.e. percentage of unique molecules among the generated valid molecules) and novel (i.e. percentage of molecules never seen in the training set among the generated molecules) molecules. We estimate these quantities by sampling 10k (5K for ZINC) $\mathbf { z }$ from the ${ \hat { q } } _ { \sigma } ( \mathbf { z } )$ and coupling each one of them with a logP value, $\mathbf { y }$ , randomly selected from the test set, and we subsequently decode the $\mathbf { z } , \mathbf { y }$ concatenation. We can see that our model has a better reconstruction performance compared to the baselines while in some cases generating slightly less valid molecules table 1. In terms of the three quality measures achieves an excellent performance across all three metrics being always one of the two best performing methods for any metric.
+
+To visualise how the conditional generation operates we randomly sample from the test set some molecule and obtain its property value $\mathbf { y } _ { 0 }$ . We then draw 50 random samples $\mathbf { z } _ { i }$ from $\hat { q } _ { \sigma } ( \mathbf { z } )$ and decode the $\left[ \mathbf { z } _ { i } , \mathbf { y } _ { 0 } \right]$ vectors. Among the generated valid molecules we compute the percentage of those that have a property value $\mathbf { y } _ { i }$ that is within a $15 \%$ range from the $\mathbf { y } _ { 0 }$ property value. In Figure 3 we present the molecules obtained for a test molecule that had a logP of $- 0 . 5 7 5 9$ . Out of the 50 generated molecules 46 were valid of which we give the five that were within a $15 \%$ range from the $\mathbf { y } _ { 0 }$ value in Figure 3. As we can see we get molecules that are structurally very different from the original one yet they have similar logP value.
+
+To quantify the quality of the conditional generations we measure the correlation between the property value we obtain by the conditional generation and the property value on which we conditioned the generation. We randomly sample $1 0 0 0 { \textbf { y } }$ values from the test set and $1 0 0 0 \textbf { z }$ values from the approximate learned prior $\hat { q } _ { \sigma } ( \mathbf { z } )$ . We decode each pair, obtain $\hat { \mathbf { x } } \sim p _ { \theta } ( \mathbf { x } | \mathbf { y } , \mathbf { z } )$ , and then measure the correlation of the original y with the $\hat { \mathbf { y } }$ of generated $\hat { \bf x }$ . In Table 2, we give the correlation estimates for our method and the Sup-VAE baselines. As we can see our method has a considerably higher correlation score between the input and the obtained property than Sup-VAE. Conditional generation seems considerably harder for the ZINC dataset for all methods.
+
+To visualise the style transfer behavior of our model we randomly sample two molecules $\mathbf { x } _ { A } , \mathbf { x } _ { B }$ from the test set. We then sample $\mathbf { z } _ { A }$ from the learned posterior $q _ { \phi } ( \mathbf { z } | \mathbf { x } _ { A } )$ . We subsequently decode $\left[ \mathbf { z } _ { A } , \mathbf { y } _ { B } \right]$ , $\mathbf { y } _ { B }$ is the property of $\mathbf { x } _ { B }$ , and get a new molecule $\hat { \mathbf { x } } _ { A B }$ . Ideally, the obtained molecule $\hat { \mathbf { x } } _ { A B }$ should have a property value (logP) close to the target $\mathbf { y } _ { B }$ and be similar to $\mathbf { x } _ { A }$ . In Figure 4 we give one such example. To put the results into context in Figure 8 in appendix, we give the results of a virtual screening method, where we select from the full dataset five molecules which are structurally similar to $\mathbf { x } _ { A }$ and have logP values close to $\mathbf { y } _ { B }$ . As we can see the molecule that our model generates is a new one.
+
+![](images/ffa61574cd2f40b5b194d3b7515745269b23e87d9fcf063708e5b80200110fb9.jpg)  
+Figure 5: Style transfer. The $\mathbf { z }$ of the nine real molecules placed in the $\mathbf { X }$ -axis is combined with 11 y property values, sampled in [-4.9, 4.9], the resulting pair is decoded to a molecule.
