Unsupervised Panoptic Interpretation of Latent Spaces in GANs Using Space-Filling Vector Quantization
Authors: Mohammad Hassan Vali
Tom Bäckström
Venue: Accepted by TMLR ()

Abstract: Generative adversarial networks (GANs) learn a latent space whose samples can be mapped to real-world images. Such latent spaces are difficult to interpret. Some earlier supervised methods aim to create an interpretable latent space or discover interpretable directions, which requires exploiting data labels or annotated synthesized samples for training. However, we propose using a modification of vector quantization called space-filling vector quantization (SFVQ), which quantizes the data on a piece-wise linear curve. SFVQ can capture the underlying morphological structure of the latent space, making it interpretable. We apply this technique to model the latent space of pre-trained StyleGAN2 and BigGAN networks on various datasets. Our experiments show that the SFVQ curve yields a general interpretable model of the latent space such that it determines which parts of the latent space correspond to specific generative factors. Furthermore, we demonstrate that each line of the SFVQ curve can potentially refer to an interpretable direction for applying intelligible image transformations. We also demonstrate that the points located on an SFVQ line can be used for controllable data augmentation.

Published in Transactions on Machine Learning Research (06/2025)
Unsupervised Panoptic Interpretation of Latent Spaces in GANs Using Space-Filling Vector Quantization
Mohammad Hassan Vali
Deportment of Computer Science, Aalto University
Tom Bäckström
tor, www.bbkkkksrom@@aaatt..
Department of Information and Communiccations Engineering, Aalto University
Reviewed on OpenReview: https: // openreview. net/ met/ forum? id- SSJ2t
Abstract
Generative adversarial networks (GANs) learn a latent space whose samples can be mapped to real-world images. Such latent spaces are difficult interpret. Some earlier super- vised methods aim to create an interpretable latent space or discover interpretable direc- tions, which requires exploiting data labels or annotated synthesized samples for training. However, propose using modification of vector quantization called space-filling vector quantization (SFVQ), which quantizes the data on a piece-wise linear curve. SFVQ can capture the underlying morphological structure of the latent space, making it interpretable. We apply this technique to model the latent space of pre-trained StyleGANZ and BigGAN networks on various datasets. Our experiments show that the SFVQ curve yields general interpretable model of the latent space such that determines which parts of the latent space correspond to specific generative factors. Furthermore, of the SFVQ curve potentially refer to interpretable direction for applying intelligible image transformations. We also demonstrate that the points located on an SFVQ line can be used for controllable data augmentation.
demonstrate that each line
1 Introduction
Generative adversarial networks (GANs) (Goodfellow et al., 2014) are powerful generative models applicd to various appli- cations, e-g., data augmentation (Antoniou et al., 2017; Shorten & Khoshgoftaar, 2019), image editing (Härkönen et al., 2020; Yüksel et al., 2021; Shen & Zhou,, 2021; Voynov & Babenko, 2020: Tzelepis et al., 2021; Aoshima & Matsubara, 2023; Abdal et al., 2021; Wang et al., 2018b; Alaluf et al., 2022; Roich et al., 2022; Pehlivan et al., 2023; Liu et al., 2023; Jahanian et al.,
(a). VQ
(b). SFVQ
2019; Plumerault et al., 2020; Yang et al., 2021; Goetschalckx et al., 2019; Shen et al., 2020; Wu et al., 2021), and video gener- ation (Wang et al., 2018a). For image data, GANs map latent space to an output image space by learning a non-linear map- ping (Voynov & Babenko, 2020). After learning such mapping, GANs can create realistic high-resolution images by sampling from the latent space (Karras et al., 2019). However, this la- tent space is a black box, making it difficult to interpret the mapping between the latent space and generative factors such as gender and age (Shen et al., 2020). In addition, the interpretable directions change these factors are not known (Voynov & Babenko, 2020). Hence, having a comprehensive interpretation of the latent space is important research problem that, if solved, leads to more controllable generations.
Figure 1: Codebook vectors (blue points) of a b (a) vector quantization, and (b) space-filling vector quantization (curve in black) on pentagon distribution (gray points). Voronoi regions for VQ are shown in green.

---

Published in Transactions on Machine Learning Research (06/2025)
In the literature, both supervised and unsupervised methods exist to find interpretable directions in the latent space. Supervised methods (Jahanian et al., 2019; Plumerault et al., 2020; Yang et al., 2021; Goetschaleke lekx et al., 2019; Shen et al., 2020; Wu et al., 2021; Shen et al., 2022) require data collections together with the use of pre-trained classifiers or human labelers to label the collected data with respect to the uscr-pree aser-prodefined directions (Shen & Zhou, 2021). In addition, these methods only find the directions that the user defines (Voynov & Babenko, 2020). On the other hand, in unsupervised methods (Härkönen et al., 2020; Shen & Zhou, 2021; Voynov & Babenko, 2020; Yüksel al., 2021; Tzelepis al., 2021; Aoshima & Matsubara, 2023; Song et al., 2023b;a), the user has to choose the discover) before training, where a large value for K results in discovering repetitive directions (Yükkel et al., 2021). In all these unsupervised methods, there is no prior knowledge about the specific transformation each of these K discovered directions yields. Hence, the user should do an exhaustive search over all available K directions to determine which directions are practical and what they refer to. For instance, as GANSpace (Härkönen et al., 2020) applics principal component analysis (PCA) on the latent space, the number of directions (K) to be examined is large (equal to the latent space dimension). Additionally, as stated in Härkönen et al. (2020), not all PCA directions are necessarily useful for changing generative factor.
K (the number of interpretable directions to
In this paper, we use modification of vector quantization, called space-filling vector quantization (SFVQ) (Vali & Bäckström, 2023), to interpret the latent spaces of the pre-trained StyleGAN2 (Karras et al., 2020) and BigGAN (Brock et al., 2018) models using FFHQ, AFHQ, LSUN Cars, CIFAR10, and ImageNet datasets. Regarding the intrinsic arrangement of SFVQ codebook vectors (or codewords), index-wise adjacent code- words model the same locality of a distribution (see Fig. 1(b)). Hence, SFVQ can be used to capture the underlying structure of the GANs' latent spaces, given that subsequent codewords refer to similar contents. In contrast supervised approaches, our unsupervised method neither requires human labeling nor imposes any constraints on the learned latent space, it uses the original learned latent spaces from pre-trained models. Moreover, our method does not need any hyper-parameter tuning, e.g., choosing the number of directions (K) as in Shen & Zhou (2021); Voynov & Babenko (2020); Yüksel et al. (2021); Tzelepis et al. (2021); Aoshima & Matsubara (2023); Song et al. (2023b;a) or tuning the coefficients of the training loss terms as in Voynov & Babenko (2020); Yüksel et al. (2021); Tzelepis et al. (2021); Aoshima. & Matsubara (2023). In our proposed method, to explore the latent space structure and find its interpretable directions, the only required effort is that the user should visually observe the generated images from the learned SFVQ codebook vectors (Fig. 6(a), Fig. 8(a)) only once. By observing the generated images, the user would have prior knowledge of the potential edit type for a discovered direction in advance, contrary to other unsuper- vised methods. Therefore, we reduce the search effort to achieve the desired edit by only searching for the suitable layers in StyleGAN2 or BigGAN to modify. Our method implementation is publicly available at /ttpps//githhn http://ggttuuu...cc/eeeehhee
by-s - git.
In Vali & Bäckström (2023), SFVQ training is prone outlier codewords, i.e., there might be some codebook vectors that end up outside the data distribution, which is an issue. In this paper, we resolve this issue by improving the initialization (Sec. 3.2.1) and codebook exponsion (Sec. 3.2.2) procedures of SFVQ such that we do not encounter any outlier codewords throughout our experiments. We show that our trained SFVQ codebook (or curve) can caplure a universal interpretation of the AN'ss latent space such that the user can identify what type of generations to expect from each part of the latent space regarding age, gender, pose, accessories for FFHQ, color, breed, pose for AFHQ, and class of data for CIFAR10 (sec See. 5.1). Further- more, we explore SFVQ from a new viewpoint and discover that SFVQ lines (the lines connecting SFVQ's subsequent codewords) can refer to interpretable directions leading to meaningful image transformations (see Sec. 5.2 and Sec. 5.3). This SFVQ property was not explored in Vali & Bäckström (2023). Qualitative (Sec. 5.4) and Quantitative (Sec. 5.5) evaluations show that the discovered interpretable directions by our proposed method outperform the directions of GANSpace (Härkönen et al., 2020), Latent (Yüksel et al., 2021), and Sela (Shen& & Zhou, 2021) methods. In addition, our proposed method is capable of finding joint interpretable directions that can change multiple attributes simultaneously (see Sec. 5.7). By improving the SFVQ training, we observe that the learned SFVQ curve (or space-filling lines) are mainly located inside the latent space. Hence, we have large number of meaningful latent vectors located on the SFVQ curve that can be used for controllable data augmentation. We observe that by sampling latent vectors from the line connecting two subsequent codewords, we can generate images that visually share the attributes of those codewords (see Sec. 5.8).
2

