FreGAN: Exploiting Frequency Components for Training GANs under Limited Data
Anonymous Author(s)
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Abstract
Training GANs under limited data often leads to discriminator overﬁtting andmemorization issues, causing divergent training.
Existing approaches mitigate theoverﬁtting by employing data augmentations, model regularization, or attentionmechanisms.
However, they ignore the frequency bias of GANs and take poorconsideration towards frequency information, especially high-frequency signalsthat contain rich details.
To fully utilize the frequency information of limited data,this paper proposes FreGAN, which raises the model’s frequency awareness anddraws more attention to producing high-frequency signals, facilitating high-qualitygeneration.
In addition to exploiting both real and generated images’ frequency information, we also involve the frequency signals of real images as a self-supervisedconstraint, which alleviates the GAN disequilibrium and encourages the generatorto synthesize adequate rather than arbitrary frequency signals.
Extensive resultsdemonstrate the superiority and effectiveness of our FreGAN in ameliorating generation quality in the low-data regime (especially when training data is less than100).
Besides, FreGAN can be seamlessly applied to existing regularization andattention mechanism models to further boost the performance.
Introduction
Generative adversarial networks (GANs) [10] have shown impressive achievements in synthesisingplausible and photorealistic visual objects, such as image [18] [17] and video [37] generation, imageinpainting [24], image translation [33] and so on.
However, a prerequisite of such success is sufﬁcienttraining data which impedes applications of GANs in areas where only dozens of data are availableor where it is challenging to collect massive data due to geographical, spatial, temporal, or privacyreasons.
Thus developing data-efﬁcient GANs that can generate plausible images under limited data,without compromising the quality, is necessary and meaningful.
Training GANs under limited data often leads to overﬁtting and instability issues [16] [14].
Speciﬁcally, when the discriminator (D) overﬁts to the limited training data, it simply remembers the input realimages and classiﬁes others as fake images, thus providing meaningless feedback to the generator (G),leading to divergent training and poor-quality generation.
Ameliorating the synthesize quality underlimited data is still an unexplored problem.
Recent approaches for this problem include enlarging thetraining set with different data augmentations [48] [34] [47] [16] [14], regularizing the output of Dwith an additional constraint [35], and devising new network architectures [23].
However, existingmethods are mainly developed from the perspective of data scale and model capacity, and they ignorea critical property of the data itself, i.e. , frequency signals.
GANs have been demonstrated to havea spectral bias in ﬁtting frequency signals [28] [32].
They preferentially ﬁt low-frequency signalsand tend to ignore high-frequency signals [42], which encode ﬁne details like vertical and horizontaledges [43] [9].
Missing them may lead to unrealistic image synthesize with unsatisfactory artifacts
(see Fig. 1).
This paper proposes a frequency-aware model, termed as FreGAN, to raise the frequencyawareness of G and D.
By encouraging G to generate more reasonable and adequate high-frequencysignals, our FreGAN ameliorates the synthesize quality under limited data, as shown in Fig.
To fully exploit the frequency information of limited training data, we ﬁrst decompose images intodifferent frequency components via Haar wavelet transformation [6].
Unlike traditional wavelettransformation that is employed at the image level, we perform it on the intermediate features ofboth D and G. We then employ a high-frequency discriminator (HFD) and frequency skip connection(FSC) to raise the frequency awareness of G and D, respectively.
However, G still has no explicitclue about what high-frequency signals it should synthesize, and D is overconﬁdent in makingreal/fake decisions after seeing real and fake images.
Such an unbalanced competition motivatesus to perform high-frequency alignment (HFA) to alleviate the information asymmetry between Gand D. Innovatively, we explicitly exploit the frequency signals of real images induced from D as aself-supervised constraint to guide G to leverage the frequency knowledge properly.
Besides, HFDand HFA are applied on multi-scale features to thoroughly excavate the frequency signals of limiteddata, mitigating frequency bias and loss of high-frequency information.
