Random Projection-Induced Gaussian Latent Features for Arbitrary Style Transfer
Authors: Weizhi Lu
Zhongzheng Li
Dongchen Gao
Mingrui Chen
Weiyu Li
jinglin zhang
Wei Zhang
Venue: Accepted by TMLR ()

Abstract: The feature transfer technique centered on  mean and variance statistics, widely known as AdaIN, lies at the core of current  style transfer research. This technique relies on the assumption that latent features for style transfer follow  Gaussian distributions. In practice, however, this assumption is often hard to meet, as the features typically exhibit sparse distributions due to the significant spatial correlation inherent in natural images. To tackle this issue, we propose first performing a random projection on the sparse features, and then conducting style transfer on these projections. Statistically, the projections  will satisfy or approximate Gaussian distributions, thereby better aligning with AdaIN's requirements and enhancing transfer performance. With the stylized projections, we can further reconstruct them back to the original feature space by leveraging compressed sensing theory, thereby obtaining the stylized features. The entire process constitutes a projection-stylization-reconstruction module, which can be seamlessly integrated into AdaIN without necessitating network retraining. Additionally, our proposed module can also be incorporated into another promising style transfer technique based on cumulative distribution functions, dubbed  EFDM. This technique faces limitations when there are substantial differences in sparsity levels between content and style features. By projecting both types of features into dense Gaussian distributions, random projection can reduce their sparsity disparity, thereby improving performance. Experiments demonstrate that the aforementioned  performance improvements   can be achieved on existing state-of-the-art approaches.

Published in Transactions on Machine Learning Research (02/2026)
Random Projection-Induced Gaussian Latent Features for Arbitrary Style Transfer
Weizhi Lu Zhongzheng Li', Dongehen Gao², Mingrui Chen', Weiyu Li²A", ,Jinglnn Zhang! Wei Zhang!.
School of Control Science and Engineering, Shandong University, China
Zhongtai Securities Institute for Financial Studies, Shandong University, China KKy Laboratory of Machine Intelligence and System Control, Ministry of Education, China
'Shandong Blue Ocean Pilot Big Data Development Company Limited, China
Reviewed on OpenReview: http://ppppawaawwwaaa/////oooobd
Abstract
The feature transfer technique centered on mean and variance statistics, widely known as AdaIN, lies at the core of current style transfer research. This technique relies on the assumption that latent fea- tures for style transfer follow Gaussian distributions. In practice, however, this assumption is often hard to meet, as the features typically exhibit sparse distributions due to the significant spatial corre- lation inherent in natural images. To tackle this issue, we propose first performing a random projec- tion the sparse features, and then conducting style transfer on these projections. Statistically, the projections will satisfy or approximate Gaussian distributions, thereby better aligning with AdaIN's requirements and enhancing transfer performance. With the stylized projections, we can further re- construct them back to the original feature space by leveraging compressed sensing theory, thereby obtaining the stylized features. The entire process constitutes a projection-stylinn stylizztion-rrcoosstuttiio module, which can be seamlessly integrated into AdaIN without necessitating network retraining. Additionally, our proposed module can also be incorporated into another promising style transfer technique based on cumulative distribution functions, dubbed EFDM. This technique faces limita- tions when there substantial differences in sparsity levels between content and style features. By projecting both types of features into dense Gaussian distributions, random projection can reduce their sparsity disparity, thereby improving performance. Experiments demonstrate that the afore- mentioned performance improvements can be achieved on existing state-of-the-aat approaches.
1 Introduction
Style transfer aims to transfer the style of one image to another while preserving the semantic content information of the latter. Recent research has shown that this objective can be efficiently realized within a deep encoder-decoder framework, by statistically extracting and integrating style and content information from deep convolutional features (Gatys et al. (016). In this approach, the statistical modeling of style features plays a pivotal role, yet it remains a challenging issue due to the inherent subjectivity and diversity in defining style features.
There are two fundamental statistical approach to model style features: One approach is grounded in the utilization of mean and variance, famously known as AdaIN (Huang & Belongie 2017). while the other leverages the cumulative distribution function, termed EFDM (Zhang al., 2022). Despite their impressive performance, both approaches have inherent limitations. This is because deep convolutional features often exhibit sparse distributions (Mahendran & Vedaldi 2015) Qin et al.) 2020), as exemplified in Appendix [ and such distributions are unfavorable for effective style transfer. The underlying reasons are as follows. Let us first analyze the AdaIN approach, which operates on the assumption that deep features have Gaussian distributions, rather than sparse distributions. For a style feature map that exhibits a sparse distribution, its style information is typically concentrated within a few large-magnitude feature elements. However, as the number of small-man magiinaa feature elements increases, the influence of these large
"Corespooning Authors: Weiyu Li (liweiyu@ddun www.eedddduu.....eeeee edu.edu.en)) and Jinglin Zhang (jinglin.rhang @sdu.edu.co)

---

Published in Transactions on Machine Learning Research (02/2026)
Content & Style
AdaIN
Ours (AdaIN+RP)
EFDM
Ours (EFDM+RP)
Figure 1: Given a style image composed of few color spots, both AdaIN (Huang & Belongie 2017) and EFDM Zhang
et al. 2 lose key content features, such as the feathers of the bird and the contour of the branch, whereas these features are preserved relatively well when incorporating our random projection (RP) module.
elements on both the mean and variance (essential for AdaIN) tends to decrease. This property suggests that the effect of style transfer with AdaIN may deteriorate, when the style feature map becomes sparser, as demonstrated by the example in Figure I In the EFDM method, the cumulative distribution function is adopted to represent style features. The function is transferred by substituting the sorted- ferteed-eattureeementt of the content feature map with corresponding elements from the style feature map. Nevertheless, this method tends to perform worse when the sparsity of the feature distributions is inconsistent between the content feature map and the image feature map. This problem is exemplified in Figure | where the style feature map is much sparser than the content feature map. It can be seen that the stylized image experiences noticeable content loss, since the content feature map has to lose few large-magnitude feature elements, after adopting the elements from the sparser style feature map. Overall, the aforementioned two problems indicate that the sparse distributions of deep features limit the application effects of AdaIN and EFDM.
To address the challenge, in the paper we propose applying random projection to deep features, before performing style transfer on them. Random projection is a technique that projects high dimensional data to low dimensional subspaces by multiplying the data with a random matrix. Statistically, when the entries of random matrices are drawn from Gaussian distributions, the projections will adhere to Gaussian distributions. Similarly, when the matrix entries are sampled from other sparse distributions, such as {0. 1} and f0, + distributions, the projections will approximate Gaussian distributions by the central limit theorem. The projection to lower dimensions can also yield distributions closer to Gaussian. (Meckes 2012). These properties suggest that random projection enables features to better meet the requirements of AdaIN. Moreover, the dense, Gaussian distribution is favorable to reducing the disparity in sparsity levels between the style image map and the content image map. This, in turn, mitigates the aforementioned sparsity- imbalance issue that can arise in the context of EFDM. By conducting style transfer on the projections of content and style feature maps, we will obtain the stylized projection. To feed the stylized projection into the decoder without network retraining, we further propose to reconstruct the stylized projection back to the original feature map space, This reconstruction relies on compressed sensing theory (Foucart & Rauhut 2013). which states that a sparse signal can be approximately reconstructed from its random projections, even in the presence of noise. In the context of our research, the stylized projection can be viewed as the projection of content features, perturbed by the projection of style features via style transfer. Then, reconstruction from the stylized projection should yield the desired stylized feature map, which is primarily characterized with content features while being complemented by style features.
The proposed random projection-base based style transfer functions as flexible plug-and play module, which can be seam- lessly integrated into decoder frameworks for style transfer, without the need for network retraining. Without loss of generality, our research will focus on incorporating this module into two fundamental models: AdaIN (Huang & Belongie 2017). and EFDM (Zhang al. 2022). The two models serve as the basis for style transfer and have been employed in most existing style transfer approaches, including attention mechanism-barn based models like AdaAttN (Liu al. 2021) and diffusion model-based approaches such as StyleID (Chung et al. (024).. If performance improvements can be realized with these two fundamental models, it is reasonable to anticipate similar improvements in other more advanced models that incorporate them. This is validated in our experiments, where our random projection module indeed empowers existing approaches to overcome the limitations handling sparse features, thereby achieving no- table improvements in preserving content details, enriching and diversifying style elements, and elevating the overall perceptual quality.
2