+
+To quantify the style transfer performance we proceed in exactly the same manner as we did to quantify the conditional generation performance. However, now instead of sampling $\mathbf { z }$ from the approximate learned prior, ${ \hat { q } } _ { \sigma } ( \mathbf { z } )$ , we first sample some $\mathbf { x }$ from the test set and then we sample $\mathbf { z }$ from the learned posterior $q ( \mathbf { z } | \mathbf { x } )$ . The results are in the second column of Table 2. As we can see the correlation values are now lower than the ones we obtained in the simple conditional generation case. This can be explained by the fact that now we are forcing a specific combination of structure, z comes from a real molecule, and property, which might simply be physically infeasible since the molecule space is discrete and not all combinations are possible. In addition, as it was the case for the conditional generation, style transfer is considerably more difficult for the ZINC dataset.
+
+We further explore the style transfer and visualize how our model covers the combined space of molecule structure and properties. We sample nine molecules from the QM9 test set, and get their $\mathbf { z }$ encodings. For each such encoding we decode the vectors $[ \mathbf { z } , y ] , y \in [ - 4 . 9 , 4 . 9 ]$ , with the $y$ (logP) interval sampled at 11 points. We give in Figure 5 the resulting valid molecules, each column there corresponds to one of the nine original molecules, the ones surrounded by dotted rectangle, and their decodings with different logP values.For each original molecule we give the generated molecules ordered along the y axis according to the y property that they actually exhibit. The x-axis does not provide an ordering of the original molecules according to $\mathbf { Z }$ , in fact we have ordered the original molecules by their y property. As we can see not all $( \mathbf { z } , y )$ combinations produce a result. These holes can be explained either by the physical infeasibility of the combination and/or a limitation of the learned model.
+
+We can use conditional generation to control in a fine manner the value of the desired property, to what can be seen as direct property optimization. We visualise the level of control we have on an experiment with a single molecule (with logP is -1.137), which we randomly sample from the test set. We obtain its $\mathbf { z }$ encoding and perform generations with increased logP taking values in 1000 point grid in $\left[ - 1 . 1 3 7 , 4 . 9 \right]$ . We then decode $\left[ \mathbf { z } , \mathbf { y } _ { i } \right]$ and compute the logP value of the generated molecules. Among the 1000 generated molecules only 19 are unique. We get an increase of logP of a very discrete nature, Figure 6. As already discussed not all combinations of structure and properties are possible. The generated molecules themselves are shown in the supplemental material.
+
+<table><tr><td>Model</td><td></td><td>z~qo(z)</td><td>z~q(z|x)</td></tr><tr><td rowspan="4">QM9</td><td>Sup-VAE-1-GRU</td><td>0.5420</td><td>0.2526</td></tr><tr><td>CGD-VAE-1-GRU</td><td>0.7185</td><td>0.5005</td></tr><tr><td>Sup-VAE-3-GRU</td><td>0.6958</td><td>0.4204</td></tr><tr><td>CGD-VAE-3-GRU</td><td>0.7414</td><td>0.4715</td></tr><tr><td rowspan="4">ZINC</td><td>Sup-VAE-1-GRU</td><td>0.2301</td><td>0.0481</td></tr><tr><td>CGD-VAE-1-GRU</td><td>0.3877</td><td>0.0880</td></tr><tr><td>Sup-VAE-3-GRU</td><td>0.3514</td><td>0.1808</td></tr><tr><td>CGD-VAE-3-GRU</td><td>0.3966</td><td>0.1559</td></tr></table>
+
+Table 2: Correlation between the desired input property and the obtained property . $\mathbf { z } \sim \hat { q } _ { \sigma } ( \mathbf { z } )$ corresponding to conditional generation), and x, $\mathbf { z } \sim q ( \mathbf { z } | \mathbf { x } )$ to property transfer case.