---

Published in Transactions on Machine Learning Research (06/2025)
2
Related Work
Prior works can be categorized into three principal approaches that aim to make the latent space of generative models more interpretable.
1. Introducing structure into the latent space using data labels. The main rationale behind these approaches (Klys et al., 2018; Xue et al., 2019; An et al., 2021) is that they take advantage of labeled data (with respect to the features of interest) and train the generative model in a supervised manner to learn a structured latent space in which data with specific labels reside in isolated subspaces of the latent distribution. Hence, this structured latent space can be interpretable, allowing the user to have control over data generation and manipulation with respect to the labels. However, these supervised methods suffer from two main drawbacks. First, they require human labeling, whose cost can increase excessively as the dataset size increases (Voynov & Babenko, 2020). Second, they might prevent the latent space from learning some intrinsic structures that a human labeler is unaware of (Voynov & Babenko, 2020).
2. Disentangling the latent space dimensions. These methods (Chen et al., 2016; Higgins et al., 2017; Ramesh et al., 2018; Lee et al., 2020; Liu et al., 2020) train the generative model in an unsupervised way to obtain disentangled latent space. In disentangled latent space, changes in each latent dimension make variations only in one specific generative factor while keeping the other generative factors unchanged. In other words, these approaches aim to model various generative factors existing in the data to different latent dimensions and make these dimensions (generative factors) independent of each other. Therefore, these methods are interpretable in that they allow control over data generation with respect to the gener- ative factors. However, the downside of these techniques is their low efficiency in generating quality and diversity (Voynov& & Babenko, 2020).
3. Exploring interpretable directions in the latent space. The main goal of these techniques is to find the directions in the latent space which lead to intelligible data transformations such as changing the age, pose, hairstyle in face synthesis task (Härkönen et al., 2020; Voynov & Babenko, 2020; Shen et al., 2020; Jahanian et al., 2019; Yüksel et al., 2021; Shen & Zhou, 2021; Abdal et al., 2021; Wang et al.,
2018b; Plumerault et al., 2020; Yang et al., 2021; Goetschalckx et al., 2019; Alaluf et al., 2022; Roich et al., 2022; Pehlivan et al., 2023; Liu al., 2023; Tzelepis et al., 2021; Aoshima & Matsubara, 2023). Here, the interpretability of the latent space refers to the user's control over the generation process by manipulating latent vectors along these discovered interpretable directions. This category is the main focus of this paper, as we also use our proposed method to discover interpretable dircctions and compare these directions with those of other methods in the literature.
Some supervised methods (Jahanian et al., 2019; Plumerault et al., 2020; Yang et al., 2021; Goetschalckx et al., 2019; Shen et al., 2020; Wu et al., 2021: Shen et al., 2022) find interpretable directions guided by human supervision or pre-trained classifiers used to label the directions of the edited images, which are going to be used for training. For instance, FacerFNN (Shen et al., 2020) extracts a large set of latent vectors from the latent spaces of pre-trained PGGAN (Karras et al.) and StyleGAN (Karras et al., 2019). It used SVM to find the hyperplanes of the attributes, such that the normal vector of each hyperplane is considered the interpretable direction. To label the generated images along interpretable directions, InterFaceGAN uses pro-trained classificrs. The downside of these supervised methods is that they require sufficient data collection to discover convincing, interpretable directions. Some methods bypass these hassles by discovering interpretable directions in an unsupervised manner from the latent space of pre-trained models, without roquiring training of any modules. GANSpacc(Härkönen et al., 2020) applied principal component analysis (PCA) on the latent spaces of StyleGAN, StyleGAN2, and BigGAN and found that PCA directions can be used as interpretable directions. Similarly, in Shen & Zhou (2021); Song et al. (2023b), the eigenvectors of the affine transformation of the pre-trained model weights are considered interpretable directions. In a somehow different technique, methods of Voynov & Babenko (2020); Yüksel et al. (2021); Yang et al. (2021); Tzelepis et al. (2021); Aoshima & Matsubara (2023) train a transformation function f that shifts a latent vector in various directions and use a pro-trained generator & to generate images (or new latent vectors w) corresponding to the original (z) and shifted latent vector (f(z) = 2 + a d). Then, a reconstructor R (or attribute asscssor) is trained to estimate or rate the direction d proposed by the transformation function f given the pair of generated images (or latent vectors). When trained, the directions d' are considered
3

---

Published in Transactions on Machine Learning Research (06/2025)
interpretable directions. In contrast to methods of Voynov & Babenko (2020); Yüksel et al. (2021); Yang et al. (2021) which only find linear directions, methods of Tzelepis et al. (2021); Aoshima & Matsubara (2023) are supposed to find non-linear directions.
GAN inversion methods (Alaluf et al., 2022; Liu et al., 2023; Katsumata et al., 2024; Dere et al., 2024; Zhu et al., 2024) revert the generation process by mapping real images to the latent space of pre-trained GANs. They take a real image as input and learn to find a latent vector for it such that the pre-trained GAN generator can reconstruct
image close to the real image as possible. After computing the new latent space Wine of pre-trained GANs, these methods mainly discover interpretable directions from Wi using InterFaceGAN (Shen et al., 2020) and GANSpace (Härkönen et al., 2020) techniques. All the above- mentioned methods provide interpretable directions for image editing tasks in the latent space of GANs, such as BigGAN, PGGAN, and various versions of StyleGAN. However, in a completely different case, recent approaches have emerged for image editing in diffusion models (Park et al., 2023; Zhang et al., 2023; Dalva & Yanardag, 2024; Haas et al., 2024; Shi et al., 2024; Chen al., 2024; Joseph et al., 2024; Sajnani et al., 2025; Feng al., 2025). This paper does not focus on image editing using diffussin models; instead, it concentrates only on interpreting the latent space of the StyleGAN2 and BigGAN pre-trained models.
3 Methods
3.1 Space-filling vector quantization (SFVQ)
1
==2
==3
r=4
r=5
6
A space-filling curve is piece-wise continuous curve created by recursion, and if the recursion repeals infinitely, the curve fills a multi-dimensional space (Sagan, 2012). Fig. 2 shows the first six recursion steps of the Hilbert curve (a well-known space-filinng curve) that fills square space, The curve is color- coded, i.e., it starts in light and ends in dark colors. It is clearly shown that there is an inherent structure in the Hilbert curve and a good arrangement. in the position of its corner points (shown in blue). For instance, adjacent corner points refer to the same locality of the space, as they are shown with similar colors. Motivated by spaco-filligg curves, spaco-filling vector quantization (SFVQ) (Vali & Bäckström, 2023) designs vector quantization (VQ) as a mapping of data on a space- filling curve, whose corner points are the codebook vectors of a VQ process. SFVQ uses a dithering technique for training its codebook, i..., it maps the input vector onto the line connecting subsequent codewords, but not necessarily onto the codewords. For an input vector E X and codebook C = [cI,... CN R-V containing N codewords, SFVQ first generates dithered codebook matrix Cdd [ct,... N- N-ID by interpolation at random places on the line connecting two subscquent codewords of the codebook C (sce Fig. 3). Then, it quantizes (or maps) z to the closest element from the dithered codebook Cd as
Figure 2: First six recursion steps (r) of Hilbert space-filling curve. The curve is color-coded, i.e., it starts in light and ends in dark colors. Corner points are shown as blue points.
f = arg min J|2 ef ISiSN-1
i 8= c = (1 (1-A)e² + Acj+1,
(1)
where ey and 6j+1 represent two subsequent codewords from the base codebook C' which their interpolation of is the the closest dithered codeword to v, and À is the dithering (or interpolation) factor. To generate the dithered codebook during training (Fig. 3), SFVQ samples À values from the uniform distribution of (0, that ensures random interpolations between subsequent vectors of the base codebook C. When sampling different À values for different training batches, this type of randomized interpolation imposes sense of continuity between subsequent vectors of C. Because the codebook C' is trained such that the line connecting ils subsequent codewords should be a valid quantization point. The mean squared error (MSE) between the input vector x and its quantized form & is used as the training loss function
MSE 2) = || -213 || - (1 - A)e3 Ac
(2)
4