The primary contributions of this paper are three-fold: 1) we propose FreGAN to raise the model’s frequency awareness, which successfully mines and exploits frequency information of limiteddata, and as a byproduct, FreGAN alleviates the unhealthy competition between G and D; 2) wedemonstrate the compatibility of our model by combining our method with other techniques likeregularization [35] and attention mechanism [21]; 3) we perform extensive experiments on variousdatasets with limited data, and our FreGAN achieves state-of-the-art performance on these datasets, indicating the effectiveness and superiority of our method for ameliorating synthesize quality,especially when training data is extremely limited.
Related Work
Generative Adversarial Networks.
Generative adversarial networks (GANs) [41] [15] [11], whichtarget at generating plausible and realistic images, have made massive progress since the pioneeringwork [10].
The capability of GANs enables various visual applications like image [18] [19] andvideo generation [37] [36], image inpainting [44] [24], image manupulation [9] [33] and superresolution [40], etc.
However, GANs are notoriously difﬁcult to train as several issues like modecollapse and instability happen easily.
Numerous techniques have been proposed to stabilize trainingand improve the synthesize quality by designing new optimization objectives or network architectures [13].
WGAN [2] and f -GAN [26] minimize the Wasserstein distance and the f -divergenceof real and generated distribution instead of minimizing JS divergence in [10].
BigGAN
[7] and StyleGAN series [15] [18] [19] [16] [17] have made breakthrough progress in producing realisticimages.
However, the performance of these models deteriorates when given limited data.
Training GANs under limited data.
Improving the synthesize quality under limited data remainsan underexplored problem, which has drawn extensive attention recently.
Insufﬁcient training dataleads to discriminator overﬁtting, thus degrading the quality of generated images.
One straightforwardway to address such data scarcity is to expand the training set with various augmentations.
Inaddition to employing conventional augmentation techniques [34] [48] (e.g., ﬂip, crop), ADA [19]and DiffAug [47] propose adaptive and differentiable augmentation to enlarge the training data,respectively.
APA [14] deceives D based on the degree of overﬁtting with an adaptive pseudoaugmentation.
Lecam [35] regularizes the output of the discriminator throughout the trainingprocess.
FastGAN [23] employs a skip-layer channel-wise excitation module and a self-superviseddiscriminator to stabilize and accelerate the training.
The most recently MoCA [21] improves fewshot image generation quality with a prototype memory with an attention mechanism.
Anothercategory of methods transfer and reuse knowledge from models that are pre-trained on large-scaledata, i.e. , few-shot GAN adaptation [39] [22] [38] [27].
In this paper, we ameliorate the synthesizequality under limited data from the frequency domain perspective.
By raising the frequency awarenessof GANs and providing more ﬁne details to G, we facilitate photorealistic image generation.
Ourwork is complementary to previous model regularization and attention mechanism approaches, andour method promotes equilibrium between G and D.
Wavelet Transformation in GANs.
Schwarz et al.
[30] prove that GANs exhibit a frequency biasand resolving frequency artifacts is necessary for photorealistic image generation.
Consequently,
GANs tend to ignore high-frequency signals as they are hard to generate, compromising the generationquality.
Wavelet transformation [6], which decomposes images into frequency components withdifferent bands, has been wildly used in various applications of GANs, such as style transfer [4] [43],image inpainting [44], image editing [9], etc.
HiFA [9] alleviates the generator’s pressure of producinghigh-frequency signals by directly feeding high-frequency components to the generator.
WaveFill [44]disentangles different frequency signals and explicitly ﬁlls the missing regions in each frequencyband, achieving superior image inpainting.
Zhang et al.
[45] propose wavelet knowledge distillationtowards efﬁcient image-to-image translation without a performance drop.
SWAGAN [8] incorporateswavelet with the hierarchical training of StyleGAN2 [19] and performs wavelets at the image level.
Our FreGAN is more ﬂexible by directly decomposing intermediate features of the generator andthe discriminator into the wavelet domain, and no additional down/up sampling are required toconvert images to higher/lower resolution as in SWAGAN, which makes our method more efﬁcient.