+
+![](images/dd9ea64a1ba0ee993b06ada6658a78a2896a28fd1475d73046b1a5c7a4f5c11d.jpg)  
+Figure 6: Property optimization. Given a start molecule (red), we combine its $\mathbf { z }$ with $1 0 0 0 \log \mathrm { P }$ values and decode (blue)
+
+![](images/6daa2bdd2b6b3d32bf6a2bb30e18d85a323167036361749ae8c33e10b946aa5e.jpg)
+
+![](images/171721555e584b5336b980f58a15f7e4a7ff8c35dce2ba5cd515c171c0be165b.jpg)  
+Figure 7: A comparison of simulated logP values and Tanimoto similarity to a target on the ZINC dataset. While the stacked LSTM model has high accuracy in terms of matching the desired property, it would require drawing many samples before finding any close matches to any particular desired prototype. The CGD-VAE-3-GRU model represents a middle ground between a standard VAE model which does not condition on the property, and the stacked LSTM model which does not learn a reusable representation.
+
+# 4.1 CONDITIONAL LSTM BASELINE
+
+Finally, we consider a variant of the stacked LSTM model of Segler et al. (2017), with no latent space, where the model is modified to take a target logP value as an additional input at each generation step. This model forms a very strong baseline for many distribution matching tasks (Liu et al., 2018; ?), though as best we are aware this has never been used directly for conditional generation given a target property. We use a modification of the implementation provided by (?) with three layers and default settings, and fit the model by maximum likelihood training on $\begin{array} { r } { p _ { \theta } ( \mathbf { x } | \mathbf { y } ) = \prod _ { t = 1 } ^ { T } p _ { \theta } ( x _ { t } | x _ { 1 : t - 1 } , \mathbf { y } ) } \end{array}$ .
+
+Training on the ZINC dataset, we find the generated molecules from this model have a very high correlation 0.975 with the target logP value, greatly outperforming any of the latent variable models we consider. This suggests that such a model would be very useful for generating candidates globally, but as the model has no latent variable it is not amenable to style transfer. We observe this in Figure 7, which samples 100 candidate molecules from both the stacked LSTM model and for CGD-VAE-3- GRU, conditioning on the property of one randomly-chosen test set example, while computing the Tanimoto similarity (computed using Morgan fingerprints of radius 2) to a second randomly-chosen test set example, across 200 pairs. The VAE has higher Tanimoto similarities as it can condition on the latent variable of the target molecule, representing a trade-off against the better adherence to the target property value of the unconditioned LSTM.
+
+# 5 CONCLUSION
+
+We presented a single step approach for the conditional generation of molecules with desired properties. Our model allows also to condition generation on a prototype molecule with a desired high-level structure. This work thus directly inverts the traditional relationship between molecules and their properties. We found that training the deep generative models conditional on target properties, following a supervised VAE approach, does not appreciably harm the quality of the unconditional generative model as measured by validity, novelty, and uniqueness of samples. Furthermore, we see that the additional act of regularizing the output using an approximate property predictor helps improve both reconstruction accuracy and property correlations in most combinations of tasks and datasets, particularly for the smaller QM9 dataset and for smaller models with fewer RNN layers. We also note that although none of the deep latent variable models are competitive with an LSTM baseline when purely considering generation conditioned on a target property value, the low Tanimoto similarity between randomly sampled candidates and an arbitrary style transfer target makes clear that such a model is not suitable for targeted generation of candidates which are close in structure to a particular prototype.
+
+In future work, we want to explore how to further improve the correlation between the desired input properties to the decoder, and the properties of the generated molecules. Moreover, we want also to condition on multiple properties; while this is in principle possible in our framework, we do not explore it empirically here. Modifying a single property while constraining the remaining to be close to the original can further aggravate the infeasibility problem, as not all combinations of molecular properties may even be feasible, perhaps requiring learning a dependency structure between multiple properties.