---

Published in Transactions on Machine Learning Research (02/2026)
2 Related Work
Statistical modeling of style features. In the early research of style transfer, Gram matrices are utilized to represent the distribution of style features, achieving impressive results but incurring relatively high computational burden. To alleviate this issue, AdaIN (Huang & Belongie 2017) introduces a style modeling approach based on mean and variance, which offers comparable performance but significantly reduces complexity. Consequently, this approach has found wide application in dewoodrrrrdeedrr--eeee
models (Jing et al., 2020) Chandran et al.;
2021] An et al. 2020 Lin
et al. 202T: An et al. 2021: Liu et al., 2021), as well as in generative adversarial models (Krrra et al.
2019] 2020).
To further address the limitation of AdaIN in dealing with sparse features, EFDM (Zhang et al.) 2022) has recently
proposed modeling style features using cumulative distribution functions. This approach reports more pronounced
results than AdaIN, attracting increasing attention in recent research (Kwon et al.) 2024 Ge et al., 2024 Zhang et al.)
2024b). However, as previously noted, EFDM encounters challenges when content and style feature distributions differ in sparsity levels. In the paper, we will demonstrate that our random projection-based feature sampling module can efficiently tackle the two problems present in AdaIN and EFDM.
Style transfer with global and local features. The primary goal of style transfer is to achieve a desired balance be- tween content and style information. Achieving this goal necessitates a delicate manipulation of both global and local feature transfers. Global features are crucial in maintaining content quality and ensuring style consistency, whereas local features are instrumental for refining local details. Initially, research primarily centers on global, channel-wise
deep features, as evidenced in works such as (Gatys et al. [2015a b; 2016 Dumoulin et al. 2016 Johnson et al. 2016:
Ulyanov et al. 2016 Gatys al. 2017] Risser et al. [2017] Huang & Belongie 2017 et al., 2017:
2019 2020;
Huang & Gupta 2020 Zhang et al.
2022). Subsequently. the focus shifts towards the modeling and transferring on
local patches or patterns, as demonstrated in
CCen & Schmidt 2016 Gu et al. 2018 Zhang et al. 2019 Wang et al.
2021 Hong et al.
2023 Park & Lee
2019).
The transition has driven the emergence of attention- baased approaches
(Chen et al. [022
Liu et al. 2021: Wu u et al.
et al.] 2022] Huang et al. 2023 Xu et al. (2023] Zhu et al.
2023 Ma et al.] 2023) Zhang et al. 2024a)) Recently, diffusion model-based approaches have significantly boosted
style manipulation capabilities. Specifically, methods such as Prompt-to-Prompl (Hertz et al. (022) and Plug-and-Play
(Tumanyan al., 2023) utilize cross-attention and self-attention maps to guide spatial arrangements during text-driven image editing. More recently. StyleID (Chung al. 2024) has pushed this paradigm further by integrating key and value features from style images into self-attention layers, facilitating training-free free artistic style transfer with precise spatial and statistical alignment. Despite these advancements, efficiently modeling and balancing between global and local features remain challenging, due to the elusive nature of style definition and perception, as well as the complexity of style transfer. In the paper, we achieve a flexible balance between global and local feature transfers, by leveraging the local patch sampling with random projection and the feature grouping on projections.
3 Methodology
As discussed before, the proposed random projection-basee based style transfer can be incorporated into arbitrary encoder- decoder framework, without the need for network retraining. In this section, we elaborate this incorporation process with the fundamental approach AdaIN, as illustrated in Figure 2 and the incorporation into other approaches, like EFDM, StyleII and AdaAuN, can be realized in the similar way, as outlined in Appendices A.2 and A.3
In Figure 2 we provide the overview of incorporating the random projection module into AdaIN, which mainly consists of three steps. First, the feature maps of the content and style images are projected to diw-dimeniional spaces by random projection. Then style transfer is conducted over the projections of the two kinds of features. To achieve balance between local details and global consistency, we here divide each projection into number of subgroups and conduct style transfer on each subgroup. Finally, with the stylized projection, the target image feature map is derived by sparse reconstruction. Overall, the above three steps constitute a ropjection-stliizatoonrrcooooooo which is detailed in subsequent parts.
module,
3.1 Random projection
Prior to introducing random projection, let us first review the feature feed-forward process involved in the encoder- decoder model, as illustrated in Figure The model takes inputs content image T, and arbitrary style image
3

---

Published in Transactions on Machine Learning Research (02/2026)
Random Projection-Bane Style Transfer
fc
cp
Tpp
c
Random Projection
Group Division
ft
f tp
1g up
Transfer
(1] rp
Content
I
Encoder
fz
f
f +
Sparse Recovery
Decoder
Transfer
Rgg Ip
Stylized image
Random Prujection
Group Division
Style
Overview of the random projection- based style transfer implemented AdaIN. By feeding the content image Je and the style image I, into the encoder, we derive the content feature map Se and the style feature map fa. which are further projected to low dimensional spaces fop and fap by random projection. The projections are divided into a number "g of subgroups: Sap [ :.p...... (( and ssp [ ,'........ ... S.p [( and style transfer is conducted each pair of subgroups fep and fap resulting in the stylized projection fig I ... f "... With the projection ftp. by sparse reconstruction we derive its counterpart in the original feature space, namely the target feature map ft Feeding fi into the decoder, the desired target (stylized) image I, is finally obtained.
Figure 2:
J,, and outputs target image I, that combines the semantic content of Ie and the style of I,. This combination is performed in a single or a few layers of the encoder. In each layer, we can derive two feature maps respectively for T and J.. Usually, each feature map will consist of multiple channels. For Tc. we denote the feature map in each channel with a vector fo E (H (H.)x..)x1 where He and W. indicate the height and width the content feature map. In the similar way, we can define fs IR (H,,, for Ig. Note that here describe the feature of each channel, rather than the features of all channels, since the random projection-based style transfer is conducted channel- basis. Given the content feature map fa and the style feature map fs. we then can derive their random projections
fep Aefe and fep Asfs
where A E (Hx.xx) and A, E MH, are the random projection matrices.
For random projection, the choice of random matrices is crucial. this paper, we investigate four commonly-used random matrices compressed sensing: the mmatixmatrix with /M, nonzero elements per column (Lu et al. 2018). the [1,-1)- and [0,1,-1 -matrices with elements taken with equal probabilities (Achlioptas) 2003 Amini & Marvasti 2011), and the Gaussian matrix (Candes & Tao 2005). It can be seen that the mmatixx exhibits very sparse structures compared to other three kinds of matrices. Empirically, the three relatively dense matrices perform well when the style feature map exhibits very sparse distributions. This is because the random projection based on dense matrices more likely to approximate Gaussian distributions. In contrast, when the style feature not very sparse, the sparse [0.1)-mane -matrix tends to perform better. The advantage may be explained with the following fact. Essentially, the mmatixx based random projection performs a random, sparse sampling over the features fe and fs. The resulting projections Sep M and Sap E RRM. have their each element related to few elements of the original features and fs, reflecting the local correlation of original features. This allows the stylization feature projections better capture the local details compared to stylization on original features.
In addition to the distribution of random matrices, style transfer is also related to the compression rate of random matrices, which can be written as r Mc/(H, W.). With the decreasing of compression rate r, the following sparse reconstruction will become hard and then introduce noise. Empirically, the increased noise tends to degrade the quality of content, but enrich the diversity of style. Moreover, the random variation of the random matrices themselves can also result in diverse styles.
4