Unlike existing methods that are performed on ample data, this paper addresses the more challengingfew-shot generation problem.
In addition to raising the frequency awareness of the model, we alsomitigate the unhealthy competition by lessening the frequency gap between G and D.
Methodology
[Figure] The overall framework of our FreGAN is illustrated in Fig.
To formulate our method, we explicitlyutilize wavelet transformation to decompose features into different frequency components.
Wethen employ high-frequency discriminator (HFD) and frequency skip connection (FSC) to raise thefrequency awareness of G and D, respectively.
Moreover, we perform high-frequency alignment(HFA) to further guide G to synthesize adequate frequency signals.
3.1 Wavelet Transformation
To decompose images into different frequency components, we adopt a simple but effective wavelettransformation, i.e. , Haar wavelet.
Haar wavelet consists of two mirror operations: wavelet poolingand wavelet unpooling.
The former converts images into the hlwavelet domain, and the latter inverselyreconstructs frequency components into the spatial domain.
There are four kernels in wavelet poolingoperation: LL T , LH T , HL T , HH T , where L T = 1 √ 2 [1 , 1] , H T = 1 √ 2 [ − 1 , 1] , L and H denotes thelow and high pass ﬁlters, respectively.
The low (L) pass ﬁlter captures the outline and surface ofimages, while the high (H) pass ﬁlter focuses on detailed information like the edges and delicatetextures.
Fig.
3 illustrates the obtained frequency components of given images via Haar wavelet.
We can observe that low-frequency component LL contains the overall surface of images, whilecomponents that are decomposed by high pass ﬁlters, i.e., LH, HL, HH , contain more ﬁne details.
Further, by summing up the three high-frequency components, we approximately obtain all detailsinformation of images, e.g. , the eyes of the cat and the teeth of Obama.
3.2 High-Frequency Discriminator
To raise the frequency awareness of D, we devise high-frequency discriminator (HFD).
HFD isresponsible for distinguishing the real images from the generated images from the perspective ofthe frequency domain.
Formally, for the i -th layer in the discriminator, we adopt wavelet poolingon the intermediate features and obtain LL iD , LH iD , HL iD , HH iD , then we combine the three highfrequency components by tensor addition, i.e. , HF iD =
LH i D + HL i D + HH i D , which containssufﬁcient details of features.
By applying traditional convolution and downsampling operationsfollowing the original discriminator, we deﬁne the adversarial loss of our HFD as:
[Equation]
[Equation]
(2) where HF real and HF fake are the high-frequency information of real and fake images, respectively.
D H is the high-frequency discriminator.
Since the high-frequency information may be eschewed by
D as the network goes deeper, we perform multi-scale HFD on multi-layers of the discriminator.
Themulti-scale operation ensures fully mine and exploit the frequency information of limited data, whichfurther improves D’s frequency awareness.
Notably, being guided by the HFD with Eq. 2, G is alsooptimized to produce rich high-frequency details.
3.3 Frequency Skip Connection
The generator is capable of producing plausible frequency signals after employing HFD (see Tab. 5).
However, as GANs ﬁt frequency signals from low to high and the high-frequency signals may be ignored as the network goes deeper.
To prevent the loss of high-frequency information and further encourage the generator to produce rich details, we propose frequency skip connection (FSC).
Concretely, we utilize wavelet unpooling operation of the frequency components LL iG , LH iG , HL iG , HH iGobtained from wavelet transformation on the features of G
’s i -th layer, which reconstructs the highfrequency representation to the original features.
Then we explicitly feed the reconstructed frequencyrepresentations to the next layer of G. Formally,
[Equation]
where F i denotes the features of the i -th layer and Unpooling is the wavelet unpooling operation.
F (cid:48)
i +1 is the obtained features after FSC, which will be fed into the subsequent layer for furtheroperation.
Such skip connection prevents loss of high-frequency information and maintains highfrequency details.
3.4 High-Frequency Alignment
Adding HFD and FSC explicitly raises the frequency awareness of G, but G can only synthesize arbitrary frequency signals.