+
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+
+# 6 APPENDIX
+
+# 6.1 THE REGULARISER AND ITS RELATION TO THE MUTUAL INFORMATION MAXIMIZATION
+
+The soft constrain in the loss 3, in fact , is equivalent to a simple maximizing mutual information formulation between generated molecules $\hat { \bf x }$ and the target property $\mathbf { y }$ provided to the generator. Assume the true conditional distribution is $\tilde { p } ( \mathbf { y } | \mathbf { x } )$ :
+
+$$
+\begin{array} { r l } & { \mathbf { I } ( \mathbf { y } ; \hat { \mathbf { x } } ) = H ( \mathbf { y } ) - H ( \mathbf { y } \vert \hat { \mathbf { x } } ) } \\ & { \qquad = H ( \mathbf { y } ) + \mathbb { E } _ { \hat { \mathbf { x } } \sim p _ { \theta } ( \mathbf { x } \vert \mathbf { y } ) } \mathbb { E } _ { \mathbf { y } ^ { \prime } \sim \tilde { p } ( \mathbf { y } \vert \hat { \mathbf { x } } ) } [ \log \tilde { p } ( \mathbf { y } ^ { \prime } \vert \hat { \mathbf { x } } ) ] } \end{array}
+$$
+
+We do not know the true distribution $\tilde { p } ( \mathbf { y } | \hat { \mathbf { x } } )$ , however, the RDKit provides an estimation $p ( \mathbf { y } \vert \hat { \mathbf { x } } )$ of the distribution assuming a Gaussian distribution over error:
+
+$$
+p ( \mathbf { y } \vert \hat { \mathbf { x } } ) = \mathcal { N } ( \mathbf { y } \vert f ( \hat { \mathbf { x } } ) , \lambda _ { 1 } ^ { - 1 } \mathbf { I } )
+$$
+
+where $f$ is the molecule property estimator, i.e., RDKit. We have:
+
+$$
+\begin{array} { l } { { \displaystyle { \bf I } ( { \bf y } ; \hat { \bf x } ) = H ( { \bf y } ) + \mathbb { E } _ { \hat { \bf x } \sim p _ { \theta } ( { \bf x } \mid { \bf y } ) } \mathbb { E } _ { { \bf y } ^ { \prime } \sim \tilde { p } ( { \bf y } \mid \hat { \bf x } ) } [ \log \frac { \tilde { p } ( { \bf y } ^ { \prime } \mid \hat { \bf x } ) } { p ( { \bf y } ^ { \prime } \mid \hat { \bf x } ) } p ( { \bf y } ^ { \prime } \mid \hat { \bf x } ) ] } \ ~ } \\ { { \displaystyle ~ = H ( { \bf y } ) + \mathbb { E } _ { \hat { \bf x } \sim p _ { \theta } ( { \bf x } \mid { \bf y } ) } [ D _ { k l } ( \tilde { p } ( { \bf y } ^ { \prime } \mid \hat { \bf x } ) \vert \vert p ( { \bf y } ^ { \prime } \vert \hat { \bf x } ) ) + \mathbb { E } _ { { \bf y } ^ { \prime } \sim \tilde { p } ( { \bf y } \mid \hat { \bf x } ) } \log p ( { \bf y } ^ { \prime } \mid \hat { \bf x } ) ] } \ ~ } \\ { { \displaystyle ~ \geq H ( { \bf y } ) + \mathbb { E } _ { \hat { \bf x } \sim p _ { \theta } ( { \bf x } \mid { \bf y } ) } [ \mathbb { E } _ { { \bf y } ^ { \prime } \sim \tilde { p } ( { \bf y } \mid \hat { \bf x } ) } \log p ( { \bf y } ^ { \prime } \mid \hat { \bf x } ) ] } } \end{array}
+$$
+
+By following the Lemma 5.1 given in Chen et al. (2016), we have
+
+$$
+\mathbf { I } ( \mathbf { y } ; \hat { \mathbf { x } } ) \geq H ( \mathbf { y } ) + \mathbb { E } _ { \mathbf { y } \sim p ( \mathbf { y } ) , \hat { \mathbf { x } } \sim p _ { \theta } ( \mathbf { x } | \mathbf { y } ) } [ \log p ( \mathbf { y } | \hat { \mathbf { x } } ) ]
+$$
+