---

Published in Transactions on Machine Learning Research (02/2026)
3.2 Grouping-based style transfer
With the feature projections Sep E RRMe and Sap E RRM, derived in the previous random projection, we are ready to perform style transfer on them. To control the impact of style transfer on local details, we propose to first divide the fea- ture projections into number Ng subgroups, namely having fep = [f . |( and fap = | M. and then perform style transfer on each pair of subgroups slp E and S E R Me evident that the greater the number Rg of subgroups, the fewer local elements are involved in style transfer. By adjusting the value of ng. we can strike a balance between local details and global consistency.
f
By conducting AdaIN on each pair of subgroups fip) and f the stylized feature is derived as
f p(TO)) + ((
=
a(fap)
Combining the results ( E
IR
Th of all subgroups, we can obtain the stylized feature on the entire projection
Jap = 111 ............................... (( " E AM.
Similarly as the content projection fop and the style projection Sep as derived in ①.. we here hypothesize that the stylized projection fip is a random projection of an underlying target (stylized) feature map ft. namely
fep = Aoft.
(3)
Here, we exploit the same projection matrix Ar with the content projection Sep. This choice is based on the fact that the stylized projection fip is predominantly characterized with the content projection fop. and is slightly altered by the style projection fap via style transfer. According to compressed sensing theory (Foucart & Rauhut 2013), a target feature map fe similar to the content feature map fe can be reconstructed through sparse reconstruction, if the noise introduced the content projection fep, namely the variation induced by style transfer, is limited. In general, the variation in Sep during style transfer is more significant when using EFDM compared to AdaIN, The difference arises because AdaIN changes only the mean and variance of fep. whereas EFDM modifies the cumulative distribution function by replacing all elements of Sep with those of Stp-
3.3 Sparse Reconstruction
With the projection hypothesis we need to reconstruct the target image feature map from its projection fip. By compressed sensing, fi can be approximately derived by
ft arg min || Sepl12 + 1l f.
(4)
if the feature Jt has adequately sparse distributions, and the projection matrix A has sufficiently low correlations between columns. The two conditions should be approximately met, as the deep convolutional feature ft is usually sparse, and the random matrices employed here are commonly utilized in compressed sensing. After obtaining the target feature map Se, we can further feed it into the encoder-decoder model to generate the desired target image J,-
As convex problem, 4 can be tackled with standard optimization algorithms. Given that deep convolution fea- tures usually have high dimensions, selecting an efficient algorithm is essential Commonly used algorithms include Fast Iterative Shrinkage- Thrihhgod-heeshlding Algorithm (FISTA) (Beck & Teboulle, 2009) and Orthogonal Matching Pursuit (OMP) (Lubonja et al.] 2024). In our experiments, we adopt FISTA due to its lower complexity while maintaining performance comparable to that of OMP, as demonstrated in Appendix [A.4] FISTA supports GPU-accelerated parallel computing (Feinman 202I), thus ensuring high computational efficiency. For instance, it typically takes less than two seconds to reconstruct a single feature map, when exccuted on a GeForce RTX 4090 GPU. The time consumption issue is comprehensively analyzed in Appendix A.5
4 Experiments
Based on the analysis presented in the previous section, our random projection- based style transfer method is subject to the influence of several parameters tied to random projection. These include the distribution and compression rate
5

---

Published in Transactions on Machine Learning Research (02/2026)
of random matrices, as well the number Bg of subgroups into which the feature projections fep and fop are divided. In this section, we will first examine how these parameters impact stylized results, enabling us to achieve desired balance between style and content by reasonably adjusting the parameters. Then, we will showcase the performance improvements achieved by integrating our approach into two fundamental style transfer models: AdalN (Huang & Belongie| 2017) and EFDM (Zhang et al., 2022), as well as into their advanced variants and other state-of- tae-art approaches, such as the diffusion model-based StyleID (Chung et al. 2024) and the attention mechanism- AdaAuNN (Liu et al. 2021). Prior these studies, will first outline the implementation details.
4.1 Implementation Details
Given the models AdaIN, AdaAuN, EFDM and StyleID, as illustrated in Figure 2 our random projection- based style transfer module is incorporated into each layer of these models that involve style transfer, without the need for network retraining. The computation cost introduced by our module primarily stems from the sparse reconstruction outlined in 4 which is implemented using the FISTA algorithm (Beck & Teboulle| 2009 Feinman 2021]. For the algorithm, we assign the regularization parameter of À = 0.5 and limit the maximum number of iterations to 10. Regarding random projection, we generally set the compression rate r M/N = 0.8 or 1. For style transfer, we set the number of subgroups within feature projections to ng = 1. Empirically, our performance is insensitive to minor variations in these parameters, and no particularly meticulous parameter tuning is required. The selection and impact of these parameters are discussed in Appendices A.6 and A.7 The code is publicly available!.
4.2 Impact of the parameters of random projection on style transfer
Distribution of random matrices. In Figure 3. we compare the stylized results derived with four popular random projection matrices: {0, 1), (-1, O, 1), (-1, 1). and Gaussian matrices. It is evident that when the style feature exhibits sparse distribution, as illustrated in the first row, the (0, 1) -matrix notably underperforms compared to the other three matrices, while the latter three exhibit comparable performance. Notably, the [0, 1 comprises only a ratio of 1/MMc nonzero entries, leading much sparser distributions than the other matrices. Consequently, it struggles in projecting the style feature towards denser, Gaussian distributions, resulting in inferior style transfer performance. Conversely, the {0, 1 --matrx excels when the style feature displays relatively dense distributions, as depicted in the second row of Figure 3 In such scenarios, generating projections towards Gaussian distributions becomes more feasible. In our experiments, unless otherwise specified, we will employ Gaussian matrices.
Compression rate of random matrices and the number of subgroups within feature projections. In Figure 4 we compare the stylized results by varying the compression rate r of random [0, 1)- I-matticess from 0.2 to and the number ni of subgroups within feature projections from to 256. It is apparent that the compression rate decreases or the subgroup number Ng increases, the style gradually becomes prominent while the content becomes less evident. The impact of compression rates can be understood as follows. In compressed sensing, lower compression rate r will lead to a higher reconstruction noise in the reconstructed stylized feature ft. Then the increased noise introduces more irregular style patterns, while degrading the content. Regarding the increase in the number of subgroups Ny. as mentioned in the previous section, it implies that the number feature elements within each subgroup for style transfer decreases. This clement-restricted style transfer may overly focus on local details and neglect global constraints, leading to content loss. The aforementioned performance trends are also observed in supplementary experiments, as presented in Figures [ 13 of Appendix A.7 Based on these trends, satisfactory performance can generally be achieved by simply setting and flg
4.3 Improvement of our random projection module over state-of-the-art approaches
Improvement over two fundamental models: AdaIN and EFDM. In Figure 5 we examine the style transfer performance by incorporating our random projection (RP) module into AdaIN and EFDM. For the sake of generality, the content images cover four distinct types of objects: human faces, fish sketches, flowers, and buildings; and, the style images are characterized by sparse lines or patches. It is seen that the original models AdaIN and EFDM exhibit inferior performance in terms of content detail preservation and style feature transfer. As discussed previously, this limitation stems from the fact that these two models are not well suited to processing style or content features that
hutp:://gthuhh.co//xx///y// Gaussian- Latent- Seeent-Feature-SSe Peatures-Style- Staiiie--Syyl--Tanffeerreee Transfer-pytore

