Original: Internalized Biases in Fréchet Inception Distance
Revised: Internalized Biases in Fréchet Inception Distance

Original: Anonymous Author(s)

Original: AfﬁliationAddress

Original: Abstract
Revised: Abstract

Original: Fréchet inception distance (FID) established itself as standard performance measuring method for generative adversarial networks (GANs).
Revised: Fréchet inception distance (FID) established itself as standard performance measuring method for generative adversarial networks (GANs).

Original: In this paper, weempirically investigate the biases that are inherited by its underlying design decision of extracting image features using the Inception v3 image classiﬁcationnetwork.
Revised: In this paper, we empirically investigate the biases that are inherited by its underlying design decision of extracting image features using the Inception v3 image classiﬁcation network.

Original: As a result, we investigate how reliable FID is in terms of rankingperformances of GANs.
Revised: As a result, we investigate how reliable FID is in terms of ranking performances of GANs.

Original: In this context, we ﬁnd that FID is not aligned withhuman perception and exchanging Inception v3 with different image classiﬁcationnetworks simply steers the ranking towards different biases. [Figure] FID [Figure]
Revised: In this context, we ﬁnd that FID is not aligned with human perception and exchanging Inception v3 with different image classiﬁcation networks simply steers the ranking towards different biases

Original: FID

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Original: DCGAN

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Original: FID

Original: FID

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Original: FID

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Original: FID

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Original: [Figure] DCGAN [Figure] The generation of photo-realistic, unseen images has made signiﬁcant progress with the introductionof generative adversarial networks (GANs) [6].
Revised: The generation of photo-realistic, unseen images has made signiﬁcant progress with the introduction of generative adversarial networks (GANs) [6].

Original: Since then, many architectures emerged competingwith each other to provide the best performance [3, 15, 13].
Revised: Since then, many architectures emerged competing with each other to provide the best performance [3, 15, 13].

Original: With it arose the question how theirperformance should be interpreted and measured to provide a ranking between different architectures.
Revised: With it arose the question how their performance should be interpreted and measured to provide a ranking between different architectures.

Original: Metrics like inception score (IS) and Fréchet inception distance (FID) were proposed to evaluateimage distributions automatically.
Revised: Metrics like inception score (IS) and Fréchet inception distance (FID) were proposed to evaluate image distributions automatically.

Original: These metrics are based on extracting features from images thatare provided by the Inception v3 image classiﬁcation network [24], and hence inspired their names.
Revised: These metrics are based on extracting features from images that are provided by the Inception v3 image classiﬁcation network [23], and hence inspired their names.

Original: While IS was proven to be not useful to compare different models [2], its successor FID is nowwidely adopted within the GAN community.
Revised: While IS was proven to be not useful to compare different models [2], its successor FID is now widely adopted within the GAN community.

Original: FID compares the distribution of features betweentwo image datasets that are estimated from training data and samples from the generator network.
Revised: FID compares the distribution of features between two image datasets that are estimated from training data and samples from the generator network.

Original: Well-performing generators are supposed to produce images that match the feature distribution of the data.
Revised: Well-performing generators are supposed to produce images that match the feature distribution of the data.

Original: Some theoretical and practical shortcomings of FID, like a bias due to sample sizes [4] andinconsistent downsampling implementations between different image processing libraries [19] arealready discussed in the literature.
Revised: Some theoretical and practical shortcomings of FID, like a bias due to sample sizes [4] and inconsistent downsampling implementations between different image processing libraries [19] are already discussed in the literature.

Original: However, none of these works discuss the shortcomings that comewith its underlying feature extractor.
Revised: However, none of these works discuss the shortcomings that come with its underlying feature extractor.

Original: The contributions of this paper are as follows:
Revised: The contributions of this paper are as follows:

Original: • We empirically show biases in the underlying assumptions of the commonly used metricFréchet Inception Distance (FID) caused by the network Inception v3 (section 1).
Revised: • We empirically show biases in the underlying assumptions of the commonly used metric Fréchet Inception Distance (FID) caused by the network Inception v3 (section 1).

Original: • We investigate if an improvement in terms of FID is a reliable indicator of improvement ingenerator performance.
Revised: • We investigate if an improvement in terms of FID is a reliable indicator of improvement in generator performance.