How G can utilize the frequency signals is still ambiguous, and D still dominates the competition since it learns discriminative knowledge from both real andgenerated images.
To balance the unhealthy competition between G and D, we propose highfrequency alignment (HFA), which involves high-frequency signals of real images induced from Das a regularizer to guide G, promoting G to synthesize more reasonable and realistic ﬁne details.
Speciﬁcally, we extract the frequency representations of intermediate features of G at different layers.
For the i -th layer of G, we obtain frequency components LL iG , LH iG , HL iG , HH iG .
We ignore LL iGand combine the three high-frequency components, i.e. , HF iG =
LH iG + HL iG + HH iF .
Then weuse the high-frequency components of the discriminator HF iD as a self-supervision constraint.
Inaddition to fool D, G is expected to minimize the distance of high-frequency information between thegenerated and real images.
The alignment loss is deﬁned as:
[Equation]
[Equation]
where (cid:107) ∗ (cid:107) 1 denotes the L 1 -norm.
Such alignment encourages G to synthesis frequency signals thatapproach real frequency signals, mitigating the unhealthy competition and facilitating generationquality.
To take full advantage of frequency signals of real images from D, we perform HFA on multiscale features like HFD as shown in Fig.
The ablative experiment results in Sec.
4.2 demonstratethe rationality and effectiveness of employing HFA and HFD on multi-scale features.
3.5 Optimization
Following [23], we adopt the hinge version of adversarial loss to train our model.
[Equation] [Equation]
We also use the reconstruction loss [23] to encourage the discriminator to extract more representativefeatures.
[Equation]
where f is the intermediate features of D, G and T denote the processing on the features f and theinput images x .
In sum, our discriminator is optimized by L D , L recons , and L HFD .
Our generator isoptimized by L G , L HFG and L align , the coefﬁcient of each loss is set to 1 .
Experiments
Datasets.
We test the effectiveness of our method on low-shot datasets from various domains withdifferent resolutions.
On 256 × 256 resolution, we use Animal Face Dogs and Cat [31], as wellas 100-shot-Panda, Obama, and Grumpy_cat [47].
On 512 × 512 resolution, we use Anime-Face,
Art Paintings, Moongate, Flat-colored, and Fauvism-still-life [23].
On 1024 × 1024 resolution, weuse Pokemon, Skulls, Shells, MetFace [16] and BrecaHAD [1].
These datasets contain a limited
Our FreGAN improves the overall quality of generated images and raises the model’s frequency awareness, encouraging the generator to produce precise high-frequency signals with ﬁne details.
number of samples (mostly less than 1,000) and cover art paintings, realistic photos, human faces, etc. For datasets that are not strictly equal to the corresponding resolution, we resize them to the closestresolution in implementation.
Besides, we use AnimalFace HQ (AFHQ) datasets [5] to evaluate theperformance of our model when training with more data ( ∼ 5k).
Evaluation metrics and baseline.
We adopt two common metrics to evaluate the synthesize quality:
Fréchet Inception Distance (FID) [12] and Kernel Inception Distance (KID) [3].
The lower FID and
KID is, the better the generation quality is.
FID quantiﬁes the distance between the distribution of thegenerated and the real images.
KID, which is designed unbiased, has been proven more descriptivefor small datasets [16], note that all KID scores reported in our paper need to × 10 − 3 following [16].
Following [23], we calculate FID and KID by measuring the distance between all available trainingimages and 5k generated images.
We also provide the LPIPS [46], IS [29], Precision, Recall [20],
Density, Coverage [25] results in the appendix.
We compare our model with: 1) the state-of-the-art generative model StyleGAN2 [19]; 2) dataaugmentation-based approaches that is designed for training GANs with limited data, i.e. , ADA [16],
DiffAug [47], APA [14]; 3) the state-of-the-art few-shot generative model FastGAN [23].
We reimplement all baselines with their released ofﬁcial code under consistent settings for a fair comparison.
Implementation details of baseline models are given in the appendix.
Implementation details.