---

Published in Transactions on Machine Learning Research (06/2025)
Similar to space-filling curves, SFVQ is trained re- cursively. SFVQ first starts with N = 4 code- words bit) and after training these codewords for a while, it expands the codcbook by doubling the number of codewords at each recursion slep. The recursion continues until SFVQ reaches N = log2 (Brorget) codewords, where Brarget is the SFVQ target bitrate. Fig. 1 illustrates a bit (N = 64) VQ and SFVQ applied on 2D pentagon distribution. To clarify more, both VQ and SFVQ have & code- book containing N = 64 codewords. However, the codewords of SFVQ are in clear arrangement be- cause their index-wise adjacent codewords refer the same locality of the distribution, and also the line connecting subsequent codewords is valid for quantization. Whereas, these two properties do not hold for VQ (in general, not in this uniform pentagon 2D distribution).
À [0.2,0.8.0.5]
cf 1)c, + Ac
C2
C2
of = (1 0.2)c 0.2c₂
Ca
c2
C3
of = (1 0.8)c² + 0.8cg
C4
cf (1 0.5)cg 0.5c,
Base Codebook
Dithered Codebook
Figure 3: Example of generating dithered codebook Cd from the base codebook C for one typical training batch of space-filling vector quantization (SFVQ) in its first recursion slep, where SFVQ starts with N codewords.
3.2 Proposed method
(a) Random Initialization
(b) Proposed Initialization
3.2.1 SFVQ initialization
As mentioned, SFVQ training starts with N = codewords. The initialization of these four code- words significantly impacts the final learned SFVQ curve obtained at the end of training. In Vali & Bäckström (2023), these codewords were initialized randomly (from normal distribution (O0 1)), and as the SFVQ codebook was expanded to reach the target bitrate, there were some unfavorable jumps (lines outside the distribution or lines breaking the codebook arrangement) the learned curve (see Fig. 4(a)).
Figure 4: Two learned SFVQ curves with N 512 codewords on a 3D moon dataset using random and our proposed initialization methods. The curves are color-coded, i.e., they start in light and end in dark colors.
To address this issue, in this paper, we change the codebook initialization. Since pre-trained models
are available, we sample 103 random vectors from the normal distribution and generate their corresponding latent vectors in the layer where we inlend to train the SFVQ (e.g., intermediate W space in StyleGAN2). Then, we compute the Euclidean norm (f2) all latent vectors and sort them in ascending order. We split these sorted latent vectors into four groups and initialize the codebook vectors with the mean of these four groups. From geometrical viewpoint, our proposed initial SFVQ curve spans from one end of the Euclidean latent space to its other end and brings a desirable order to SFVQ codewords, which aligns with the intrinsic SFVQ codebook arrangement, this fact, Fig. 4 shows two learned SFVQ curves (with N = 512 codewords) using random and our proposed initialization methods on a 3D moon dataset. The SFVQ curves are color-coded, i.e., they start in light and end in dark colors. As shown, our proposed initialization results in a perfect codebook arrangement with only one jump (which is inevitable as the curve should pass to the other cluster of the data). Whereas, the random initialization causes several unfavorable jumps that break the codebook arrangement.
the curve starts from low norm to high norm latent vectors. To confirm
3.2.2 SFVQ codebook expansion
When training SFVQ, codebook expansion occurs at the beginning each recursion step by doubling the codebook size. In Vali & Bäckström (2023), the new codebook vectors are defined in the center of the line connecting two adjacent codewords (which already exist on the curve), ie., Cnew = (c, + C++1) /2, where c, is the i-th codeword. Grew can be useless if it is located outside the latent space, in the of undesirable
5

---

Published in Transactions on Machine Learning Research (06/2025)
jumps (as shown in Fig. 4(a)), and it takes long time (or many training batches) to be pushed inside. As discussed in Sec. 3.2.1, Vali & Bäckström (2023) uses random initialization that incurs unfavorable jumps, and hence, it can result in creating new codewords (Crew) out of the latent distribution in the codebook expansion step. To address this issue, in this paper, we define the new codeword by shifting the existing codebook vectors slightly such that Grew = 0.99 e + 0.01 C++1- Now, the new codewords most. likely reside inside the latent space, and thus, after being selected actively during training, they will be optimized to their optimum locations. In contrast to Vali & Bäckström (2023), our proposed codebook expansion and imitialization for SFVQ lead to no outlier codewords throughout our experiments.
PCA2
3.2.3 Why are SFVQ lines likely to refer to interpretable directions?
After training SFVQ with only N = codewords on W space of Style- GAN2 pro-trained FFHQ dataset, the obtained images from learned codewords are shown in Fig. 8(b). From the images, it can be inferred that SFVQ lines refer to two directions of gender and rotation (see Fig. 8(c)). Fig. 8(b) and Fig, 8(c) remind us of the PCA-based method of GANSpace (Härkönen et al., 2020) that finds PCA directions as interpretable direc- tions. Similar to the first two PCA directions of GANSpace, which refer to changes in gender and rotation, the SFVQ lines are also located along the directions in which the training data has the most variance, i.c., gen- der and rotation. The reason is that SFVQ trains the codebook such that the points on the line connecting subsequent codewords should be valid quantization points. Hence, to minimize the MSE loss (Eq. (2)), SFVQ locates the codewords to some corners of the distribution so that their connecting lines lie along the directions that the distribution has the highest variances (sce Fig. 5).
PCA1 1
SFVQ
SFVOI
SFVQ
SFVQ
Figure 5: Directions found by SFVQ tochnique (in red) and PCA-based method of GANSpace (in orange) on an example distribution (shown in gray). The SFVQ curve is shown in black with its code- words shown in blue.
Fig. 5 shows directions found by two methods of SFVQ and GANSpace an example distribution (shown in gray). According to the figure, the number of directions that GANSpace can find is restricted to the data dimension (in this case D = 2). In contrast, SFVQ can potentially find N 1 distinct directions where N is the number of codewords. Furthermore, the PCA directions of GANSpace are constrained to be orthogonal, meaning that they are perpendicular to each other. However, in the pre-trained W space of StyleGAN2, the interpretable directions are not necessarily orthogonal to cach other, and that is why only the first 100 (out of 512) GANSpace's PCA orthogonal directions lead to noticcable changes (Härkönen et al., 2020). In contrast, in the SFVQ curve, the directions do not have an orthogonality constraint, and thus, each direction (or each SFVQ line) can potentially work for meaningful and obvious change (see Fig. 5). Therefore, with regard to interpretable directions, SFVQ is somewhat similar to the PCA technique, but it has more degrees of freedom. Because SFVQ directions do not have the orthogonality constraint, SFVQ can potentially find N T-11 1 distinct meaningful directions. These observations and discussions motivate us to use the SFVQ curve to discover interpretable directions, which we study in Sec. 5.2.
3.2.4 How to find SFVQ interpretable directions?
(a)
(b)
(c)
After training SFVQ on the latent space and ob- taining the learned codebook, we generate the im- ages corresponding to SFVQ codewords (Fig. 6(a) and similarly Fig. 7(a), Fig. 8(a)). This visualiza- tion reveals the underlying structure of the latent space in terms of generative factors, which we refer to as the universal interpretation of the latent space (Sec. 5.1). Similar to space-filing curves (Fig. 2), adjacent codewords of SFVQ refer to similar con- tents in the latent space. Hence, the learned SFVQ codebook (with its intrinsic arrangement) can cap- ture the underlying structure of the latent space.
Cie d
Ci+1
d= Ci+1 - Ci
1c - cillz
W o.
Figure 6: (a) Observation of generated images from learned SFVQ codebook (similar to Fig. 8(a)) to find a sensible direction between & and G41- (b) Compu-
tation of the direction d. (c) Applying the direction on a random latent vector w by shift magnitude of a.
6

---

Published in Transactions on Machine Learning Research (06/2025)
(b)
Coldbnak Vector Indox 48
Cat & Dog
60
80
16 24 32 40 Cldcbook Vector Index
Figure 7: (a) Generated images from the codebook of 6 SFVQ (N =64) trained on W space of StyleGAN2 pre-trained on the CIFARIO dataset. (b) Heatmap of Euclidean distances between all codebook vectors.
In this paper, we take step forward in extracting more information from the SFVQ codebook, which results in finding interpretable directions. Fig. 6 shows how we find the interpretable directions using SFVQ. Due to the intrinsic arrangement of SFVQ codebook vectors, subsequent images refer to similar content, i.e, they share many similar features while differing in minimal attributes. For example, in Fig. 6(a), the images for two subsequent codewords of G and 4++1 share most of the attributes except the rotation. Hence, we can infer that the direction (d) connecting these two codewords (Fig. 6(b)) refers to the rotation direction. Then, by shifting any latent vector along this direction (Fig, 6(c)), we can observe the change in rotation attribute for that latent vector.
By a quick observation of the subsequently generated images from the SFVQ codebook (Fig. 6(a)), the user can readily spot the interpretable direction. Hence, the user has prior knowledge of the direction, and the only required action is to find the proper layers of the GAN to edit along this direction (Härkönen et al., 2020). In this way, the user achieves the desired edit with less search effort compared to other unsupervised methods (Härkönen et al., 2020; Shen & Zhou, 2021; Voynov & Babenko, 2020; Yüksel et al., 2021; Tzelepis et al., 2021; Aoshima & Matsubara, 2023), in which apart from the layer-wise search, they should do an exhanstive search over all K discovered directions to inspect whether they are practical and what directions they refer to.
4 Experiments
To evaluate how SFVQ can be used to interpret the latent spaces in GANs, similarly to GANSpace (Härkönen et al., 2020), we chose the intermediate latent space (W) of StyleGAN2 (Karras al., 2020) and the first lincar layer of BigGAN512-dcep (Brock et al., 2018), and then trained the SFVQ on these layers. These layers are more favorable for interpretation because they render more disentangled representations, are not constrained to any specific distribution, and suitably model the structure of real data (Karras et al., 2019: Härkönen et al., 2020; Shen et al., 2020). For StyleGAN2, we employ the pre-trained models on FFHQ (Karras et al., 2019), AFHQ (Choi et al., 2020), LSUN Cars (Yu et al., 2015), CIFAR10 (Krizhevsky et al., 2009) datasets, and also the pre-trained BigGAN on ImageNet datset (Deng et al., 2009).
We trained the SFVQ with various bitrates ranging from 2 to 12 bit (N to N 4096 codebook vectors). Since the training of SFVQ is not sensitive to dyper-parameted tuning, we adopt general setup that works for all pre-trained models and datasets. In this setup, trained SFVQ with batch size of 64 over 100 k number of training batches (for each recursion step) using the Adam optimizer with the initial learning rate of le-3 We used a learning rate scheduler such that during each recursion step, we halve the learning rate after 60k and 80k training batches. To show that SFVQ and its interpretation ability are not sensitive to the training syper-parameters, we trained the SFVQ on the intermediate latent space (W) of StyleGAN2 pre-trained on CIFAR10 dataset over different SFVQ bitrates, batch sizes, and learning rates. The results are provided in Appendix A.S.
7