Original: Here, we show cases where FID clearly fails to align its ranking with human perception (section 2; see Figure 1 for an example). 
Revised: Here, we show cases where FID clearly fails to align its ranking with human perception (section 2; see Figure 1 for an example). [Figure]

Original: b r i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u
Revised: g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u

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Original:  Fréchet Inception Distance and its Biases
Revised:  Fréchet Inception Distance and its Biases

Original: To compute FID between two image datasets, image features are extracted by sampling images fromthose datasets and feeding them into the pretrained Inception v3 [24] image classiﬁcation network.
Revised: To compute FID between two image datasets, image features are extracted by sampling images from those datasets and feeding them into the pretrained Inception v3 [23] image classiﬁcation network.

Original: Inthe following, we denote Inception v3 by function φ that returns feature column vectors given singleimages and feature matrices with samples on rows given image datasets.
Revised: In the following, we denote Inception v3 by function φ that returns feature column vectors given single images and feature matrices with samples on rows given image datasets.

Original: FID is then computed viathe Wasserstein-2 distance
Revised: FID is then computed via the Wasserstein-2 distance

Original: [Equation]
Revised: [Equation]

Original: between two image sources, where tr ( · ) is the trace operator,
Revised: between two image sources, where tr ( · ) is the trace operator,

Original: [Equation]
Revised: [Equation]

Original: and

Original: [Equation]

Original: are the mean vector and covariance matrix of feature vectors of dataset X .
Revised: are the mean vector and covariance matrix of feature vectors of dataset X .

Original: The motivation of FID isthat, given a sufﬁciently large number of samples, the ﬁrst two moments of the feature distributionsshould match if the images are sampled from the same dataset.
Revised: The motivation of FID is that, given a sufﬁciently large number of samples, the ﬁrst two moments of the feature distributions should match if the images are sampled from the same dataset.

Original: Hence, the closer the generatornetwork gets to reproducing the Inception v3 feature distribution of the training data, the smaller FIDbecomes.
Revised: Hence, the closer the generator network gets to reproducing the Inception v3 feature distribution of the training data, the smaller FID becomes.

Original: FID is related to model robustness.
Revised: FID is related to model robustness.

Original: While pretrained feature extractors can facilitate certaintasks in meaningful ways, like object recognition or detection, we argue that caution needs to betaken in the context of comparing image distributions.
Revised: While pretrained feature extractors can facilitate certain tasks in meaningful ways, like object recognition or detection, we argue that caution needs to be taken in the context of comparing image distributions.

Original: The Inception v3 network is trained on the
Revised: The Inception v3 network is trained on the

Original: ImageNet object recognition challenge [5], where the task is to classify images into 1000 distinct [Equation]
Revised: ImageNet object recognition challenge [5], where the task is to classify images into 1000 distinct classes.

Original: classes. Hence, the network learns to extract features from images that discriminate classes found in
Revised: Hence, the network learns to extract features from images that discriminate classes found in

Original: ImageNet.
Revised: ImageNet.

Original: For this task, it is beneﬁcial for the network to become robust against several distributionshifts, like color or intensity changes and diverse spatial transformations.
Revised: For this task, it is beneﬁcial for the network to become robust against several distribution shifts, like color or intensity changes and diverse spatial transformations.

Original: A common way to equipimage classiﬁcation networks with robustness against before-mentioned shifts is to augment thetraining data.
Revised: A common way to equip image classiﬁcation networks with robustness against before-mentioned shifts is to augment the training data.

Original: For example, Inception v3 was trained with the following augmentation pipeline [1]: a)cropping the input image with a random scale (8%-100%) and aspect ratio ( 3 / 4 to 4 / 3 ), b) randomlyﬂipping the input image horizontally, and c) randomly introducing color distortions in terms of hue,saturation, brightness, and contrast.
Revised: For example, Inception v3 was trained with the following augmentation pipeline [1]: a) cropping the input image with a random scale (8%-100%) and aspect ratio ( 3 / 4 to 4 / 3 ), b) randomly ﬂipping the input image horizontally, and c) randomly introducing color distortions in terms of hue, saturation, brightness, and contrast.

Original: Consequentially, we assume that the network is at least robustto some degree of corruption.
Revised: Consequentially, we assume that the network is at least robust to some degree of corruption.