+As $H ( \mathbf { y } )$ is constant, minimizing $\mathbb { E } _ { \hat { \mathbf { x } } \sim p _ { \theta } ( \mathbf { x } | \mathbf { y } _ { i } ) } \| f ( \hat { \mathbf { x } } ) - \mathbf { y } _ { i } \| ^ { 2 }$ is equivalent to maximizing $\mathbf { I } ( \mathbf { y } ; \hat { \mathbf { x } } )$ under the assumption that $p ( \mathbf { y } \vert \hat { \mathbf { x } } )$ is close to $\tilde { p } ( \mathbf { y } | \hat { \mathbf { x } } )$
+
+# 6.2 ARCHITECTURE AND TRAINING PROCEDURE DESCRIPTION
+
+We use the same encoder and decoder network structure as Dai et al. (2018) with the only difference that our decoder takes as input the concatenation of $\mathbf { y } , \mathbf { z }$ . As GRU layers become computationally expensive when the sequences length increase, we also examined the model using less layer GRU. To be precise, the decoder in Dai et al. (2018) takes the from of a dense hidden layer with ReLU activation followed by three layers GRU Chung et al. (2014). We tried two different settings of decoder: in the first setting, we feed the concatenation of $\mathbf { y } , \mathbf { z }$ to dense layer then apply one layer GRU, in the second setting, to enhance the effect of $\mathbf { y }$ in the decoder, we feed y not only to the dense layer but also to each layer of GRU. Furthermore, we set the dimension of the latent representation to 56. For the oracle function estimator $f _ { w }$ , we use the same network architecture as the encoder (there is no parameter sharing) and we add one more fully connected layer followed by a Tanh transformation.
+
+To speed up convergence, we initialize the $f _ { w }$ from a pre-training, where we train $f _ { w }$ on the welltrained (maximum 500 epochs with early stopping) supervised VAE’s decoder output to predict the molecules property value. We also initialize the parameters of the encoder/decoder networks with the partially trained supervised VAE model (after 40 epochs for QM9, 100 epochs for ZINC). We do not update $\omega$ and $\phi , \theta$ simultaneously, instead we do an alternate optimization. We update $\omega$ continuously for five epochs while holding $\phi , \theta$ and do the same for updating $\phi , \theta$ . We set the hyper-parameter value $\lambda _ { 1 }$ to 50 and $\lambda _ { 2 }$ to 1. The mini-batch size is set to 300 for QM9 and 100 for ZINC. We use ADAM optimizer with learning rate 0.0001 and pytorch lr-schedular on the validation loss. The general training algorithm is described in below algorithm block1. In our experiment, to train $f _ { \omega }$ , we skipped the second term in step 7, which means we only train $f _ { \omega }$ on the training data but not the newly generated molecules obtained by permuting the property. The reason for this is that, during the training, we found that it is easy for the model to learn to reconstruct but hard to conditionally generate the molecules with given properties while we have no guidance of what the molecules should look like. Further more, some combination of $\mathbf { z }$ and $\mathbf { y }$ are physically not feasible. In this case, when the conditional generation is not good enough yet during the training, we end up fitting $f _ { \omega }$ on the miss represented molecules representations and it makes the optimization harder.