---

Published in Transactions on Machine Learning Research (06/2025)
(b)
Famale to Male
1. Right Rotation
90.7
I1I Left LettRiiooon Roation
159.6
Figure 8: (a) Generated images from the codebook of a bit SFVQ (N = 32) trained on W space of StyleGAN2 pre-trained on the FFHQ dataset. (b) Similar generated images for a 2 bit SFVQ (N = 4), and (c) their semantic directions. Numbers (in blue) show the angle between directions.
5 Results and discussions
5.1 StyleGAN2: universal interpretation
To explore a universal interpretation of the latent space, we apply the SFVQ on the latent space and plot the generated images from the obtained SFVQ codebook vectors. According to the inherent arrangement of the SFVQ codebook (see Sec. 3.1), adjacent codewords refer to similar contents of the latent space. Therefore, we expect the SFVQ learned codebook to capture a universal morphology of the latent space. As the first experiment, we apply the SFVQ on the intermediate latent space (W) of StyleGAN2 (Karras et al., 2020) pre-trained on the CIFAR10 dataset. During training, the number of extracted latent vectors is unbiased for all CIFAR10 classes. In Fig. 7(a), we plot the generated images corresponding to 6 bit SFVQ codebook (N = 64), i.e., each image corresponds to a codebook vector. At first glance, we observe a clear arrangement with respect to the image class, where images from the same category are organized into groups. Also, apart from the horse class, all animal types and industrial vehicles are located next to each other. Furthermore, there are some visible similarities for subsequent codewords within a class, such as similar objects' rotation, scale, color, and background.
We also see those clear interpretations consistently when training SFVQ with different bitrates (sce Ap- pendix A.S). Furthermore, when increasing the SFVQ bitrate by one (doubling the codebook size), the number of specified codewords to each CIFAR10 class will be approximately doubled, and as result, the proportion of different classes from the codebook remains unchanged. For instance, the horse class is always the dominant class of data in the StyleGAN2 latent space by occupying about 25% of the codewords (see Appendix A.8). The reason is that the latent vectors of the horse class have the highest diversity compared to other classes (see Appendix A.1). As a result, when training SFVQ with N = 4 initial codewords, and then expanding the codebook from N = 4 to larger eodebook, big portion of codewords tend to model the latent vectors of the horse class to minimize the MSE loss (Eq. (2)). However, when initializing the SFVQ with N = {8, 16) codewords, the horse class would not take up to 25% of the learned SFVQ codebook vectors (see Appendix A.1).
To inspect the learned SFVQ from another viewpoint, we plotted the heatmap of Euclidean distances between all SFVQ codebook vectors in Fig. 7(b). Again, we observe a clear separation between different classes, as each dark box shows data class. It is essential to note that the SFVQ captures this class separation property due to its inherent orderliness and in a completely unsupervised manner. Additionally, we observe larger dark box shared between the cat and dog classes, they are the most similar classes and reside close to each other in the latent space.
In the second experiment, we applied a bit SFVQ -N=32) 32) on the W space of the pre-trained StyleGAN2 on the FFHQ dataset. Images corresponding to the SFVQ codebook are represented in Fig. 8(a). We observe similarities among neighboring codebook vectors, such as baby-aged faces for indices 6-7, hat accessory for indices 13-16, eyeglasses for indices 18-19, rotation from right to left from index 17 to 20, and rotation from left to right from index 27 to 31. Based our investigations, the StyleGAN2's W space for FFHQ, AFHQ, and LSUN Cars are much denser and entangled than CIFAR10 because they are trained on not very diverse data like CIFAR10. That is why the learned SFVQ curve shown in Fig. 8(a) does not show perfect distinctive universal interpretation. We provided a similar figure for a 6 bit SFVQ for the AFHQ dataset in Appendix A.2.
8

---

Published in Transactions on Machine Learning Research (06/2025)
As the third experiment, we examine 2 bit SFVQ (N = 4) applied to the W space of StyleGAN2, pre-trained on the FFHQ dataset, and display the generated images in Fig. 8(b). We observe a clear separation between females and males, with only two unique identities, each representing the average face for females and males. From this SFVQ curve, we can infer some more interesting properties. We hypothesize that each SFVQ line corresponds to an interpretable direction shown in Fig. 8(c). Direction I (the direction from codebook vectors 1 to 2) is for changing rotation to the right, direction II refers to the gender change, and direc- tion III is for changing rotation to the left. We also compute the angles between these directions in degrees, which somehow confirms our hypothesis. Direction II is almost orthogonal to the two other directions, and directions I and III are approximately inverse.
Direction
Result
(b)
StyleGAN2
Agg
Coocle
Spale
Hav Har
5.2 StyleGAN2: interpretable directions
As discussed in Sec. 3.2.3, SFVQ lines that connect the subsequent codewords can refer to meaningful interpretable directions. Honce, we apply SFVQ curves (from to 12 bit) to the W space of StyleGAN2, pre-trained on the FFHQ, AFHQ, and LSUN Cars datasets, and observe the generated images corresponding to the SFVQ curves. By observation, we spot some uscful interpretable directions, shown in Fig. 9. Columns (a) and (b) represent the discovered direction from two SFVQ subsequent codebook vectors, column (c) is the test vector in the latent space to which we apply the direction, and column (d) is the final result after applying the direction. Similar to the GANSpace naming convention, the term Wi-jj means we only manipulate the style blocks within the range [i-j]- Note that we take the directions only from SFVQ's subsequent codebook vectors, but not from two necessarily similar, though far apart, codebook vectors. Otherwise, one can accidentally find directions by taking two codebook vectors from an ordinary VQ that might lead to a meaningful direction. To show the practicality of the directions better, we applied them only on one identical test image (except for the Beard and Bald directions, which are specified to males).
Mikrog
Wio WL 1105-105 WL- 192 223 WD-M7 thitee T00- WHT-NY
One significant advantage of our proposed method over other approaches that it maintains the identity of the test image (column (c)) to a great extent when applying the interpretable directions. Another advantage is that we could find some new and unique directions that were not found in previous methods, such as Hat, Beard for FFHQ, Age, Bicolor for AFHQ, and Classic for LSUN Cars.
Zocule Rucation Colir
These unique directions are not limited only to these, as users can find other di- rections by their own observations. More importantly, our approach detects an inclusive set of directions, whereas other methods in the literature can only find a portion of them. It is important to note that the directions for the AFHQ dataset
are class-agnostie (see Appendix A.3), ie., the direction for one animal works for other animal species because in Fig. 9 we find the directions from Wolf and Cat classes, but we apply them to Dog class. However, some directions do not nec- essarily work for all animal species in the AFHQ because the transformations are restricted by the dataset bias of individual animal classes (Jahanian et al., 2019)
BigGAN
(see Appendix A.3). Another interesting observation is how the Hat direction (discovered for males) works logically but differently for females.
AARORS Mprk Ley Dove
5.3 BigGAN: interpretable directions
BigGAN (Brock et al., 2018) samples a random vector 2 from a normal prior distribution p(z) and maps to an image. Since BigGAN's intermediate layers also take the random vector z as input (i.c., skip-s connections), the vector 2 has the most significant effect the generated output image. Hence, we should
Figure 9: SFVQ inter- pretable directions.
9