Original: In the following, we investigate i) how robust Inception v3 is againstcertain corruption types, and ii) how these ﬁndings impact the applicability of FID as a metric.h
Revised: In the following, we investigate i) how robust Inception v3 is against certain corruption types, and ii) how these ﬁndings impact the applicability of FID as a metric. h

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Revised: i c a l _ f li p t r a n s l a t i o n _ x t r a n s l a t i o n _ y t r a n s l a t i o n _ xy

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Original: by transforming CIFAR10 [16] test images a) with increasing likelihood of horizontal or vertical ﬂips and b) by moving the image in x, y, or both directions up to an increasing distance (reﬂection padding).
Revised: by transforming CIFAR10 [16] test images a) with increasing likelihood of horizontal or vertical ﬂips and b) by moving the image in x, y, or both directions up to an increasing distance (reﬂection padding).

Original: The ﬁgure depicts the FID between a corruption at a certain level with the original CIFAR10 test dataset.
Revised: The ﬁgure depicts the FID between a corruption at a certain level with the original CIFAR10 test dataset.

Original: We ﬁrst look into how different kinds of corruptions inﬂuence
Revised: We ﬁrst look into how different kinds of corruptions inﬂuence

Original: FID.
Revised: FID.

Original: Research in the area of robustness has produced severalbenchmark dataset collections, one of which is ImageNet-C [8].
Revised: Research in the area of robustness has produced several benchmark dataset collections, one of which is ImageNet-C [8].

Original: This collection contains the ImageNet [5] validation imageswith 19 corruption types at 5 severity levels, hence, a total of95 image datasets.
Revised: This collection contains the ImageNet [5] validation images with 19 corruption types at 5 severity levels, hence, a total of 95 image datasets.

Original: On this benchmark, we can uncover whichtypes of corruptions inﬂuence the feature distribution providedby Inception v3 (and therefore FID) to which degree.
Revised: On this benchmark, we can uncover which types of corruptions inﬂuence the feature distribution provided by Inception v3 (and therefore FID) to which degree.

Original: In Figure 2 we depict the corresponding FIDs between the original
Revised: In Figure 2 we depict the corresponding FIDs between the original

Original: ImageNet validation images and all datasets in ImageNet-C.
Revised: ImageNet validation images and all datasets in ImageNet-C.

Original: We interpret larger FIDs as indicator that the distribution offeatures extracted by Inception v3 is inﬂuenced more by certain corruptions, and hence we derive that the model is moresensitive to these types of corruptions.
Revised: We interpret larger FIDs as indicator that the distribution of features extracted by Inception v3 is inﬂuenced more by certain corruptions, and hence we derive that the model is more sensitive to these types of corruptions.

Original: We can make the following observations from Figure 2: First, Inception v3 is mostlyrobust to deviations in brightness, saturation, and contrast upto a certain degree.
Revised: We can make the following observations from Figure 2: First, Inception v3 is mostly robust to deviations in brightness, saturation, and contrast up to a certain degree.

Original: While information about colors and intensities is lost in these cases, edges are mostly preserved.
Revised: While information about colors and intensities is lost in these cases, edges are mostly preserved.

Original: In thefrequency domain, we can see these corruptions acting on lowfrequencies [25], while high frequencies are mostly untouched.
Revised: In the frequency domain, we can see these corruptions acting on low frequencies [24], while high frequencies are mostly untouched.

Original: Second, Inception v3 is sensitive to noise that acts on the highfrequency spectrum, either by adding high frequency artifacts(impulse noise, shot noise, speckle noise), or by removing highfrequency information (glass blur, Gaussian blur).
Revised: Second, Inception v3 is sensitive to noise that acts on the high frequency spectrum, either by adding high frequency artifacts (impulse noise, shot noise, speckle noise), or by removing high frequency information (glass blur, Gaussian blur).

Original: These observations lead us to the assumption that Inception v3 has a biastowards extracting features based on edges and textures rather than color and intensity information.
Revised: These observations lead us to the assumption that Inception v3 has a bias towards extracting features based on edges and textures rather than color and intensity information.

Original: This aligns with its augmentation pipeline that introduces color distortions, but keeps high frequencyinformation intact (in contrast to, for example, augmentation with Gaussian blur).
Revised: This aligns with its augmentation pipeline that introduces color distortions, but keeps high frequency information intact (in contrast to, for example, augmentation with Gaussian blur).

Original: Consequently, FIDinherits this bias.
Revised: Consequently, FID inherits this bias.