+
+# Algorithm 1 Training algorithm
+
+1: Initialize $p _ { \theta } ( \mathbf { x } | \mathbf { z } , \mathbf { y } )$ , $q _ { \phi } ( { \bf z } | { \bf x } )$ , $f _ { w }$   
+2: for i=1,2, . . . , N (maximum epoch number) do   
+3: for ${ \bf j } = 1 , 2 , \ldots , { \bf L }$ , sample a minibatch $D = ( { \bf X } , { \bf Y } ) = \{ { \bf x } _ { i } , { \bf y } _ { i } ) \} _ { i = 1 } ^ { M }$ of M samples do   
+4: randomly permute the property set $\mathbf { Y }$ to obtain $\mathbf { Y } ^ { \ast }$ and define a label permuted mini   
+batch $D ^ { * } = ( \mathbf { X } , \mathbf { \bar { Y } } ^ { * } ) = \{ \mathbf { x } _ { i } , \mathbf { y } _ { i } ^ { * } \} _ { i = 1 } ^ { \bar { M } }$   
+5: $\begin{array} { l } { { \displaystyle \theta ^ { j } = \theta ^ { j - 1 } - \gamma \big ( - \nabla _ { \theta } \mathcal { L } _ { E L B O } \big ( \theta , \phi , \omega \big ) + \frac { \lambda _ { 1 } } { 2 } \sum _ { \substack { ( \mathbf { x } _ { i } , \mathbf { y } _ { i } ) \in D ^ { * } } } \mathbb { E } _ { q ( \mathbf { z } | \mathbf { x } _ { i } ) } \nabla _ { \theta } \| f _ { \omega } \big ( g _ { \theta } \big ( \mathbf { z } , \mathbf { y } _ { i } \big ) \big ) - \mathbf { y } _ { i } \| ^ { 2 } \big ) } } \\ { { \displaystyle \phi ^ { j } = \phi ^ { j - 1 } - \gamma \big ( - \nabla _ { \phi } \mathcal { L } _ { E L B O } \big ( \theta , \phi , \omega \big ) \big ) } } \\ { { \displaystyle w ^ { j } = w ^ { j - 1 } - \gamma \big ( \frac { \lambda _ { 2 } } { 2 } \sum _ { \substack { ( \mathbf { x } _ { i } , \mathbf { y } _ { i } ) \in D } } \mathbb { E } _ { q ( \mathbf { z } | \mathbf { x } _ { i } ) } \nabla _ { \omega } \| f _ { \omega } \big ( g _ { \theta } ( \mathbf { z } , \mathbf { y } _ { i } ) \big ) - \mathbf { y } _ { i } \| ^ { 2 } + \frac { \lambda _ { 1 } } { 2 } \sum _ { \substack { ( \mathbf { x } _ { i } , \mathbf { y } _ { i } ) \in D ^ { * } } } \mathbb { E } _ { q ( \mathbf { z } | \mathbf { x } _ { i } ) } \nabla _ { \omega } \| f _ { \omega } \big ( g _ { \theta } ( \mathbf { z } , \mathbf { y } _ { i } ) \big ) - \mathbf { y } _ { i } \| ^ { 2 } \big ) } } \end{array}$   
+6:   
+7:
+
+# 6.3 USE A FIXED PRE-TRAINED PROPERTY PREDICTION FUNCTION
+
+We also investigate the case where we train the property prediction function $f _ { \omega }$ on the well trained supervised VAE output and keep it fixed during the training of the main model. We give the performance in tables 3, 4. Using a fixed $f _ { \omega }$ , in terms of reconstruction and generation performance, delivers mixed results 3. However, in terms of conditional generation 4, it does perform better than the baselines but worse compared to the case where we also update $f _ { \omega }$ during the learning.
+
+Table 3: Sup-VAE-1-GRU /Sup-VAE-3-GRU: supervised version of SD-VAE model where y is been feed to only the first layer/all layer decoder. CGD-VAE: our model, conditional generation with disentangling. The result for CVAE and GVAE are taken from the literature, ”-” refers that those measures are not reported. The rest of baseline result is obtained by rerunning (SD-VAE) and editing the original code (Sup-VAE).   