---

Published in Transactions on Machine Learning Research (06/2025)
find the semantic directions in p(2) space. However, p(2) is an isotropic distribution, it is difficult to find useful directions from it (Härkönen et al., 2020). Therefore, similar to GANSpace, we first train the SFVQ on the first linear layer (C) of BigGAN to search for interpretable directions within this space, and afterward, we transfer these directions back to p(z) space. To this end, we sample 10 random vectors from p(z) and generate their corresponding vectors codebook vectors such that each sample will be mapped to its closest codebook vector using Euclidean distance. Therefore, for each codebook vector in &, we have its corresponding samples in p(z). Finally, for each codebook vector in L, compute its corresponding codebook vector in p(2) by taking the mean of the vectors in p(z) which get mapped to this SFVQ codebook vector. We obtain the corresponding SFVQ curve in p(z) by doing this operation for all codebook vectors. Now, we use this computed SFVQ codebook (in p(=)) to interpret the latent space of BigGAN. Note that to compute the SFVQ curve for BigGAN, we select a class label and keep it fixed.
space. We map these vectors (in L) to the learned SFVQ
We computed the SFVQ curve over different bitrates (from to bit) in the p(2) space of BigGAN for golden retriever class and discovered some interpretable directions, which shown in Fig. 9. Columns (a) and (b) represent the discovered direction from two SFVQ subsequent codebook vectors, column (c) is the test vector in the p(2) to which we apply the direction, and column (d) is the final result after applying the direction. Similar to the GANSpace naming convention, the term Zi-Zj means we only manipulate the ship-z connections within the range [i-j]. Apart from basic geometrical directions (Rotation and Zoom In), we discovered some more specific directions such as Lay Down and Open Mouth as found in Yüksel et al. (2021), and Add Grass as found in Härkönen et al. (2020). Note that the discovered directions by SFVQ for golden retriever class are class-agnostic, i.e. they also work for other classes (see Appendix A.4).
5.4 Qualitative comparison
We compared our interpretable directions with GANSpace (Härkönen et al., 2020), LatentCLR (Yüksel et al., 2021), and ScFa (Shen & Zhou, 2021) qualitatively and quantitatively. The reason for choosing these methods is that. their interpretable directions for StyleGAN2- were readily available in their GitHub repositories. Hence, skipped other methods that were not trained on StyleGAN2-FFHO or did not share their directions. We focus SlyleGAN2-PFHQ for comparisons, networks of Zhang et al. (2017); Karkkainen & Joo (2021); Jiang et al. 22021); Doosti et al. (2020); Deng et al. (2019) for face attribute rating in our quantitative comparisons. For SeFa, there were no annotations for the discovered directions of StyleGAN2-FFHO Hence, we used their interactive tool to examine their first K 25 semantics and identify their interpretable directions. In SeFa interactive tool, there were only three
planned to use the pre-trained
Rank 1
Rank 2
Rank 3
Rank 4
Rotation
Smile
Hair Color
Gender
Age
Bald
Race
100
16
16
32
75
45
67
Count
50
59
80
25
31
72
56
25
72
40
45
19
17
20
24
0
SFVQ (Ours)
GANSpace
SeFa
LatenCLRR
SFVQ (Ous)
GANSpace
SeFa
LatenCLR
SFVQ (Ours)
GANSpace
ScFa
LatenCLR
SFVQ (Ows)
GANSpace-
SeFa
SFVQ (Ours)
SeFa
LatenCLR
SFVQ (Ouns)
SeFa
LatentLLR
SFVQ (Ours)
SeFa
Figure 10: Subjective test results by asking 20 human subjects to rate the interpretable directions of our proposed method, GANSpace, SeFa, and LatentCLR from best (Rank 1) to worst (Rank 4). These seven directions are assessed using 100 random latent vectors, with latent vectors assigned to each human subject.
10

---

Published in Transactions on Machine Learning Research (06/2025)
possible options for the layer-wise edits (WO-W1, 52-W5, W6-W133, but to have a fair comparison, we further searched precisely and found the best layer-wise edits for each direction. We provided the information of Sela interpretable directions in Appendix A.6.
Suicee
SPVg EatrnCt GANtrar
Fig. 11 shows the qualitative comparison. We provided a similar compari- son over 50 different random vectors in the Supplementary Material (shown as SM in the rest of the paper). To have a fair comparison, use the same amount of shift (σ) toward each direction because, mentioned in Tzelepis et al. (2021), it is the advantage of a direction if it reaches the desired change in the attribute within a shorter path. The image in the red square is the initial test image to which we apply the changes. For the Smile direction, our method effectively opens and closes the smile in both positive and negative paths while maintaining the identity and age attributes with minimal changes. Whereas GANSpace is highly entangled with the age al- tribute and SeFa changes the identity. In Hair Color direction, our method keeps the identity better than the others. However, GANSpace and ScFa alter the face highlights, LatentCLR is highly entangled with gender, and SeFa is highly entangled with age. For Age direction, our method covers a wider range of ages than LatentCLR, while LatentCLR and SeFa are highly entangled with gender, and SeFa alters the identity too much. For Gender direction, GANSpace and SeFa are entangled with age, and our method remains in the valid range of generations better than GANSpacc. In Bald direction, our method keeps the identity better than Sela, while SeFa adds beard to the face, and our method renders a better baldness than Latent- CLR. To see a more comprehensive qualitative comparison, we encourage the readers to make subjective comparisons with different random vectors using our GitHub repository or to inspect subjective comparisons over 50 random vectors in S..
SPVO Leartn CANNON
SyXqq Eatentta GANPAe Sata
We conducted subjective test to compare the interpretable directions of various methods over 100 different random vectors. For each random vector and each direction, we generated the edited images with the steps of (-3o, -2a,- -l0, 0o, 10, 20, } for all methods, where o = 2.67. We delivered the generated images of different. random vectors to each of 20 human subjects, and asked them to rate the interpretable directions by answering this question: "Sort the methods that apply the desired change on the test image convincingly, and simaltaneously keep the other attributes of the test image (especially the identäty) fired'. In the case of M different methods, the subject would rate them by assigning number from (1..... 1)) where the best is ranked 1 and the worst is ranked M. Fig. 10 shows the results of the subjective test. Based on the results, our method clearly outperforms the other methods for Smále, Hair Color, Age, Bald, and Race directions. For Rotation and Gender directions, our method performs comparably to
GANSpace and SeFa, respectively.
5.5 Quantitative comparison
For quantitative comparison, we adopted the evaluation criteria and pre- trained networks used in Tzelepis et al. (2021) and Aoshima & Matsubara (2023)to rate an image's attributes. We use Zhang et al. (2017) to spot the face bounding box, FairPace (Karkkainen & Joo, 2021) to rate the age, race, and gender attributes, CelebA-HQ (Jiang et al., 2021) to measure the smile attribute, Hopenet (Doosti et al., 2020) find the face direction (yaw, pitch, roll attributes), and ArcFace (Deng et al., 2019) to evaluate how much the face identity is preserved after shifting along direction.
SPXQ
Figure 11: Qualitative Com- parison.
11