Original: When used as ranking metric, architectures reproducing textures well mightbe preferred over architectures that reproduce color distributions well .
Revised: When used as ranking metric, generative models reproducing textures well might be preferred over models that reproduce color distributions well .

Original: Since ImageNet-C contains no corruptions that test robustness to translations, we further investigatethis aspect by introducing additional corruptions (see Figure 3 in appendix).
Revised: Since ImageNet-C contains no corruptions that test robustness to translations, we further investigate this aspect by introducing additional corruptions (see Figure 3 in appendix).

Original: We are interestedin knowing how FID is inﬂuenced by a) ﬂipping images either horizontally or vertically, and b)by translating the images in certain directions.
Revised: We are interested in knowing how FID is inﬂuenced by a) ﬂipping images either horizontally or vertically, and b) by translating the images in certain directions.

Original: Our results indicate that Inception v3 is mostlyrobust towards horizontal ﬂips and translations, while being more sensitive in the vertical direction.
Revised: Our results indicate that Inception v3 is mostly robust towards horizontal ﬂips and translations, while being more sensitive in the vertical direction.

Original: Again, this ﬁts well with the training data augmentation of Inception v3 that reinforces robustness inhorizontal directions via random horizontal ﬂips [1].
Revised: Again, this ﬁts well with the training data augmentation of Inception v3 that reinforces robustness in horizontal directions via random horizontal ﬂips [1].

Original: GAN performance is related to deep fake detection.

Original: Before IS and FID were introduced toautomatically assess the performance of GANs, user studies were the main source of performanceevaluation [27, 21].

Original: Here, the user acts as deep fake detector, and model performance is interpretedas the ability of the model to fool human judgement.

Original:  Reinforcing the Bias by minimizing FID
Revised:  Reinforcing the Bias by minimizing FID

Original: If FID is a metric that aligns with human judgement, we can assume that the visual appearance ofimages generated by any GAN model should improve if we optimize the generator by minimizing
Revised: If FID is a metric that aligns with human judgement, we can assume that the visual appearance of images generated by any GAN model should improve if we optimize the generator by minimizing

Original: FID [17].
Revised: FID [17].

Original: But can this assumption hold?
Revised: But can this assumption hold?

Original: To verify, we train two GAN architectures, DCGAN [20] and SNGAN [18], on FFHQ [14] downscaled to 64 2 image resolution (further called FFHQ64) and
Revised: To verify, we train two GAN architectures, DCGAN [20] and SNGAN [18], on FFHQ [14] downscaled to 64 2 image resolution (further called FFHQ64) and

Original: CIFAR10 [16].
Revised: CIFAR10 [16].

Original: We consider three training procedures, a) GAN G+D where we train the model inits common setting in which a discriminator network provides the training signal for the generatornetwork (baseline), b) GAN FIDG+D where we extend a) by adding an additional loss for the generatornetwork given by Equation 1 (further called FID loss), and c) GAN FIDG where we drop the discriminatornetwork and train the generator solely by minimizing the FID loss.
Revised: We consider three training procedures, a) GAN G+D where we train the model in its common setting in which a discriminator network provides the training signal for the generator network (baseline), b) GAN FIDG+D where we extend a) by adding an additional loss for the generator network given by Equation 1 (further called FID loss), and c) GAN FIDG where we drop the discriminator network and train the generator solely by minimizing the FID loss.

Original: Depictions of b) and c) are givenin Figure 6.
Revised: Depictions of b) and c) are given in Figure 6.

Original: In each iteration that we minimize FID loss directly, we generate 400 images for DCGANand 360 images for SNGAN to approximate the current FID.
Revised: In each iteration that we minimize FID loss directly, we generate 400 images for DCGAN and 360 images for SNGAN to approximate the current FID.

Original: During training we measure FID totrack the training progress after each epoch by sampling 10 000 images from the generator.
Revised: During training we measure FID to track the training progress after each epoch by sampling 10 000 images from the generator.

Original: [Figure]
Revised: [Figure]

Original: different training proce FID loss stabilizes the training and achieves better performances (smaller FID) whereas the discriminatoronly marginallyimproves the generator performance
Revised: discriminator marginally

Original: The progress for each training setting is shown in Figure 4.
Revised: The progress for each training setting is shown in Figure 4.