+
+<table><tr><td></td><td colspan="3">QM9</td><td colspan="5">ZINC</td></tr><tr><td>Model</td><td>Reconstruction %</td><td>Valid%</td><td>Unique %</td><td>Novel %</td><td>Reconstruction %</td><td>Valid%</td><td>Unique %</td><td>Novel %</td></tr><tr><td>CVAE</td><td>3.61</td><td>10.30</td><td>1</td><td>90.00</td><td>44.60</td><td>0.70</td><td>-</td><td>100</td></tr><tr><td>GVAE</td><td>96.00</td><td>60.20</td><td>=</td><td>80.90</td><td>53.70</td><td>7.20</td><td></td><td>100</td></tr><tr><td>SD-VAE</td><td>97.84</td><td>98.40</td><td>99.28</td><td>91.97</td><td>76.20</td><td>43.50</td><td>-</td><td>、</td></tr><tr><td>Sup-VAE-1-GRU</td><td>97.53</td><td>93.66</td><td>91.30</td><td>92.05</td><td>74.12</td><td>32.84</td><td>95.61</td><td>100</td></tr><tr><td>CGD-VAE-1-GRU</td><td>98.96</td><td>95.03</td><td>92.77</td><td>89.74</td><td>67.46</td><td>17.38</td><td>82.44</td><td>100</td></tr><tr><td>Sup-VAE-3-GRU</td><td>97.81</td><td>97.9</td><td>95.09</td><td>89.47</td><td>82.40</td><td>36.16</td><td>86.26</td><td>100</td></tr><tr><td>CGD-VAE-3-GRU</td><td>96.9</td><td>93.8</td><td>98.29</td><td>89.55</td><td>81.80</td><td>37.78</td><td>98.70</td><td>100</td></tr></table>
+
+<table><tr><td></td><td>Model</td><td>z~qq(z)</td><td>z ~ q(z|x)</td></tr><tr><td rowspan="4">QM9</td><td>Sup-VAE-1-GRU</td><td>0.5420</td><td>0.2526</td></tr><tr><td>CGD-VAE-1-GRU</td><td>0.6331</td><td>0.3835</td></tr><tr><td>Sup-VAE-3-GRU</td><td>0.6958</td><td>0.4204</td></tr><tr><td>CGD-VAE-3-GRU</td><td>0.6665</td><td>0.4507</td></tr><tr><td rowspan="4">ZINC</td><td>Sup-VAE-1-GRU</td><td>0.2301</td><td>0.0481</td></tr><tr><td>CGD-VAE-1-GRU</td><td>0.2981</td><td>0.0866</td></tr><tr><td>Sup-VAE-3-GRU</td><td>0.3638</td><td>0.1818</td></tr><tr><td>CGD-VAE-3-GRU</td><td>0.3765</td><td>0.1310</td></tr></table>
+
+Table 4: Correlation between the desired input property and the obtained property when z is sampled from the approximate learned prior, $\mathbf { z } \sim \hat { q } _ { \sigma } ( \mathbf { z } )$ , (conditional generation), and when $\mathbf { z }$ is sampled from the learned posterior given some x, $\mathbf { z } \sim q ( \mathbf { z } | \mathbf { x } )$ , (property transfer).
+
+# 6.4 VIRTUAL SCREENING
+
+The figure 8 displays the results of a virtual screening method, where we select from the full dataset five molecules which are structurally similar to $\mathbf { x } _ { A }$ in figure 4 in section 4 and have logP values close to $\mathbf { y } _ { B }$ . As we can see the molecule that our model generates is a new one.