---

Published in Transactions on Machine Learning Research (06/2025)
We sample 102 vectors from N(0, 1) and generate their corresponding latent. vectors in the W space of StyleGAN2. Following Tzelepis et al. (2021), to assess a discovered direction for cach latent vector, we create a sequence of images by shifting the la- tent vector for 20 steps in both positive and neg- ative paths along that direction. Therefore, each sequence contains 41 images, with the original in- tact image positioned in the middle. Then, for each image within this sequence, we use the above- mentioned pre-trained networks to measure its at- tributes. Next, we calculate the correlation between the step indices (from to 41) and cach attributc's scores. Thus, for each direction, we obtain a vector of seven correlation values (one per each attribute) which is then Ll-normalized, similar to Tzelepis et al. (2021). Table 1 shows the results averaged over 10s latent, vectors for our method, GANSpace, LatentCLR and SeFa. Values are shown in red the direction is correlated the most with a wrong attribute.
Table 1: Quantitative comparison of interpretable di- rections. Values in each row show the L1-normalized correlation of each direction to the attributes. Best values are shown in Bold, and values in red mean the
direction is correlated the most with a wrong attribute.
Direction
Method
Gender
Age
Smile
Race
Yaw
Pitch
Roll
GANSpace
0.63
0.12
0.017
0.13
0.0093
0.05
0.0074
Geuder
SeFa
0.74
0.11
0.06
0.06
0.018
0.0036
0.01
SFVQ (Qurs)
0.87
0.0027
0.037
0.039
0.011
0.031
0.0052
LateatCLR
0.31
0.38
0.031
0.21
0.014
0,00119
0.0067
Amp
Sela
0.48
0:25
0.081
0.14
0.0074
0.029
0.013
SFVQ (Ouns)
0.11
0.37
0.14
0,018
0.09
0.24
0.067
GANSpaice
0.047
0.53
0.0052
0.36
0.0005
0.057
0.000S
Sucile
LatenrCLR
0.15
0.15
0.17
0.1
0.052
0.32
0.066
SeFa
0.26
0.12
0.46
0.023
0.0011
0.12
0.0027
SPVQ (Ours)
0.31
0 078
0.4
0.077
0.022
0.052
0.061
SeFa
0.066
0.17
0.31
0.37
0.0057
0.027
0.025
Race
SFVQ (Oun))
0.037
0.07
0.33
0.52
0.0015
0.031
0.0011
GANSpace
0.11
0.037
0.0023
0.022
0.76
0.063
0.0032
LateatCLR
0.12
0.051
0.11
0.0027
0.67
0.032
0.01
Rotation
Sela
0.3
0 0.024
9.01
0.0049
0.51
0.15
0.0033
SFVQ (Ouns)
0.084
0.013
0.16
0.021
0.58
0.07
0.072
LL
0.25
0.083
0.17
0.16
0.032
0:23
0.073
Beld
SeFa
0.21
0.32
0.053
0.31
0.021
0,013
0.013
SFVQ (Ours)
0.47
0.14
0.12
0.019
0.059
0.16
0.027
GANSpacr
0.006
0.084
0.47
0.4
0:012
0.014
0.0083
Table 1 shows that for Gender dircction, our method works better than the others with higher correla- tion to gender attribute, whereas GANSpace and ScFa are correlated with age and race attributes. For the Age direction, our method has almost the same correlation with the age altribute as LatentCRR, but is higher than SeFa. However, Cat and Sel'a remarkably alter the gender and race attributes, which is undesirable. In contrast, our method modifies the smile and pitch attributes, which are visually more acceptable (sce Fig. 11). For Smile direction, SeFa renders a higher correlation to the smile altribule than others. However, the smile direction of GANSpace and LaR methods are improperly correlated the most with age and pitch attributes, respectively. In Rotation direction, similar to other methods, our method is mainly correlated with the yaw attribute but with less correlation than GANSpace and LatentCLR. At the same time, it changes other face rotations' attributes (i.e., pitch and roll) more than they do. Our Rotation direction causes fewer changes in gender attributes compared to others, specifically SeFa. Note that in Table 1, if a method is not listed for a direction, it means that direction does not exist for the method.
LateatCLR
0.33
0.099
0.27
0,22
0.0003
0.03
0.046
Halrr
ScFa
0.027
0.4
0.43
0.08
0.02
0.013
0.027
SFVQ (Ours)
0.11
0.015
0.17
0.38
0.0022
0.012
0.019
We also compare our method with others on how they preserve identity when shifting latent vectors for various shift values in different directions. Table 2 provides the identity scores (averaged over 10x latent vectors) that range from 0 to 1, such that a higher value means a higher similarity to the original test image in terms of identity. We observe that our method maintains the identity better than others by a significant margin for Smile, Race, and Hair Color directions. For the Gender direction, our method outperforms GANSpace and is comparable to SeFa. In Age direction, our method performs comparably to LatentCLR and SeFa. Based on qualitative comparisons (Fig. 11), since Latent applies minimal changes to the face compared to others, it gives higher identity scores for Rotation and Bald directions. Ignoring the LatentCLR scores, our method performs comparably to GANSpace and SeFa in Rotation direction, and better than SeFa for Bald direction. Furthermore, we computed the commutatinity error (defined in Aoshima & Matsubara (2023)) for our method, GANSpace, LatentCLR, and SeFa over all directions. As expected, all four methods are commulative because they all apply linear transformations on the latent vectors. Ultimately, we believe that the most effective way to compare the interpretable directions between different methods remains subjective comparisons. Therefore, to better assess the efficiency of our discovered directions compared to other methods, encourage readers to make subjective comparisons with different random vectors using our Hit demo directory or to inspect subjective comparisons over 50 random vectors in S.M
12

---

Published in Transactions on Machine Learning Research (06/2025)
5.6 Ablation study on SFVQ bitrate
We conducted an ablation study on the effect of different SFVQ bitrates (ranging from 2 to 12) on the interpretations of pre- trained StyleGAN2 models on the FFHQ, AFHQ, and LSUN Cars datasets. Regarding universal interpretation, for all bi- trates, we observe the inherent structure in SFVQ's subse- quent codebook vectors, which share similar generative fac- tors, such as rotation, background, and accessories, for FFHQ. When increasing the bitrate, ages (e.g., more identitios for FFHQ) because we model the latent space with more clusters (or codebook vectors). We provide images corresponding to SFVQ codebooks from 2 to bit in Appendix A.7.
Table Identity preservation scores of interpretable directions for our proposod method, GANSpace, LatentCLi CLR, and SeFa. Values in row show the identity scores for different shifts (a). Best values are shown in Bold.
Direction
Method
1.47
5:8c
9-12z
18 16.
17:2
more diversity in the im-
GANSpaoe
0.58
0.22
0.078
Gonder
Sita
0.94
0.78
0.68
0.51
0.4
SFVQ (Ours)
0.85
0.76
0.61
0.47
0.35
LatensCiRR
0.95
0.73
0.50
0.29
Age
S-FF
0.95
0.78
0.50
0.42
0.29
SFVQ (Ours)
0.94
0.76
0.56
0.39
0.25
GANSpuce
0.94
0.76
0.57
0.41
0.20
Regarding the interpretable directions, a higher SFVQ bitrate allows the curve to get more turned and twisted in the latent space, increasing the chance of spotting more detailed or in- tricate directions. Based on our investigations, the directions that alter images more structurally can be found from lower bitrates and vice versa. For example, for StyleGAN2-FFHO, we found rotation, gender and age directions from 2, 5, and bit SFVQ, respectively. On the other hand, we detected the directions that cause a partial change on the face, such as smile, hair color, makeup, race, and bald from 12 bit SFVQ.
Smile
Seli
LatestCLR
0.35
0.93
0.78
0.8
0.62
0.47
0.47
0.35
0,312
SFVQ (Ours)
0.96
0.8G
0.72
0.59
0.48
SiFa
0.333
0.7
0.22
SFVQ (Ouns)
0.88
0.88
0.74
0.0
0.48
GANSpase
0.33
0.77
0.02
0.51
0.412
Rotation
Selaa
LatmoCLR
0.98
0.92
0.77
0.85
0.79
0.5
0.71
0.4
SPVQ (Ours)
0.93
0.76
0.61
0.49
0.4
LatensCLR
0.96
0.86
0.73
0.61
0.51
Bald
Selua
0.95
0.8
0.64
0.49
0.36
SFVQ (Ouns)
0.96
0.84
0.55
0.41
GANS
0.38
0.38
0.75
0.02
0.51
Holor
LatessCLR
0.955
0.81
0.63
0.47
0.30
SilFa
0.56
SFVQ (Ouns)
0.89
0.97
0.94
0.89
0.85
5.7 Joint interpretable directions
By observing images of the learned SFVQ curve (Fig. 8(a)) to find interpretable directions, we can also discover joint in- terpretable directions from subsequent codcbook vectors that differ in multiple attributes. By joinl, we mean to change, for
Direction
Test Image
aei
example, rotation and gender attributes simultaneously. Joint directions are the directions in which multiple attributes are entangled. Supervised methods cannot find joint directions because they use pre-trained networks or labeled data with respect to only one attribute. Furthermore, finding joint direc- tions will be laborious for the unsupervised methods of Härkö nen et al. (2020); Shen & Zhou (2021); Voynov & Babenko (2020); Yüksel et al. (2021); Tzelepis et al. (2021); Aoshima & Matsubara (2023) because 1) their training strategy is not designed for this task, 2) they have to blindly search over all detected directions and hope to find the direction to change their desirable joint attributes. However, in our method, the prior knowledge of potential directions obtained by observing the SFVQ curve helps to quickly identify the desirable joint directions. Fig. 12 shows some joint directions found by our proposed method. Note that the joint directions are not limited to these, users discover their desired directions by their own inspections.
Rotation Gender Wo-W2 W4-W7| 2.4
Smile
Hair Color W4-W4 Ws-W8 a 2.6
Eyeglass + Anti-Bald| W2-W2 & W3-W6
2.4
Figure 12: Some examples of SFVQ joint interpretable directions.
5.8 Controllable data augmentation
According to the training objective SFVQ, to map input vectors onto the line connecting subsequent codebook vectors, SFVQ has the property that its lines are mainly located within the distribution's space. This property is desirable for controllable data augmentation because we have many meaningful points (located on the SFVQ curve) available to generate valid images. By looking at images corresponding to
13