Original: Giventhe training curves provided by evaluating FID after each epoch,one could assume that applying FID loss stabilizes the training.
Revised: Given the training curves provided by evaluating FID after each epoch, one could assume that applying FID loss stabilizes the training.

Original: Wecould go even further and assume that the discriminator is not evennecessary for GAN training, since the results measured in FID differonly slightly.
Revised: We could go even further and assume that the discriminator is not even necessary for GAN training, since the results measured in FID differ only slightly.

Original: However, the story changes after examining the imageseach of these models generate (see Figure 1 and appendix for furtherexamples).
Revised: However, the story changes after examining the images each of these models generate (see Figure 1 and appendix for further examples).

Original: By inspecting samples, we observe no visual improvement in image quality between GAN G+D and GAN FIDG+D despite thelarge gaps in terms of FID.
Revised: By inspecting samples, we observe no visual improvement in image quality between GAN G+D and GAN FIDG+D despite the large gaps in terms of FID.

Original: We even argue that images producedby GAN FIDG+D contain more artifacts and are less visually pleasing,which we see as a sign of overﬁtting to the FID loss.
Revised: We even argue that images produced by GAN FIDG+D contain more artifacts and are less visually pleasing, which we see as a sign of overﬁtting to the FID loss.

Original: We hypothesizethat the generator learns to produce unsuitable features to match thetraining data distribution.
Revised: We hypothesize that the generator learns to produce unsuitable features to match the training data distribution.

Original: This observation becomes more severe inthe case of GAN FIDG .
Revised: This observation becomes more severe in the case of GAN FIDG .

Original: Here, we notice that the missing discriminator leads to spatially incoherent feature distributions.
Revised: Here, we notice that the missing discriminator leads to spatially incoherent feature distributions.

Original: For example
Revised: For example

Original: SNGAN FIDG adds mostly single eyes and aligns facial characteristicsin a daunting manner.
Revised: SNGAN FIDG adds mostly single eyes and aligns facial characteristics in a daunting manner.

Original: We assume that this is the result of the choiceof layer that features are extracted from Inception v3.
Revised: We assume that this is the result of the choice of layer that features are extracted from Inception v3.

Original: Features arespatially pooled and therefore lose all spatial information before theyare extracted.
Revised: Features are spatially pooled and therefore lose all spatial information before they are extracted.

Original: While human annotators would surely prefer imagesproduced by SNGAN D+G over SNGAN FIDG (in cases where data ﬁdelity is preferred over art), we see that this is not reﬂected by FID.
Revised: While human annotators would surely prefer images produced by SNGAN D+G over SNGAN FIDG (in cases where data ﬁdelity is preferred over art), we see that this is not reﬂected by FID.

Original: Hence, FID is not aligned with human perception .
Revised: Hence, FID is not aligned with human perception .

Original: We argue thatdiscriminative features provided by image classiﬁcation networksare not sufﬁcient to provide the basis of a meaningful metric.
Revised: We argue that discriminative features provided by image classiﬁcation networks are not sufﬁcient to provide the basis of a meaningful metric.

Original: To further emphasize this point, we substitute Inception v3 by an extensivechoice of different image classiﬁcation networks.
Revised: To further emphasize this point, we substitute Inception v3 by an extensive choice of different image classiﬁcation networks.

Original: We evaluate FIDson ImageNet-C at different severities for each backbone network(details are provided in the appendix).
Revised: We evaluate FIDs on ImageNet-C at different severities for each backbone network (details are provided in the appendix).

Original: Here we see that biases present in Inception v3 are also widelypresent in other classiﬁcation networks.
Revised: Here we see that biases present in Inception v3 are also widely present in other classiﬁcation networks.

Original: Additionally, we see that different networks would producedifferent rankings in-between corruption types.
Revised: Additionally, we see that different networks would produce different rankings in-between corruption types.

Original:  Conclusion
Revised:  Conclusion

Original: We provided an overview of inherent biases that are present due to the design decision of FID touse Inception v3 as feature extractor.
Revised: We provided an overview of inherent biases that are present due to the design decision of FID to use Inception v3 as feature extractor.

Original: We showed that the way Inception v3 was trained enforcedit to become robust to corruptions related to color, intensity, saturation, and horizontal translations,while being sensitive to corruptions of textures and to vertical translations.
Revised: We showed that the way Inception v3 was trained enforced it to become robust to corruptions related to color, intensity, saturation, and horizontal translations, while being sensitive to corruptions of textures and to vertical translations.