We choose the current state-of-the-art few-shot generative model FastGAN [23] as the backbone and implement our proposed techniques upon it. all other settings remainthe same as [23].
We decompose the intermediate 8 × 8, 16 × 16, 32 × 32 features of G and Dinto frequency components for our frequency skip connection, high-frequency discriminator, andhigh-frequency alignment.
More implement details are given in the appendix.
4.1 Main Results
Quantitative comparison on datasets with limited data amounts.
The quantitative comparisonresults of our FreGAN and baseline methods on different resolutions are given in Tab. 1, Tab. 2 and
Tab. 3.
We save the best training snapshots of each method and generate 5k images to compute FIDand KID.
The whole training set is adopted as the referenced distribution.
We can observe from theresults that, although evaluated on various datasets that have different resolutions and data amounts,our proposed FreGAN achieves superior performance on all these datasets.
Our FreGAN consistentlyimproves both FID and KID metrics on 14 of the 15 datasets, demonstrating the effectiveness andgeneralizability of our proposed techniques.
Notably, for those datasets with extremely limited data(less than 100), i.e. , Flat (Tab. 2), Shells and Skulls (Tab. 3), our method improves the performancemore signiﬁcantly, e.g. , the FID from 216.27 to 178.10 on Flat and from 101.94 to 86.12 on Skulls,and the corresponding KID is improved doubled, further reﬂecting our model’s potential for training
GANs with extremely limited data.
More quantitative results are presented in the appendix. [Table] [Table] [Table]
Qualitative Comparison.
The qualitative results of FastGAN and our FreGAN on various datasetsare illustrated in Fig.
For each dataset in Fig. 4, from left to right are generated images, thevisualization of the low and high-frequency components of the generated images.
The imagesgenerated by FastGAN contain unsatisfactory artifacts and some of them are incongruous, e.g. , thegenerated images of cat and dog in the bottom right of Fig.4, the cat has artifacts around the head,and the dog’s ears are distorted.
Our FreGAN signiﬁcantly facilitates image quality in coordination,rationality, and ﬁne details.
As can been seen from Fig.
4, the human face Obama generated by our
FreGAN is more photorealistic, the details of the anime face, such as eye color and hair texture, aremore realistic, and the synthesized animal faces of cats and dogs are also more plausible.
Besides,the frequency components of the images generated by our FreGAN contain wealthier details.
Forexample, the generated image of AnimalFace-Cat has a richer background, and the generated imageof Skulls has more clear contours of the eye and nose.
Such observation reﬂects that the proposed
FreGAN: 1) ameliorates the quality of generated images under limited data; 2) raises frequencyawareness of synthesizing high-frequency signals with richer ﬁne details of images; and 3) takes fulladvantage of limited data’s frequency information.
More qualitative results are given in the appendix.
Effectiveness under datasets with more data.
To investigate the effectiveness of our FreGAN morecomprehensively, we evaluate the performance on datasets with more training data, i.e. , AnimalFaceHQ (AFHQ) [5], which includes 3 sub-datasets with close to 5k images, the results are shown in Tab. 4.
Similarly, our method yields compelling improvements on both FID and KID metrics whentraining with more data.
Combined with the generated images in Fig.
4, the results further validateour FreGAN’s contribution to the synthesize quality.
Our method boosts the performance underdifferent amounts of data, suggesting the generalization of our model.
[Table] [Table]
[Table]
4.2 Ablation Studies
Ablation studies on variants of FreGAN.
There are three ingredients of our FreGAN, i.e. , the highfrequency discriminator (HFD), high-frequency alignments (HFA), and frequency skip connection(FSC).
We evaluate the efﬁcacy of each component by removing each of them from the full versionof our FreGAN.
We choose one from each of the different resolution datasets, i.e. , 100-shot-Obama,
Anime face and pokemon for 256, 512 and 1024 resolution, respectively.
As shown in Tab.
5,removing any of the three techniques leads to a performance drop, reﬂecting the contribution ofeach component.
Still, all these variants outperform baseline FastGAN on both FID and KID, whichimplies that the combination of different components of our method consistently boosts modelperformance.