---

Published in Transactions on Machine Learning Research (02/2026)
Style
Content
{0, 1}
{-1, 0, 13
{-1
Gaussian
Figure 3: Stylized results derived with four different random matrices: (0. 1), (-1, 11, (-1, and Gaussian matrices.
Content
1hg 256
Style
r 0.8
r= r= 0.4
Y 0.2
Figure 4: Stylized results derived by varying the compression rate random matrices from 0.2, and the number of subgroups ng within feature projections from 256. Random projection implemented with (0, 1) matrices.
follow sparse distributions. In contrast, by incorporating our random projection module into these two models, the resulting AdaIN+RP and EFDM+RP achieve notable performance improvements by transforming the features from sparse distributions toward Gaussian distributions. Our success with the two foundational models not only validates the effectiveness of our method but also suggests its broad applicability, given that the two models form the core of most existing style transfer approaches, as elaborated later.
Improvement over the diffusion model-based approach: StyleID. To validate the effectiveness and generalizabil- ity of our method, we examine how it improves the performance of the state-of-the-an approach StyleID by keeping either the content the style constant while varying the other, as depicted in Figures 6 and 7 In Figure 6 facial im- age undergoes stylization with various style images. It is evident that across the various styles, our method consistently brings about significant enhancements in texture details and contrast, color saturation, and overall visual perception. Similar improvements are also noticeable in Figure 7 where various content images are stylized using a black-liner portrait sketch featuring red lips. Particularly, can be seen that our method successfully and significantly transfers the color of the red lips, even though this color constitutes only very small portion of the entire style image. This validates the advantage of our random projection module in capturing minor but crucial sparse features.

---

Published in Transactions on Machine Learning Research (02/2026)
Content & Style
AdaIN
AdaIN+RP
Content & Style
AdaIN
AdaIN+RP
Content & Style
EFDM
EFDM-RP
Content & Style
EFDM
EFDM-RP
Figure 5: Stylized results derived by incorporating vs, not incorporating our random projection (RP) module into the two fundamental models: AdaIN and EFDM.
StyleID
StyleID+RP
Figure 6: Stylized results derived by incorporating vs. not incorporating our random projection (RP) module into the diffusion model-based approach: StyleID, with a fixed content but various styles.
Content & Style
4
StyleID
6
StyleID+RP
11
Figure 7: Stylized results derived by incorporating vs. not incorporating our random projection (RP) module into the diffusion model-based approach: StyleID, with various contents but fixed style (a black-line portrait with red lips).
8

---

Published in Transactions on Machine Learning Research (02/2026)
Content & Style
AdaAttN
AdaAIN-+R
Figure 8: Stylized results derived by incorporating vs. not incorporating our random projection (RP) module into the iitention-basee approach: AdaAttN.
Table 1: Quantitative results of LPIPS, ArtFI and User Study. The better results are marked with underline.
Metric
AdaIN
AdaIN+RP
EFDM
EFDM+RP
StyleID
StyleID+RP
LPIPS +
0.665
0.579
0.686
0.592
0.650
0.568
ArtFID
31.01
29.65
33.88
31.37
28.51
26.42
Preference ratiot
0.26
0.74
0.19
0.81
0.13
0.87
Improvement over the attention-based approach: AdaAttN. Figure g illustrates notable performance improve- ments texture clarity and contrast, when integrating our random projection module into the AdaAttN. Furthermore, the resulting AdaAuN+RP also outperforms other well-recognized approaches, including AesPA (Hong et al.) 2023). RAST(Ma al. 2023). StyTr² (Deng et al., 2022). IEST Chen et al. 2021). Styleformer Wu al. 2021). and Art- flow(An al. 2021). demonstrated in Figures 16 18 of the Appendix A.8 Note that our AdaAtNN+RP performs well not only visually sparse images but also visually dense ones. This broader applicability visually dense images arises from the fact that such images typically exhibit sparse feature distributions due to the spatial continuity and correlation of image pixels. As a result, our random projection module can be used to further enhance the style transfer performance by transforming these sparse feature distributions towards the desired Gaussian distributions.
Quantitative results. The results shown in Figures 58 demonstrate that random projection module significantly improves the quality of content, delivering superior perceptual performance in style transfer. This property is further supported by the quantitative results presented in Table [ where I.IPS (Zhang et al., 2018) measures the content fidelity of stylized results, and ArtFID (Wright & Ommer 2022) assesses the overall style transfer performance by considering both content and style qualities. Moreover, we conducted a user study with 50 participants who selected their preferred stylized results from 60 trials based on overall perceptual quality. All these results validate the advan- tage of our approach.
Potential limitation. The main advantage of our random projection module is that it can prevent the loss of critical features in either content or style images, when their latent features exhibit extremely sparse distributions. Typical examples include the body contour (content features) of the bird in Figure T and the red lips (style features) of the lady Figure 7 In practical scenarios, however, the feature loss of content or style caused by existing style transfer approaches may be imperceptible to human vision, resulting in an unobvious performance gain of our method. Never- theless, even without improved perceptual quality, module will not degrade the quality, since compressed sensing

---

Published in Transactions on Machine Learning Research (02/2026)
enables reliable feature reconstruction from random projections when the compression rate is not extremely low. This indicates that our module can be universally integrated into existing style transfer approaches without concerns about performance degradation.
5
Conclusion
Existing style transfer approaches based on the encoder-decoder architecture typically employ either the mean-and- variance strategy (proposed in AdaIN) or the cumulative distribution function (introduced EFDM) to model the distribution of style features. The two methods implicitly favor the scenarios where the features of both style and content images roughly follow Gaussian distributions. Nevertheless, this requirement is often hard satisfy, as deep encoder features usually exhibit sparse distributions. Consequently, when handling highly sparse features, the two methods often result poor perceptual quality, with significant loss of texture details, contrast, color, and content. In this paper, we have for the first time identified and tackled this issue by incorporating random projection module into the srcoder-decoder architecture, in order to transform features from sparse distributions towards the desired Gaussian distributions. This module operates as a flexible plug-and-play component, without the need for network retraining. When integrated into the fundamental models AdaIN and EFDM, as well as other cutting-edge approaches like the diffusion model-based StyleID and the attention mechanism-bait based AdaAttN, this module brings about notable performance improvements.
Acknowledgements
We sincerely thank the editors and anonymous reviewers for their precious time and invaluable suggestions. Further- more, we gratefully acknowledge the support provided by the National Key Research and Development Program of China (Grant Nos. 2022YFB3206900 and 2023YFA 2023Y1A1008701) and the National Natural Science Foundation of China (Grant Nos. 61991412, 61801264, and 12001318).
References
D. Achlioptas. Drtabase-friendly random projections: Johnson-LLindenstrauss with binary coins. J. Comput. Syst. Sci., 66(4):671-687 2003.
Arash Amini and Farokh Marvasti. Deterministic construction of binary, bipolar, and ternary compressed sensing matrices. IEEE Transactions on Information Theory, 57(4):2300-2370, 2011.
Jie An, Tao Li, Haozhi Huang. Li Shen, Xuan Wang, Yongyi Tang, Jinwen Ma, Wei Liu, and Jiebo Luo. Real-time universal style transfer on high-resolution images via zero-channel pruning. arXiv preprint arXiv:2006.0900 2020,
Jie An, Siyu Huang, Yibing Song. Dejing Dou, Wei Liu, and Jiebo Luo. Artflow: Unbiased image style transfer via reversible neural flows. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 871, 2021.
Amir Beck and Mare Teboulle. A fast iterative shrinkage-threshollingg algorithm for linear inverse problems. SIAM journal on imaging sciences, 2(1):183-202, 2009.
E.J. Candes and Tao. Decoding by linear programming. IEEE Transactions on Information Theory, 51(12):4203
4215, Dec. 2005.
Prashanth Chandran, Gaspard Zoss, Paulo Gotardo, Markus Gross, and Derek Bradley. Adaptive convolutions for structure-aware style transfer. In Proceedings of the IEEE/CVF conference on computer vision and pattern recog- nition, pp. 7972-7981. 2021.
Haibo Chen, Zhizhong Wang, Huiming Zhang, Zhiwen Zuo, Ailin Li, Wei Xing, Dongming Lu, et al. Artistic style transfer with externll-external learning and contrastive learning. Advances in Neural Information Processing Sys- tems, 34:26561-266733, 2021.
Tian Qi Chen and Mark Schmidt. Fast patch-based style transfer of arbitrary style. arXiv preprint arXiv.1612.04337. 2016.
10