Original: These biases inﬂuence theranking when different architectures are compared and need to be taken into account.
Revised: These biases inﬂuence the ranking when different architectures are compared and need to be taken into account.

Original: Additionally,we showed that FID as a metric is not aligned with human perception by minimizing FID as a lossterm.
Revised: Additionally, we showed that FID as a metric is not aligned with human perception by minimizing FID as a loss term.

Original: Here, we showed that generators trained with FID loss produce images with substantiallyimproved FIDs, but worse visual appearance.
Revised: Here, we showed that generators trained with FID loss produce images with substantially improved FIDs, but worse visual appearance.

Original: The plotted training curves showing the developmentof FID are misleading in those cases.
Revised: The plotted training curves showing the development of FID are misleading in those cases.

Original: Finally, we showed that substituting Inception v3 with anotherimage classiﬁcation network would simply mean to exchange different biases.
Revised: Finally, we showed that substituting Inception v3 with another image classiﬁcation network would simply mean to exchange different biases.

Original: Hence, we hope toinspire further research to close the gap towards a humanly aligned and unbiased metric that enablesto fairly rank generator architectures.
Revised: Hence, we hope to inspire further research to close the gap towards a humanly aligned and unbiased metric that enables to fairly rank generator architectures.

Revised: Acknowledgement

Revised: The authors thank Abdullah-Al-Zubaer Imran for his thorough feedback and valuable mentorship.

Revised: We thank Kalun Ho for his support with the classiﬁcation networks.

Revised: Lastly, we thank all anonymous reviewers for their constructive remarks and suggestions.

Original: Appendix A: Inception v3 architecture
Revised: Appendix A: Inception v3 architecture

Original: [Figure]
Revised: [Figure]

Original: Appendix B: Training Settings (section 2)
Revised: Appendix B: Training Settings (section 2)

Original: [Figure]

Original: D
Revised: D

Original: G

Original: [Figure]

Original: GAN

Original: G

Original: [Figure]
Revised: [Figure]

Original: and train the generator solely by minimizing FID loss.

Original: Appendix C: Implementation Details to Minimizing FID (section 2)
Revised: Appendix C: Implementation Details to Minimizing FID (section 2)

Original: We train each of the models for 48 hours and report the best FID measured during training.
Revised: We train each of the models for 48 hours and report the best FID measured during training.

Original: FIDs aremeasured after each epoch.
Revised: FIDs are measured after each epoch.

Original: We train DCGAN with the minimax loss
Revised: We train DCGAN with the minimax loss

Original: [Equation]
Revised: [Equation]

Original: [Equation] and for optimization we use Adam with β = (0 . 5 , 0 . 999) , (cid:15) = 10 − 8 , learning rate = 0 . 0002 , andweight decay = 0 .
Revised: 4) and for optimization we use Adam with β = (0 . 5 , 0 . 999) , (cid:15) = 10 − 8 , learning rate = 0 . 0002 , and weight decay = 0 .

Original: We train SNGAN with the hinge loss
Revised: We train SNGAN with the hinge loss

Original: [Equation]
Revised: [Equation]

Original: [Equation] and for optimization we use Adam with β = (0 . 0 , 0 . 9) , (cid:15) = 10 − 8 , learning rate = 0 . 0002 , andweight decay = 0 .
Revised: and for optimization we use Adam with β = (0 . 0 , 0 . 9) , (cid:15) = 10 − 8 , learning rate = 0 . 0002 , and weight decay = 0 .

Original: We combine all results in the following table.
Revised: We combine all results in the following table.

Original: [Table]
Revised: [Table]

Original: Appendix D: Improving generator architectures with FID loss
Revised: Appendix D: Improving generator architectures with FID loss

Original: Images produced by DCGAN FIDG (see Figure 1 and Figure 10) are only hardly recognizable due tonoise covering the images.
Revised: Images produced by DCGAN FIDG (see Figure 1 and Figure 10) are only hardly recognizable due to noise covering the images.

Original: In this case, minimizing FID without discriminator exposes possibleﬂaws in its architecture.
Revised: In this case, minimizing FID without discriminator exposes possible ﬂaws in its architecture.