+
+![](images/a7e485939ef9875fdba8293f1eb15bcfd2c0bfca822f4dd0ac966cbb93a44c64.jpg)  
+Figure 8: Molecules selected with virtual screening over the full dataset in a manner that they are structurally similar to the A molecule of figure 4 while they have a logP value which is close to the logP value of the B molecule also of figure 4
+
+# 6.5 METRICS AS FUNCTION OF $\mathbf { y } - \mathbf { y } ^ { \prime }$
+
+The validity and novelty were mainly used to assess purely the generative model performance. However, it is also interesting to see if the model capable of generating valid and novel molecules if we start from an existing molecules and drift away from the original label, i.e., if we get $\mathbf { z }$ from $q ( \mathbf { z } | \mathbf { x } )$ , and then compare different values from $p ( \mathbf { \bar { x } } | \mathbf { z } , \mathbf { y } ^ { \prime } )$ as $\mathbf { y } ^ { \prime }$ moves far from y. We randomly sample a molecule $\mathbf { x }$ whose LogP is y from the test set, then sample $1 0 \textbf { z }$ from $q ( \mathbf { z } | \mathbf { x } )$ . For each such $\mathbf { z }$ we couple it with a $\mathbf { y } ^ { \prime }$ that is different that $\mathbf { y }$ , and sample 10 molecules from $p ( \mathbf { x } | \mathbf { z } , \mathbf { y } ^ { \prime } )$ . Eventually, for each such $\mathbf { y } ^ { \prime }$ , starting from original molecule $\mathbf { x }$ , we generated 100 molecules, and we report the validity, uniqueness and novelty as a function of $\mathbf { y } - \mathbf { y } ^ { \prime }$ . The figure 9 displays result of repeating above process for 20 randomly sampled $\displaystyle ( \mathbf { x } , \mathbf { y } )$ along 100 grid points for $\mathbf { y } - \mathbf { y } ^ { \prime }$ . The result confirms that on a big data set, conditional generative models uniqueness, validity and novelty performance is not affected by the size of the modification done on the property. However, on a small dataset, uniqueness is not affected. As expected, novelty increases as the properties modification size increases and validity drops slightly as the property modification size increase.
+
+![](images/05561149d0652633c285e17687e4cc57ccdd333927040429da49e149095794c1.jpg)  
+Figure 9: CGD-VAE-3-GRU model validity, novelty, uniqueness performance on property transfer task as a function of $\mathbf { y } - \mathbf { y } ^ { \prime }$ on QM9 dataset.
+
+![](images/7e913f7fbf7e5ee958020cae4f83630081d3c4db545c8f072beab85a15a4684d.jpg)  
+Figure 10: CGD-VAE-3-GRU model validity, novelty, uniqueness performance on property transfer task as a function of $\mathbf { y } - \mathbf { y } ^ { \prime }$ on ZINC dataset.
+
+With our model, during the generation, we observe that sampling from the approximated marginal posterior improves generation performance when compered to sampling from the prior. Here we investigate if this findings holds for other baseline models or not. We explored the behavior of baselines when the $\mathbf { z }$ is sampled from the approximate marginal posterior, we observe that for CVAE and GVAE the validity did not change (as the ${ \hat { q } } ( \mathbf { z } )$ and $p ( \mathbf { z } )$ are essentially identical); for the SD-VAE the validity increases (Table 5).
+
+SDVAE   
+Table 5: Baseline model performance on ZINC   
+
+<table><tr><td></td><td>Valid%</td><td>Unique %</td><td>Novel %</td></tr><tr><td>z ~qσ(z)</td><td>56.05</td><td>80.69</td><td>100</td></tr><tr><td>z ~p(z)</td><td>43.50</td><td>82.26</td><td>100</td></tr></table>
+
+# 6.7 MOLECULE PROPERTY OPTIMIZATION
+
+Figure 11 is the visualization of the generated molecules from property optimization task, given in figure 6 section 4. The molecules are generated by increasing the logP of a given molecule, i.e. we hold $\mathbf { z }$ fixed and increase the y value. Among the all generated molecules, 19 of them are unique.
+
+![](images/cc585b7043d323b6f84b9809b8adc19b851ad1196e606dc71b64fabbf987c156.jpg)  
+Figure 11: Molecules generated with an increasing logP

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