---

Published in Transactions on Machine Learning Research (06/2025)
SFVQ SFVQ VQ
Figure 13: Generated images from 20 equally-spaced points on the line connecting two neighboring codebook vectors of VQ and two subsequent codebook vectors of SFVQ trained on the W space of StyleGAN2 pre- trained on FFHQ dataset.
the SFVQ curve Fig. 8(a), we have an idea of the possible generations from each part of the curve. For instance, to generate baby-aged faces, we select 20 equally-spaced points on the line connecting codebook vectors of indices 6 to 7 in Fig. 8(a), and we plot the generations corresponding to these 20 points in the middle row of Fig. 13. Similarly, we take 20 equally-spaced points on the line connecting two subsequent codebook vectors of indices 15 and 16 in Fig. 8(a) and generate their corresponding images in the bottom row of Fig. 13. We observe that all 20 generations contain the hal accessory for a male person.
We also take the line connecting two neighboring codebook vectors (under Euclidean distance) of a bit VQ and plot similar generations in the top row of Fig. 13. To obtain a more diverse representation of generations, for all generations in Fig. 13, we added normal noise (O 0.3)) to the selected points. As expected, all generations of SFVQ consistently follow the properties of their corner points, such that they are all faces of babies or males wearing hats. However, the generations for two neighboring codebook vectors of VQ do not follow any specific rule as we observe changes in gender, age, and race among them. Thus, here, by controllable, we mean that the users have control over what type of images with specific characteristics they intend to generate.
6 Conclusions
Generative adversarial networks (GANs) are well-known image synthesis models widely used to generate high-quality images. However, there is still insufficient control over generations in GANs bocause their latent spaces act as black box, making them hard to interpret. In this paper, we use the unsupervised space-filling vector quantizer (SFVQ) technique to obtain universal interpretation of the latent spaces of GANs and to find their interpretable directions. Our experiments demonstrate that the SFVQ can capture the underlying morphological structure of the latent space and discover more effective and consistent interpretable directions compared to GANSpace, Latent CLR, and SeFa methods. SFVQ provides the user with proper control over generating and manipulating images, and reduces the effort required to find the desired direction of a change. SFVQ is a generic tool for modcling distributions that is neither restricted any specific neural network architecture nor any data type (e.g., image, video, speech, etc.).
Acknowledgments
We gratefully acknowledge the participants for their involvement in the subjective evaluation tests. We also acknowledge the computational resources provided by the Aalto Science-IT project.
References
Rameen Abdal, Peihao Zhu, Niloy J Mitra, and Peter Wonka. Styleflow: Attribate-conddttoonee exploration of stylegan-gennealed images using conditional continuous normalizing llows. ACM Transactions on Graphics (ToG), 101311121,, 2021.
Yuval Alahuf, Omer Tov, Ron Mokady, Rinon Gal, and Amit Bermano. Hyperstyle: Stylegan inversion with hypernetworks for real image editing. In Proceedings of CVPR, pp. 18511-18522 2022.
14

---

Published in Transactions on Machine Learning Research (06/2025)
SeungHwan An, Hosik Choi, and Jong-June Jeon. EXoN: Explainable encoder network. orXiv preprint arXiv:2105. 2021.
Antreas Antoniou, Amos Storkey, and Harrison Edwards. Data augmentation generative adversarial net- works. arXiv preprint arXiv: 171.04444 2017.
Takehiro Aoshima and Takashi Matsubara. Deep curvilinear editing: Commutative and nonlinear image manipulation for pretrained deep generative model. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition, pp. 5957-5967, 2023.
Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. In International Conference on Learning Representations, 2018.
Siyi Chen, Hujjie Zhang, Minzhe Guo, Yifu Lu, Peng Wang, and Qing Qu. Exploring low-dimensional subspaces in diffusion models for controllable image editing, arXiv preprint orXiv:2409.02374 2024.
Xi Chen, Yan Duan, Rein Houthooft, John Schulman, Πya Sutskever, and Pieter Abbeel. Infogan: Inter- pretable representation learning by information maximizing generative adversarial nets. In Proceedings of NewrIPS, 2016.
Yunjey Choi, Youngjung Uh, Jaejun Yoo, and Jung-Woo Woo Ha. Stargan v2: Diverse image synthesis for multiple domains. Tn Proceedings of the IRFE/CVV conference computer vision and pattern recognition, pp. 8188 8197, 2020.
Nicos Christofides.
Worst-case analysis of a new heuristic for the traveling salesman problem. Graduate School of Industrial Administrution, Carnegie Mellon Universily, 1976.
Yusuf Dalva and Pinar Yanardag. Noisecl:: contrastive learning approach for unsupervised discovery of interpretable directions in diffusion models. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 24209 24218, 2024.
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hicrarchical image database. In 2009 JEEE conference on compuler vision and pallern recognition, pp. 248 255, 2009.
Jiankang Deng, Jia Guo, Niannan Xue, and Stefanos Zafeiriou. Areface: Additive angular margin loss for deep face recognition. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 4690-4699, 2019.
Vedant Vasant Dere, Amita Shinde, and Prachi Vast. Conditional reiterative high-fidelity gan inversion for image editing. Pattern Recognition, 147:110068, 2024. ISSN 0031-3203. doi: https://doi.org 1016/j. patcog.2022 2023.110062
Bardia Doosti, Shujon Naha, Majid Mirbagheri, and David J Crandall. Hope-net: A graph-based model for hand-object pose estimation. In Proceedings of the IEEE/CVES conference on computer vision and pattern recognition, pp. 6608 0617, 2020.
Kunyu Feng, Yue Ma, Bingyuan Wang, Chenyang Qi, Haozhe Chen, Qifeng Chen, and Zeyu Wang. Dit4edit: Diffusion transformer for image editing. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 2969-220 2977, 2025.
Merrill M Flood. The traveling-salesmaa problem. Operulions research, ((1):61-75, 1956.
Lore Goetschalckx, Alex Andonian, Aude Oliva, and Phillip Isola. Ganalyze: Toward visual definitions of cognitive image properties. In Proceedings of ICCV, pp. 5744-5753, 2019.
Ian Goodfellow, Jean Pouget-Abadic, Mchdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua. Bengio. Generative adversarial nets. In Advances in Neural Information Processing Systems, 2014.
15

---

Published in Transactions on Machine Learning Research (06/2025)
René Haas, Inbar Huberman-Spiegelllaa, Rotem Mulayoff, Stella Graßhof, Sami S Brandt, and Tomer Michaeli. Discovering interpretable directions in the semantic latent space of diffusion models. Tn 2024 IEEE 18th International Conference on Automatic Face and Gesture Recognition (FG), pp. 1 1-9, IEEE 2024.
Erik Härkönen, Aaron Hertzmann, Jaakko Lchtinen, and Sylvain Paris. Ganspace: Discovering interpretable gan controls. In Proceedings of NewrIPS, pp. 9841-9850) 2020.
Irina Higgins, Loic Matthey, Arka Pal, Christopher Burgess, Xavier Glorot, Matthew Botvinick, Shakir
Mohamed, and Alexander Lerchner. beta-vae: Learning basic visual concepts with a constrained variational
framework. In Proceedings of International Conference on Learning Representations, 2017.
Ali Jahanian, Lucy Chai, and Phillip Isola. On the' steerability' of generative adversarial networks. In International Conference on Learning Representations, 2019.
Yuming Jiang, Ziqi Huang, Xingang Pan, Chen Change Loy, and Ziwei Liu. Talk-to-edit: Fine-grained facial editing via dialog. In Proceedings of the IEEE/C/V International Conference Computer Vision, pp. 13799-13808, 2021.
David S Johnson and Lyle McGeoch. The traveling salesman problem: A case study local optimization. Local search in combinatorial optimization, 1997.
KJ Joseph, Prateksha Udhayanan, Tripti Shukla, Aishwarya Agarwal, Srikrishna Karanam, Koustava Goswami, and Balaji Vasan Srinivasan. Iterative multi-granular image editing using diffusion models. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pp. 8107-8116, 2024.
Kimmo Karkkainen and Jungseock Joo. Fairface: Face attribute dataset for balanced race, gender, and age for bias measurement and mitigation. In Proceedings of the IEEE/CVP winter conference on applications of compuler vision, pp. 1548 1558, 2021.
Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of gans for improved quality, stability, and variation. In International Conference Learning Representations.
Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 4401-4410, 2019.
Tero Karras, Samuli Laine, Milk Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of stylegan. In Proceedings of the IEEE/CVP conference on computer vision and pattern recognition, pp. 8110-8118 2020.
Kai Katsumata, Duc Minh Vo, Bei Liu, and Hideki Nakayama. Revisiting latent space of gan inversion for robust real image editing. In Proceedings of the IEEE/CVF Winter Conference Applications of Computer Vision, pp. 5313-5322, 2024.
Jack Klys, Jake Snell, and Richard Zemel. Learning latent subspaces in variational autocncoders. In Proceedings of NewrIPS, pp. 6445 6455, 2018.
Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. Learning multiple layers of features from tiny images. 2009.
Wonkwang Lee, Donggyun Kim, Seunghoon Hong, and Honglak Lee. High-fidelity synthesis with disentan- gled representation. In Computer 23-28, 2020, Proceedings, Part XXVI 16, pp. 157-174. Springer, 2020.
2020: 16th European Conference, Glasgou, UK, August
Bingchen Liu, Yizhe Zhu, Zuohui Fu, Gerard De Melo, and Ahmed Elgammal. Oogan: Disentangling gan with one-hot sampling and orthogonal regularization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pp. 4836-4843, 2020.
16