Original: Indeed, when we exchange transpose convolutions in DCGAN with bilinearupsampling followed by convolutional kernels we observe that the noise vanishes (see Figure 7).
Revised: Indeed, when we exchange transpose convolutions in DCGAN with bilinear upsampling followed by convolutional kernels we observe that the noise vanishes (see Figure 7).

Original: [Figure]
Revised: [Figure]

Original: Appendix E: Generated Images (DCGAN/FFHQ)
Revised: Appendix E: Generated Images (DCGAN/FFHQ)

Original: Appendix 
Revised: Appendix F: Generated Images (SNGAN/FFHQ)

Original: Appendix G: Generated Images (DCGAN/CIFAR10)
Revised: Appendix G: Generated Images (DCGAN/CIFAR10)

Original: FID: 10 . 77 .
Revised: FID: 10 . 77 .

Original: Appendix H: Generated Images (SNGAN/CIFAR10)
Revised: Appendix H: Generated Images (SNGAN/CIFAR10)

Original: Appendix I: FIDs when substituting backbone networks on ImageNet-C
Revised: Appendix I: FIDs when substituting backbone networks on ImageNet-C

Original: b r i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u
Revised: b r i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u

Original: ss
Revised: ss

Original: i
Revised: i

Original: a n _ n
Revised: a n _ n

Original: o
Revised: o

Original: i s e g l a ss _ b l u r i m p
Revised: i s e g l a ss _ b l u r i m p

Original: u l s e _ n
Revised: u l s e _ n

Original: o i s e j p e g _ c o m p
Revised: o i s e j p e g _ c o m p

Original: r
Revised: r

Original: e
Revised: e

Original: ss i o n m o t
Revised: ss i o n m o t

Original: i o n _ b l u r p
Revised: i o n _ b l u r p

Original: i x
Revised: i x

Original: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p
Revised: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p

Original: e c k l e _ n
Revised: e c k l e _ n

Original: o i s e z oo m _ b l u r pca
Revised: o i s e z oo m _ b l u r pca

Original: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg
Revised: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg

Original: N
Revised: N

Original: [Figure]
Revised: [Figure]

Original: largest b r i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u
Revised: largest b r i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u

Original: ss
Revised: ss

Original: i
Revised: i

Original: a n _ n
Revised: a n _ n

Original: o
Revised: o

Original: i s e g l a ss _ b l u r i m p
Revised: i s e g l a ss _ b l u r i m p

Original: u l s e _ n
Revised: u l s e _ n

Original: o i s e j p e g _ c o m p
Revised: o i s e j p e g _ c o m p

Original: r
Revised: r

Original: e
Revised: e

Original: ss i o n m o t
Revised: ss i o n m o t

Original: i o n _ b l u r p
Revised: i o n _ b l u r p

Original: i x
Revised: i x

Original: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p
Revised: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p

Original: e c k l e _ n
Revised: e c k l e _ n

Original: o i s e z oo m _ b l u r pca
Revised: o i s e z oo m _ b l u r pca

Original: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg
Revised: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg

Original: N e t largest b r
Revised: N e t largest b r

Original: i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u ss i a n _ n o i s e g l a ss _ b l u r i m p
Revised: i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u ss i a n _ n o i s e g l a ss _ b l u r i m p

Original: u l s e _ n
Revised: u l s e _ n

Original: o i s e j p e g _ c o m p
Revised: o i s e j p e g _ c o m p

Original: r
Revised: r

Original: e
Revised: e

Original: ss i o n m o t
Revised: ss i o n m o t

Original: i o n _ b l u r p
Revised: i o n _ b l u r p

Original: i x
Revised: i x

Original: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p
Revised: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p

Original: e c k l e _ n
Revised: e c k l e _ n

Original: o i s e z oo m _ b l u r pca
Revised: o i s e z oo m _ b l u r pca

Original: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg
Revised: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg

Original: N e t largest b r
Revised: N e t largest b r

Original: i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u ss i a n _ n o i s e g l a ss _ b l u r i m p
Revised: i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u ss i a n _ n o i s e g l a ss _ b l u r i m p

Original: u l s e _ n
Revised: u l s e _ n

Original: o i s e j p e g _ c o m p
Revised: o i s e j p e g _ c o m p

Original: r
Revised: r

Original: e
Revised: e

Original: ss i o n m o t
Revised: ss i o n m o t

Original: i o n _ b l u r p
Revised: i o n _ b l u r p

Original: i x
Revised: i x

Original: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p
Revised: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p