---

Published in Transactions on Machine Learning Research (02/2026)
Jiwoo Chung, Sangeek Hyun, and Jae-Pil Heo. Style injection in diffusion: A training-free free approach for adapting large-scale diffusion models for style transfer. In Proceedings of the IEEF/CVE conference on computer vision and pattern recognition, pp. 8795-8805, 2024.
Yingying Deng, Fan Tang, Weiming Dong, Chongyang Ma, Xingjia Pan, Lei Wang, and Changsheng Xu. StyTr²: Image style transfer with transformers. In Proceedings of the IEEE/CVF conference computer vision and pattern recognition, pp. 1 11326-12 173361 2022.
Vincent Dumoulin, Jonathon Shlens, and Manjunath Kudlur. A learned representation for artistic style. arXiv preprint arXiv:/610.07662, 2016.
Reuben Feinman. A pytorch library for Ll-regularized least squares (lasso) problems. 2021. URL https/////ggtt rfeinman/pytorch- lasso
Simon Foucart and Holger Rauhut. A Mathematical Introduction to Compressive Sensing. Birkhäuser Basel, 2013. ISBN 081 0817649476.
Leon Gatys, Alexander S Ecker, and Matthias Bethge. Texture synthesis using convolutional neural networks. Ad- vances in neural information processing systems, 28, 2015a.
Leon A Gatys, Alexander S Ecker, and Matthias Bethge. A neural algorithm of artistic style. arXiv preprint 1rXXiv/508.066 2015b.
Leon A Gatys, Alexander S Ecker, and Matthias Bethge. Image style transfer using convolutional neural networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 2414-2423, 2016.
Leon A Gatys, Alexander S Ecker, Matthias Bethge, Aaron Hertzmann, and Eli Shechtman. Controlling perceptual factors in neural style transfer. In Proceedings of the IEEE conference computer vision and pattern recognition, pp. 3985-3999999 2017.
Bin Ge, Zhenshan Hu, Chenxing Xia, and Junming Guan. Arbitrary style transfer method with attentional feature distribution matching. Multimedia Systems, 30(2):96, 2024.
Shuyang Gu, Congliang Chen, Jing Liao, and Lu Yuan. Arbitrary style transfer with deep feature reshuffle. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.
2018.
Amir Hertz, Ron Mokady, Jay Tenenbaum, Kfir Aberman, Yael Pritch, and Daniel Cohen-Or. Prompt-to-prompt image editing with cross attention control. arXiv preprint arXhv:2208.01620 2022.
Kibeom Hong, Seogkyu Jeon, Junsoo Lee, Namhyuk Ahn, Kunhee Kim, Pilhyeon Lee, Daesik Kim, Youngjung Uh. and Hyeran Byun. Aespa-net: Aesthetic pattern-aware style transfer networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 22758-22767, 2023.
Eddie Huang and Sahil Gupta. Style is a distribution of features. arXiv preprint arXiv:2007. 13010, 2020.
Siyu Huang, Jie An, Donglai Wei, Jiebo Luo, and Hanspeter Pfister. Quantart: Quantizing image style transfer towards high visual fidelity. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 5947-5956, 2023.
Xun Huang and Serge Belongie. Arbitrary style transfer in real-time with adaptive instance normalization. In Pro- ceedings of the IEEE international conference on computer vision, pp. 1501-1510, 2017.
Yongcheng Jing, Xiao Liu, Yukang Ding, Xinchao Wang, Errui Ding, Mingli Song, and Shilei Wen. Dynamic in-
stance normalization for arbitrary style transfer. In Proceedings of the AAAI conference artificial intelligence, volume 34, pp. 4369-43433 4376, 2020.
Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. In Proceedings of the European Conference Computer Vision, pp. 694-711. Springer, 2016.
Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEF/CVF conference computer vision and pattern recognition, pp. 4401-4410 2019.

---

Published in Transactions on Machine Learning Research (02/2026)
Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improv- ing the image quality of stylegan. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 81 10-8119, 2020.
Joonwoo Kwon, Sooyoung Kim, Yuewei Lin, Shinjae Yoo, and Jiook Cha. Aesfa: An aesthetic feature-aware arbitrary neural style transfer. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 13310-13319 2024.
Pan Li, Dan Zhang, Lei Zhao, Duanqing Xu, and Dongming Lu. Style permutation for diversified arbitrary style transfer. /EEE Access, 8:199147-199158, 2020.
Xueting Li, Sifei Liu, Jan Kautz, and Ming- Hing-Hsuan Yang. Learning linear transformations for fast image and video style transfer. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 3809-3817, 2019.
Yijun Li, Chen Fang, Jimei Yang, Zhaowen Wang, Xin Lu, and Ming- Hssan Yang. Universal style transfer via feature transforms. Advances in neural information processing systems, 30, 2017.
Tianwei Lin, Zhuoqi Ma, Fu Li, Dongliang He, Xin Li, Errui Ding, Nannan Wang, Jie Li, and Xinbo Gao. Drafting and revision: Laplacian pyramid network for fast high-quality artistic style transfer. In Proceedings of the IEEE/CVF conference computer vision and pattern recognition, pp- 5141-5150, 2021.
Songhua Liu, Tianwei Lin, Dongliang He, Fu Li, Meiling Wang, Xin Li, Zhengxing Sun, Qian Li, and Errui Ding. Adaattn: Revisit attention mechanism arbitrary neural style transfer. In Proceedings of the IEEE/CVF interna- tional conference on computer vision, pp. (659,6658, 2021.
W. Lu, T. Dai, and S. T. Xia. Binary matrices for compressed sensing. IEEE Transactions Signal Processing, 66 (1):77-85, Jan. 2018. ISSN 1053-587X.
Ariel Lubonja, Sebastian Kazmarek Præsius, and Trac Duy Tran. Efficient batched cpu/gpu implementation of orthog- onal matching pursuit for python. arXiv preprint arXiv: 2407.06434 2024.
Yingnan Ma, Chenqiu Zhao, Xudong Li, and Anup Basu. Rast: Restorable arbitrary style transfer via multi-restoration. In Proceedings of the IEEE/CVF Winter Conference Applications Computer Vision, pp. 331-340, 2023.
Aravindh Mahendran and Andrea Vedaldi. Understanding deep image representations by inverting them. In Proceed- ings of the IEEE conference on computer vision and pattern recognition, pp. 5188-5196, 2015.
Elizabeth Meckes. Approximation of projections of random vectors. Journal of Theoretical Probability, 25:333-352, 2012.
Dae Young Park and Kwang Hee Lee. Arbitrary style transfer with style-attentional networks. In proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 5880-5888, 2019.
Haotong Qin, Ruihao Gong, Xianglong Liu, Xiao Bai, Jingkuan Song, and Nicu Sebe. Binary neural networks: A survey. Pattern Recognition, 105:107281, 2020.
Eric Risser, Pierre Wilmot, and Connelly Barnes. Stable and controllable neural texture synthesis and style transfer using histogram losses. arXiv preprint urXiv::/01, 708999893, 2017.
Narek Tumanyan, Michal Geyer, Shai Bagon, and Tali Dekel. Plug aagg-and-lay diffusion features for text-driven image- to-image translation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1921-1930, 2023.
Dmitry Ulyanov, Vadim Lebedev, Andrea Vedaldi, and Victor Lempitsky. Texture networks: Feed-forward synthesis textures and stylized images. arXiv preprint arXiv:1603.03417 2016.
Zhizhong Wang. Lei Zhao, Haibo Chen, Zhiwen Zuo, Ailin Li, Wei Xing, and Dongming Lu. Divswapper: Towards diversified pateh- arbitrary style transfer. arXiv preprint arXiv:2101.06388 2021.
12