Moreover, the performance drops the most when removing the HFD module, which isreasonable because the HFD raises the frequency awareness of G and D, and the frequency awarenessof D serves as a self-supervision to guide G to synthesize adequate and reasonable frequency signals.
Qualitative comparison results of ablation studies are given in the appendix.
Ablation studies on different scale of features.
We employ our proposed HFD and HFA on multiscale features of G and D, namely, 8, 16, and 32 scales of features.
Here we provide the ablationstudies on different scales in Tab. 6.
It can be seen that performing HFD and HFA on multi-scalefeatures boosts the model performance.
Besides, when only performing HFD and HFA on single-scalefeatures, the obtained results still outperform the FastGAN baseline, suggesting the effectivenessof HFA and HFD.
Notably, despite adding more scales of features may bring further performanceadvancement, the required additional convolutional and downsampling layers increases for higherscales features( e.g. , 128, 256), bringing non-negligible computational costs.
Ablation studies on different frequency components.
Three high-frequency components are obtained from wavelet transformation on the features, i.e. , LH , HL , and HH .
Each of them encodesdifferent details of features as shown in Fig.
3, we sum them to fuse all the detail information forfurther operation in our main experiments.
Here we conduct experiments on the three componentsrespectively to verify their contribution and the necessity of fusing them.
As shown in Tab. 6, eachhigh-frequency component contributes to the model performance compared with the baseline, andfusing them can better promote the generation quality. [Table]
4.3 Analysis on Compatibility and GAN Equilibrium
Compatibility of Our Model.
Lecam [35] and MoCA [21] exploit regularization and attentionmechanism for training GANs under limited data, respectively.
We implement our proposed techniques on them to test the compatibility of our method.
We keep the original setting unchanged andthe set the regularization weight to 0.1. The FID results are given in Tab. 7, from which we can seethat FreGAN can further boost the performance of MoCA and Lecam, demonstrating that our methodis complementary to the model regularization and attention mechanism methods.
GAN Equilibrium is improved.
Our HFA module aligns the frequency components of real andgenerated images, guiding G to synthesize precise instead of arbitrary high-frequency signals.
Meanwhile, as a byproduct, the HFA mitigates the domain gap between G and D, alleviating the unhealthycompetition.
As shown in Fig.
5 (a), our discriminator converges to a better point, and our generatorcan better fool the discriminator, while the discriminator of FastGAN surpass the generator, thusproviding less informative guidelines and degrading the synthesize quality.
Besides, we plot the FIDand KID curves throughout the training process in Fig.
5 (b), from which we can observe that
our
FreGAN are consistently better.
Moreover, we plot the multi-scale HFA loss curves in Fig.
5 (c),where each line denotes the loss of each scale.
These curves indicate that the frequency signals arewell aligned, lessening the domain gaps and promoting the GAN equilibrium.
Discussion
Conclusions.
In this paper, we propose a frequency-aware method for training GANs under limiteddata, i.e. , FreGAN.
The proposed FreGAN ameliorates the synthesize quality by raising the model’sfrequency awareness, encouraging the model to pay more attention to frequency signals, especiallyhigh-frequency signals, which encode ﬁne details of images.
We conduct extensive experiments onvarious datasets with different amounts of data and different resolutions to demonstrate the efﬁcacyof our proposed method.
Qualitative results suggest that our model successfully makes the generatorto generate precise high-frequency signals, facilitating high-quality image generation.
Quantitativeresults indicate that our method 1) substantially boosts the performance, especially when data isextremely limited (less than 100), and 2) is complementary to existing regularization and attentionmodels.
Moreover, the proposed model alleviates the disequilibrium of GANs by lessening thefrequency information gap.
In the future, we plan to implement our techniques on more backbones,e.g. , StyleGAN2 [19] and apply our method to more applications.
Limitations.
Despite achieving signiﬁcant improvements on various low-data datasets, our FreGANstill struggles in generating photorealistic images when given datasets with limited data but variouscontents, e.g. , only dozens of images, and their contents vary widely.
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