Original: e c k l e _ n
Revised: e c k l e _ n

Original: o i s e z oo m _ b l u r pca
Revised: o i s e z oo m _ b l u r pca

Original: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg
Revised: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg

Original: N e t  largest b r i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u ss i a n _ n o i s e g l a ss _ b l u r i m p
Revised: N e t ImageNet largest b r i g h t n e ss c o n t r a s t d e f o c u s _ b l u r e l a s t i c _ t r a n s f o r m f o g f r o s t g a u ss i a n _ b l u r g a u ss i a n _ n o i s e g l a ss _ b l u r i m p

Original: u l s e _ n
Revised: u l s e _ n

Original: o i s e j p e g _ c o m p
Revised: o i s e j p e g _ c o m p

Original: r
Revised: r

Original: e
Revised: e

Original: ss i o n m o t
Revised: ss i o n m o t

Original: i o n _ b l u r p
Revised: i o n _ b l u r p

Original: i x
Revised: i x

Original: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p
Revised: e l a t e s a t u r a t e s h o t _ n o i s e s n o w s p a tt e r s p

Original: e c k l e _ n
Revised: e c k l e _ n

Original: o i s e z oo m _ b l u r pca
Revised: o i s e z oo m _ b l u r pca

Original: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg
Revised: inception bninception deit_s deit_t densenet inceptionresnetv nasnetamobile polynet resnet resnet vgg vgg

Original: N e t largest
Revised: N e t largest

Original: Appendix J: Deep Fake Detection with FID
Revised: Appendix J: Deep Fake Detection with FID

Original: We map 70 000 images from FFHQ and 70 000 images generated by StyleGAN2 (with and withouttruncation) into the Inception v3 feature space by using the FID PyTorch implementation.
Revised: We map 70 000 images from FFHQ and 70 000 images generated by StyleGAN2 (with and without truncation) into the Inception v3 feature space by using the FID PyTorch implementation.

Original: We spliteach into 60 000 training and 10 000 testing images, and hence, end up with balanced training datasetscontaining 120 000 images and balanced test datasets containing 20 000 images.
Revised: We split each into 60 000 training and 10 000 testing images, and hence, end up with balanced training datasets containing 120 000 images and balanced test datasets containing 20 000 images.

Original: We train skleanlogistic regression models and report the accuracy on the test dataset.
Revised: We train sklean logistic regression models and report the accuracy on the test dataset.

Original: A selection of correspondingimages is shown in Figure 27.
Revised: A selection of corresponding images is shown in Figure 27.

Original: We argue that a meaningful metric should be visually aligned withhuman perception.
Revised: We argue that a meaningful metric should be visually aligned with human perception.

Original: Hence, if a human can be fooled by a generator network, then this generatorshould be considered superior to one that is not able to do so.
Revised: Hence, if a human can be fooled by a generator network, then this generator should be considered superior to one that is not able to do so.

Original: We see that truncation decreases FIDsigniﬁcantly, and consequently improves the ability of detecting StyleGAN2 generated images asfake.
Revised: We see that truncation decreases FID signiﬁcantly, and consequently improves the ability of detecting StyleGAN2 generated images as fake.

Original: In contrast, we show images produced by StylegAN2 without and with truncation in Figure 27.
Revised: In contrast, we show images produced by StylegAN2 without and with truncation in Figure 27.

Original: By inspecting the images we observe that truncation removes textures (and also artifacts).
Revised: By inspecting the images we observe that truncation removes textures (and also artifacts).

Original: Wehypothesize that its bias towards textures facilitates Inception v3 to extract features that allow almostperfect detectability (98% when truncation is applied).
Revised: We hypothesize that its bias towards textures facilitates Inception v3 to extract features that allow almost perfect detectability (98% when truncation is applied).

Original: However, we expect humans to be more easilyfooled by truncated images than untruncated ones.
Revised: However, we expect humans to be more easily fooled by truncated images than untruncated ones.

Original: Hence, we argue that this is a hint towards that
Revised: Hence, we argue that this is a hint towards that

Original: FID is not aligned with human perception.
Revised: FID is not aligned with human perception.

Original: [Table]
Revised: [Table]

Revised: [Table]

Revised: StyleGAN ψ =1.

Original: [Equation]
Revised: [Equation]

Revised: =0.