---

Published in Transactions on Machine Learning Research (02/2026)
Matthias Wright and Bjöm Ommer. Artfid: Quantitative evaluation of neural style transfer. In DAGM German Conference on Pattern Recognition, pp. 560-576. Springer, 2022.
Xiaolei Wu, Zhihao Hu, Lu Sheng, and Dong Xu. Styleformer: Real-time time arbitrary style transfer via parametric style composition. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 14618-14627, 2021.
Wenju Xu, Chengjiang Long, and Yongwei Nie. Learning dynamic style kernels for artistic style transfer. In Proceed- ings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 10083-10092, 2023.
Chiyu Zhang, Xiaogang Xu, Lei Wang, Zaiyan Dai, and Jun Yang. S2wat: Image style transfer via hierarchical vision transformer using strips window attention. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 7024-7032, 2024a.
Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 586-595, 2018.
Tianlong Zhang, Jing Lv, and Ming Yang. Semi- Semi-parametric style transfer with multi-perspective feature fusion and information-guided alignment. In Proceedings of the International Conference on Multimedia Retrieval, pp. 943- 950, 2024b.
Yabin Zhang, Minghan Li. Ruihuang Li, Kui Jia, and Lei Zhang, Exact feature distribution matching for arbitrary style transfer and domain generalization. In Proceedings of the IEEE/CVF conference computer vision and pattern recognition, pp. 8035-8045, 2022.
Yulun Zhang, Chen Fang, Yilin Wang, Zhaowen Wang, Zhe Lin, Yun Fu, and Jimei Yang. Multimodal style transfer via graph cuts. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 5943-5951, 2019.
Mingrui Zhu, Xiao He, Nannan Wang, Xiaoyu Wang, and Xinbo Gao. All-to-key attention for arbitrary style transfer. In Proceedings of the IEEF/CVF International Conference on Computer Vision, pp. 23109-231 19, 2023.
13

---

Published in Transactions on Machine Learning Research (02/2026)
A Appendix
A.1
Sparsity of latent features
In this part, we investigate the sparsity of latent features generated by the encoders of the studied style transfer ap- proaches. These features indeed tend to follow sparse distributions for most images, for two main reasons. First, most images contain relatively large smooth regions, which facilitate the generation of sparse feature distributions. Second, notably, these encoders not reduce the input image dimensions to a considerably lower level. Specifically, unlike conventional encoders designed for dimensionality reduction, the encoders in AdaIN, AdaAttN and EFDM increase the feature dimension from the channel size of [3, 512, 512] to [512, 64, 64] (with vector dimension greater than 2,000,000), whereas the encoder of StyleID reduces the feature dimension from the channel size of [3, 512, 512] to 14, 64, 64] (with vector dimension greater than 10,000). These feature dimensions are substantially larger than those of encoder features from conventional VAEs and GANs, which are usually on the order of hundreds. Such high dimensionality inevitably leads to feature redundancy, thereby resulting in sparse structures.
quantify the sparsity of these encoder features, as illustrated in Figure we further investigate their kurtosis, a canonical statistical metric for quantifying the sparsity of random variables. Kurtosis defined as E (====">² where their mean and standard deviation. A larger kurtosis value
J; denotes the i-th elements of vector æ, and p and indicates sparser distribution. If the kurtosis value of variable is larger than that (equal to 3) of Gaussian variables, the variable can be roughly regarded as following sparse (or called heavy-tailed) distribution. From Figure 2 it is seen that the kurtosis of AdaIN features is higher than that of StyleID features, which can be attributed to their higher feature dimensions. For most images, the kurtosis values of both feature types are notably higher than the Gaussian baseline (i.c., 3), indicating sparse feature distributions.
AdaIN feature:
24.49
23.12
15.10
17.98
16.05
13.84
StyleID feature:
6.31
5.71
4.74
4.16
3.64
2.88
AdaIN feature:
19.36
15.48
11.16
13.59
14.25
14.88
StyleID feature:
4.31
3.51
3.18
3.70
3.43
3.54
AdaIN feature:
15.08
19.65
19.35
13.30
27.49
22.81
StyleID feature:
4.29
3.47
6.43
5.15
2
AdaIN feature: 11.28
17.13
21.74
16.10
10.38
13.78
StyleID feature:
2.50
4.42
5.55
4.23
2.36
3.44
Figure 9: The kurtosis values of the AdaIN and StylelD features extracted from the content and style images studied in the paper. For most images, these values are markedly higher than the Gaussian baseline (i.e., 3), indicating sparse feature distributions.
14

---

Published in Transactions on Machine Learning Research (02/2026)
A.2 Overview of incorporating random projection into AdaAttN
Random Projection-Basee Based Style Transfer
M
A
Handom Projection
Group Divisinn
S
Sy
Sp
Style
Encoder
Uisision
Sparse Xecovesy
Decoder
lond Imagee
Fa
Fep
Content
Handom Projection
Group
Norm
Figure 10: Overview of the random projection-based style transfer implemented on AdaAttN. By feeding the style image I, and the content image I, into the VGG encoder, we derive the style feature map F, and the content feature map Fg. Then the weighted mean M and standard variance S are obtained from Fe, and the specific method is mentioned AdaAttN (Liu et al. 2021). M, S and Fg are further projected to low dimensional spaces Mp. Sp and Fop by random projection. The projections divided into number ny of subgroups: Mp [M .... , A ".," Sp = 1S ,..",) (S(")) and Fep [P F( and Fep further mean-variance channel-wise normalized, represented by Norm in the figure. Then style transfer is conducted on each pair of subgroups M1 s and (()) resulting in the stylized projection Fip = [F .... ,. The formula for style transfer is formulated as F ( * 50 + _ With the projection Ftp. by sparse reconstruction we derive its counterpart in the original feature space, namely the target feature map F.. Feeding F, into the decoder, the desired target (stylized) image 1; is finally obtained.
15

---

Published in Transactions on Machine Learning Research (02/2026)
A.3 Overview of incorporating random projection into StylelD
Content noise
Content image z6
Random Projection- Based Style Transfer
Init. noise
Stylized image 26
Random Projection- Based Style Transfer
Style noise z
Style image 26
T
DDIM Inversion
DDIM coversion(commtnt and style)
Reverse process(style transfer)
Figure 11: Overview of the random projection-base based style transfer implemented on StyleID. First, content and style images undergo identical DDIM inversion process, with attention-basee style injection module strictly following StyleID's original implementation. Subsequently, our random projection-based style transfer module operates within StyleID's Initial Latent AdaIN module, performing the operations of random projection and style transfer as illustrated Figure 2 Finally, the modified latent progresses through StyleID's reverse diffusion process for image synthesis.
16

---

Published in Transactions on Machine Learning Research (02/2026)
A.4 Comparison of two representative sparse reconstruction algorithms: FISTA and OMP
AdaIN-RP
EFDM+RP
AdaAttN-RP
StyleID+RP RP
Content & Style
FISTA
OMP
Figure 12: Stylized results derived with two commonly-used sparse reconstruction algorithms: the optimization based
FISTA (Feinman 2021) vs. the greedy search-bare based OMP (Lubonja et al. 2024). It is seen that the visual effects of the two algorithms are highly similar.
17

---

Published in Transactions on Machine Learning Research (02/2026)
A.5 Time consumption of our random projection module
In Tables and we present the time consumptions of feature encoding, style transfer, and decoding for AdaIN (which shares the same framework as EFDM), AdaAtN, and StylelI implemented on GeForce RTX 4090 GPU. Additionally, we provide the time costs of random projection and sparse reconstruction involved in our random pro- jection (RP) module. It is evident that the time overhead introduced by our RP module is minimal, particularly when compared the substantial time savings achieved by eliminating the need for network retraining.
Table 2: Time consumption of AdaIN/EFDM incorporating our RP module
AdaIN/EFDM
Our RP module
Encoding
Style transfer
Decoding
Random projection
Sparse reconstruction
136ms
18ms
22ms
196ms
203ms
Table Time consumption of AdaAttN incorporating our RP module
AdaAttN
Our RP module
Encoding
Style transfer
Decoding
Random projection
Sparse reconstruction
872ms
172ms
371ms
2401ms
2303ms
Table 4: Time consumption of StylelD incorporating our RP module
StyleID Style transfer
Our RP module
Encoding
Decoding
Random projection
Sparse reconstruction
10533ms
10ms
5603ms
590ms
626ms
18

---

Published in Transactions on Machine Learning Research (02/2026)
A.6 Selection of key parameters
For ease of parameter tuning and practical application, the selection of key parameters is outlined as follows:
I) Random projection matrices: In most cases, Gaussian matrices with zero mean and unit variance deliver satis- factory performance. Gaussian matrices fail to meet requirements (e.g., for dense content features as illustrated in Figure 3), binary {0, 1 -mmarricss may yield better performance.
2) Compression rate M/N: According compressed sensing theory, perfect sparse recovery requires the compression to satisfy M 2k: where k denotes the feature sparsity, namely the number of nonzero entries in the N-dimensional feature vectors. For style transfer tasks, besides recovery accuracy, perceptual quality of the stylized results. Empirically, as illustrated in Figure 4 and Figures 13 15 can usually yield satisfactory performance. A lower compression rate r tends to introduce more recovery errors (i.e. noise), thereby degrading the content feature quality.
also need to consider the setting r 2 0.6
3) Number ng of subgroups in feature projections: For simplicity, ng can be in Figure 4 increasing "g from 256 leads slight variations in stylized effects, and such variations are far less pronounced than those caused by the compression rate
most cases. As observed
4) Sparse recovery algorithms: We recommend two commonly-used algorithms: FISTA and OMP. For FISTA, in our experiments the regulation parameter is set to À = 0.5 and the iteration number is limited to 10; and for OMP, its sparsity parameter k can be determined based on feature sparsity.
19

---

Published in Transactions on Machine Learning Research (02/2026)
A.7 Impact of the varying of compression rate and number ny of subgroups
In Figures 13 to 15 following the investigation in Figure 4 we further evaluate the performance gains of our random projection module when integrated into AdaAuN, EFDM and StylelD, by decreasing the compression rate from I to 0.2 and increasing the number nh of subgroups from to 256. The results demonstrate that as the compression rate r decreases, the content quality tends to degrade while the stylized effect tends to be enhanced, owing to the introduction of more recovery errors (i.e. noise). Similarly, increasing the subgroup number ng slightly boosts stylization effects. Regarding parameter tuning, simply setting r 1 and ng suffices for our method to achieve notable performance gains the aforermentioeed style transfer approaches.
Content & Style
EFDM
EFDM+RP
II
EFDM-RP
Content
Ti = 256
Style
0.8
0.6
0.4
0.2
Figure 13: The stylized results derived by integrating random projection module into EFDM, where the compres- sion rate r is decreased from to 0.2 and the number n, of subgroups is increased from to 256. Compared to EFDM. our method BFDM+RP exhibits better texture-detall performance, when the compression rate is sufficiently large.
20

---

Published in Transactions on Machine Learning Research (02/2026)
Content & Style
AdaAttN
AdaAttN+RP
nig
AdaAtN--P
Content
ng = 256
Style
0.8
0.4
0.2
The stylized results derived by integrating our random projection module into AdaAttN, where com- pression rate is decreased from 0.2 and the number ny subgroups is increased from 256. Compared to AdaAtt,, our method AdaAt:NRR achieve markedly superior performance when the compression rate is suffi- ciently large, clearly manifested in the refined details of eyes and individual hair strands.
Figure 14:
21

---

Published in Transactions on Machine Learning Research (02/2026)
Content Style
StyleID
StyleID+RP
StyleID+RP
Content
nig 256
Style
1 == 0.8
r == 0.6
0.4
7 0.2
Figure 15:
The stylized results derived by integrating our random projection module into StyleID, where the com- pression rate r is decreased from to 0.2 and the number ny of subgroups is increased from 1 to 256. Compared to StylelID, our method StyleID+RP outperforms notably in transferring weak style features (e.g., the lady's red lips), when the compression rate sufficiently large.
22

---

Published in Transactions on Machine Learning Research (02/2026)
A.8 Comparison between our AdaAttN+RP and other well-recognized approaches
Style
Content
AesPA
RAST
StyTr²
IEContraA ST
Sty StyleFormer
ArtFlow
A daA +RP
Figure 16: Stylized results derived by our AdaAtNN+R and other approaches. Among the approaches, our AdaAuN+RP stands out for its more saturated and evenly distributed red color.
Table 5: User Study Results for Figure 16
AesPA
RAST
StyTr²
IEContraAST
StyleFormer
ArtFlow
AdaAuNN+P
Preference ratio
0.13
0.00
0.00
0.07
0.02
0.00
0.78
23

---

Published in Transactions on Machine Learning Research (02/2026)
S
Style
Content
A esPA
RAST
StyTr
IEContraA ST
StyleFormer
A rtFlow
A daa +RP
Figure 17:
Stylized results derived by our AdaAuN+RP and other approaches. When rendering the textures of branches, leaves, and petals in black-and-white style, our AdaAttN+RP outperforms all others.
Table 6: User Study Results for Figure
17
AesPA
RAST
StyTr²
IBContraAST
StyleFormer
ArtFlow
AdaAuN++P
Preference ratio f
0.08
0.13
0.00
0.01
0.05
0.00
0.73
24

---

Published in Transactions on Machine Learning Research (02/2026)
Style
Content
AesPA
RAST
StyTr2
IEContraAST
StyleFormer
ArtFlow
AdaAttN+RP
Figure 18: Stylized results derived by our AdaAuN+RP and other approaches. Our AdaAtN+RR achieves good balance between style transfer and content preservation. In contrast, other approaches either overemphasize styles at the expense of content details, seen with StylcFormer, or lack sufficient stylistic features, like RAST.
Table User Study Results for Figure
18
AesPA
RAST
StyTr²
IEContraAST
StyleFormer
ArtFlow
AdaAuN++R
Preference ratio
0.02
0.11
0.07
0.00
0.27
0.01
0.52
25


Reviews:
[{"review_id": "06djwpac7d", "reviewer": "Reviewer_s4a3", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The primary contribution of this paper is the introduction of a plug-and-play random projection module designed to address the sparsity issue inherent in deep convolutional features for style transfer. This module projects sparse style features into low-dimensional, Gaussian-like distributions, enhancing compatibility with existing methods and enabling the reconstruction of stylized features through compressed sensing, all without the need for network retraining. \n\nKey advantages include its broad applicability across various style transfer frameworks, significant improvements in content preservation and style richness, as demonstrated by both qualitative and quantitative results, and efficient implementation with GPU acceleration. \n\nHowever, potential limitations include the need for careful parameter tuning (e.g., random matrix type, compression rate) to achieve optimal performance, as well as a slight increase in computational cost due to sparse reconstruction, although this is minimal in practice.", "claims_and_evidence_yn": "Yes", "claims_explanation": "1. Qualitative results visually demonstrate that RP-enhanced models outperform baselines in preserving details, transferring subtle style elements, and balancing content with style. \n\n2. The RP models consistently achieve lower LPIPS/ArtFID scores, indicating better content fidelity and overall quality, and higher user preference ratios, reaching up to 87%.\n3. The methodology is grounded in established theories, such as the Johnson-Lindenstrauss lemma for random projection and compressed sensing for reconstruction, ensuring technical rigor. \n\n4. The authors also test multiple parameters, including matrix types and compression rates, to confirm the robustness of the approach.", "audience_yn": "Yes", "audience_explanation": "The paper tackles the issue of sparse feature incompatibility in state-of-the-art methods, providing a generalizable solution that seamlessly integrates with popular frameworks. Researchers in generative models, computer vision, and representation learning will benefit from the insights on feature distribution alignment. Practitioners will appreciate the plug-and-play design, which enhances performance without the need for retraining, making it highly suitable for real-world applications.", "requested_changes": "(1) Please provide ablation studies on the impact of different sparse reconstruction algorithms. I am wondering if these different choices would affect the results slightly?\n\n(2) While GPU acceleration is mentioned, including specific runtime comparisons would offer a clearer understanding of the practical feasibility of the approach.\n\n(3) Another important aspect to consider is the performance of random projection in edge cases, such as when dealing with extremely dense features or very low compression rates. Addressing these scenarios would enhance the comprehensiveness of the work.\n\n(4) Finally, offering guidance for parameter tuning could significantly improve usability. A concise table or flowchart outlining how to select the random matrix type, compression rate, and subgroup number based on input feature sparsity would be a valuable addition for users implementing the method.", "broader_impact_concerns": "No major ethical concerns require a Broader Impact Statement or additional addressing.", "additional_comments": "This is a well-written and technically robust paper that addresses a significant gap in style transfer research. The plug-and-play design is a standout feature, as it lowers the adoption barrier across existing models. The integration with diffusion models and attention-based methods highlights the module’s versatility, which is especially valuable given the increasing popularity of these frameworks. The experimentation further validates their findings. By making the code publicly available, as promised, they will facilitate reproducibility and enable further research in this area.", "extra_scores": {}, "extra_text": {}}, {"review_id": "q6YXcJCJsg", "reviewer": "Reviewer_jf7m", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a simple plug-and-play module for arbitrary image style transfer based on random projection induced Guassian latents. The main idea is that deep encoder features are typically sparse and therefore violate the Gaussian assumptions underlying the AdaIN and EFDM formulations. This work first applies random projection to both content and style features to obtain lower-dimensional features that more closely resemble Gaussian distributions. Style transfer (AdaIN or EFDM) is then performed in this projected space. Finally, the stylized projection is mapped back to the original feature space via sparse recovery using compressed sensing. The method is training-free and can be integrated into AdaIN, EFDM, AdaAttN, and StyleID.\n\nThe paper claims improved performance, especially when style features are sparse, and provides qualitative comparisons, ablations on projection matrices and grouping, and quantitative evaluations with LPIPS, ArtFID, and user studies.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The core claim—that AdaIN and EFDM degrade when the style feature distribution is sparse—is well supported through the provided qualitative examples. The proposed module alleviates content loss in sparse-style settings, and the improvements show up across multiple approaches (AdaIN, EFDM, AdaAttN, StyleID). Quantitative metrics support the trend.\n\nThe paper does not provide quantitative evidence for the central premise that random projection makes features “more Gaussian.” Runtime overhead from sparse reconstruction is also not discussed.", "audience_yn": "Yes", "audience_explanation": "## Strength\n\n- The motivation is clear and grounded in a real limitation of both AdaIN and EFDM: sparse deep features lead to poor statistics matching against Gaussian. The failure cases of the popular methods shown in the paper support this point well.\n- The proposed module is lightweight and training-free, and integrates easily into many existing style transfer pipelines. \n- The improvements on sparse-style cases (e.g., red-lip sketch, sparse point patterns) are convincing and consistent across methods.\n- The ablations on compression ratio, projection matrix types, and grouping shows that the proposed method is effective in style transfer.\n\n## Weakness\n\n- The entire method is built on the claim that random projection makes sparse features “more Gaussian,” but there is no quantitative evidence for this. Some normality metrics would make the motivation much more solid.\n- The method appears strongest on sparse style images. Improvements on dense or highly textured styles are less clear, and in some cases, only slightly different from the baseline. The work would benefit from a more explicit discussion of when the method is helpful and when it is not.", "requested_changes": "- Quantify the “Gaussianization” assumption: this work claims that random projection makes sparse features approximately Gaussian, which requires more concrete evidence. \n- Sparse reconstruction is non-trivial. The per-image latency and comparisons to AdaIN, EFDM, AdaAttN, and StyleID with and without the RP module is needed for concrete run-time analysis.", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "5yxykOZ6Xa", "reviewer": "Reviewer_JV3C", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper addresses a well-known discrepancy in modern style transfer methods like AdaIN: the assumption that latent features follow a Gaussian distribution. The authors correctly point out that features from natural images are, in practice, often sparse, which violates this core assumption and can degrade transfer quality. To solve this, the paper proposes an approach based on random projections. Sparse, high-dimensional features are first mapped to a lower-dimensional space using random projection. Based on statistical theory, these projections become denser and more closely approximate a Gaussian distribution. Existing style transfer methods (like AdaIN or EFDM) are then applied in this new, more \"Gaussian-friendly\" latent space, where their underlying assumptions are better met. Finally, the stylized low-dimensional features are recovered back into the original high-dimensional feature space using techniques from compressed sensing. The paper provides experimental validation showing that this module improves performance for both AdaIN and EFDM, leading to results that better preserve content structure.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The authors provide experimental validation.", "audience_yn": "Yes", "audience_explanation": "This paper should be of high interest to the TMLR audience, particularly researchers and practitioners in computer vision, generative models, and creative AI. The contribution is solid, well-motivated, and technically sound. The fact that the module is model-agnostic and avoids the need for retraining makes it highly practical and more likely to be adopted by the community. The paper clearly demonstrates its value by improving upon two different (and recent) state-of-the-art methods.", "requested_changes": "The authors state that the compressed sensing optimization is solved quickly in absolute terms, but this is vague. Could the authors please add a breakdown of the runtime for each component: the initial feature extraction (forward pass); the random projection; the stylization step; and the compressed sensing reconstruction step? This would clarify the practical overhead introduced by the proposed module compared to the baseline methods.\n\nThis new module introduces several new hyperparameters, such as the target dimension for the random projection and any parameters related to the compressed sensing solver. In general, how much tuning is required for good performance, and are there default recommended values for these hyperparameters?\n\nPlease double-check the manuscript's formatting against the TMLR journal style. The font used in the current draft does not appear to match the official TMLR template.", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)