---

Published in Transactions on Machine Learning Research (06/2025)
Hongyu Liu, Yibing Song, and Qifeng Chen. Delving stylegan inversion for image editing: A foundation latent space viewpoint. In Proceedings of CVPR, pp. 10072-10082, 2023.
Yong-Hyun Park, Mingi Kwon, Junghyo Jo, and Youngjung Uh. Unsupervised discovery of semantic latent directions in diffusion models. arXiv preprint arXiv:2902.12) 12469, 2023.
Hamza Pehlivan, Yusuf Dalva, and Aysegul Dundar. Styleres: Transforming the residuals for real image editing with stylegan. In Proceedings of CVPR, pp. 1828 1837, 2023.
Antoine Plumerault, Hervé Le Borgne, and Céline Hudelot. Controlling generative models with continuous factors of variations. arXiv preprint arXiv:2001.0023, 2020.
Aditya Ramesh, Youngduck Choi, and Yann LeCun. A spectral regularizer for unsupervised disentanglement. arXiv preprint arXic:1812.01100 2018
Daniel Roich, Ron Mokady, Amit H Bermano, and Daniel Cohen-Or. Pivotal tuning for attentbbased editing of real images. ACM Transactions on graphics (TOG), 42(1):1-11 13, 2022.
Hans Sagan. Space-filinng curves. Springer Science & Business Media, 2012. URL https://doi.org:: 10079978-144612-10
Rahul Sajnani, Jeroen Vanbaar, Jie Min, Kapil Katyal, and Srinath Sridhar. Geodiffuser: Geometry-based image editing with diffusion models. In 2025 IEEE/CVF Winter Conference Applications of Computer Vision (WACV), pp. 472-482. IEEE, 2025.
Yujun Shen and Bolei Zhou. Closod-form factorization of latent semantics in gans. In Proceedings of the IEEE/CVP conference on computer vision and pallern recognition, pp. 1532 1540, 2021.
Yujun Shen, Jinjin Gu, Xiaoou Tang, and Bolci Zhou. Interpreting the latent space of gans for semantic face editing. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp.
1243-92524 2020.
Yujun Shen, Ceyuan Yang, Xiaoou Tang, and Bolei Zhou, Interfacegan: Interpreting the disentangled face representation learned by gans. IEFE Transactions on Pattern Analysis and Machine Intelligence, 44(4): 2004-2018, 2022. doi:
Yujum Shi, Chuhui Xue, Jun Hao Liew, Jiachun Pan, Hanshu Yan, Wenqing Zhang, Vincent YF Tan, and Song Bai. Dragdiffusion: Harnessing diffusion models for interactive point-based image editing, In Proceedings of the LEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8839-8849 2024.
Connor Shorten and Taghi M Khoshgoftaar. A survey image data augmentation for deep learning. Journal of big data, 6(1):1-48, 2019.
Yue Song, T Anderson Keller, Nicu Sebe, and Max Welling. Latent traversals in generative models as potential flows. arxiv preprinl arxiv:2304. 12944, 2023a.
Yue Song, Jichao Zhang, Nicu Sebe, and Wei Wang. Houscholder projector for unsupervised latent semantics discovery. In Proceedings of the IEEE/CVE international conference on computer vision, pp. 7712-7722, 2023b.
Christos Tzelepis, Georgios Teimiropoulos, and Ioannis Patras. Warpedganspace: Finding non-linear rbf paths in gan latent space. In Proceedings of the IEEE/CVF International Conference on Computer Vision pp. 6393 (088-600, 2021.
Mohammad Hassan Vali and Tom Bäckström. Interpretable latent space using space-filling curves for pho- netic analysis in voice conversion. In Proceedings of Interspeech, 2023.
Andrey Voynow and Artem Babenko. Unsupervised discovery of interpretable directions in the gan latent space. In Proceedings of International Conference on Machine Learning, pp- 9786 07666,976,669 2020.
17

---

Published in Transactions on Machine Learning Research (06/2025)
Ting-Chun Chun Wang, Ming- Yu Liu, Jun-Yan Zhu, Guilin Liu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. Video-to-video synthesis. Advances in Newral Information Processing Systems, 31, 2018a.
Ting-Chun Chun Wang, Ming- Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. High- resolution image synthesis and semantic manipulation with conditional gans. In Proceedings of CVPR, 2018b.
pp.
Zongze Wu, Dani Lischinski, and Eli Shechtman. Stylespace analysis: Disentangled controls for stylegan image generation. In Proceedings of the IEEE/CVE conference on computer vision and pattern recognition, pp. 12863 12872, 2021.
Yifan Xue, Michael Ding, and Xinghua Lu. Supervised vector quantized variational autoencoder for learning interpretable global representations. arXiv preprint arXiv:1909.111 2019.
Huiting Yang, Liangyu Chai, Qiang Wen, Shuang Zhao, Zixun Sun, and Shengfeng He. Discovering in- terpretable latent space directions of gans beyond binary attributes. In Proceedings of the IEEE/CVP Conference on Computer Vision and Paltern Recognation, pp. 12177 12185, 2021.
Fisher Yu, Ari Scff, Yinda Zhang, Shuran Song, Thomas Funkhouser, and Jianxiong Xiao. Lsun: Con- struction of a large-scale image dataset using deep learning with humans in the loop. arXiv preprinl arXiv:1506. 0336:55 2015.
Oguz Kaan Yüksel, Enis Simsar, Ezgi Gülperi Er, and Pinar Yanardag. Latentclr: A contrastive learn- ing approach for unsupervised discovery of interpretable directions. In Proceedings of the IEFE/CVP International Conference on Computer Vision, pp. 14263 14272, 2021.
Shifeng Zhang, Xiangyu Zhu, Zhen Lei, Hailin Shi, Xiaobo Wang, and Stan Z Li. S3fd: Single shot scale- invariant face detector. In Proceedings of the IEEE international conference on computer vision, pp. 192-201 201, 2017.
Zijian Zhang, Luping Liu, Zhijie Lin, Yichen Zhu, and Zhou Zhao. Unsupervised discovery of interpretable directions in h-space of pre-trained diffusion models. arXiv preprint ar arXi:223000000 0.9912, 2023.
Jiapeng Zhu, Yujun Shen, Yinghao Xu, Deli Zhao, Qifeng Chen, and Bolei Zhou. In-domain gan inversion for faithful reconstruction and editability. IEEE Transactions on Pottern Analysis and Machine Intelligence, 46(5):2607-266) 2621, 2024. doi: 10.1109/TPAMI 2018.230
18

---

Published in Transactions on Machine Learning Research (06/2025)
A Appendices
A.1 StyleGAN2: universal interpretation of the CIFAR10 dataset
As discussed in Sec. 5.1, when we initialize the SFVQ with N = 4 initial codewords and train it on the W space of StyleGAN2 pre-trained on CIFAR10 dataset, about 25% of the learned codewords would model the horse class (see Fig. 7(a)). To find out the reason, for each CIFARIO class, we extracted 10 latent vectors, and computed three metrics: the mean and variance of Euclidean distances among all latent vectors, and the sum of the eigenvalues of the latent vectors. Fig. 14 shows the computations of these three metrics for all CIFAR10 different classes. According to the figure, the horse class takes the widest area of the latent space while its latent vectors have the highest diversity compared to other classes. However, the computed metrics for the horse class do not show significant difference from other classes, and thus it does not conform to train SFVQ with higher numbers
the fact that it accounts for 25% of the learned codewords. Therefore, of initial codewords (N = {8, 16)), and we plot the generated images corresponding to the learned SFVQ codebook in Fig. 15 and Fig. 16 where SFVQ was initizl with N = and N = 16 codewords, respectively. In these cases, we observe more normalized proportion of CIFAR10 classes occupying the codebook, which better aligns with the computed metrics in Fig. 14.
(b)
Variance of Euelidean distance among latent vectors
Mean of Euclidean distance among latent vectors
300
Sum of eigenvalues of latent vectors
200
68-
SE
104
Inc
52
Go
86
92
245
235
43
100-
211
con
198
217
Alppan
Bid
Oat
Dap
Poy
Hesr
stop
Alplaee
Ca
Bed
Deg
Fegt
Houe
dlip
Traak
Figure 14: (a) Mean and (b) variance of Euclidean distances among 10k latent vectors of each CIFARIO class, and (c) sum of the eigenvalues of the latent vectors in W space of pre-trained StyleGAN2.
10
12
13
14
15
16
17
1
19
20
22
23
24
25
26
27
28
29
30
32
33
34
35
36
38
39
40
43
46
60
Figure 15: Generated images from the codebook of a bit SFVQ (N = 644 trained on W space of StyleGAN2
pre-trained on the CIFAR10 dataset, when SFVQ is initialized by N = =8 codewords.
19

---

Published in Transactions on Machine Learning Research (06/2025)
10
12
13
14
15
20
27
28
29
32
35
36
37
38
39
40
42
43
45
46
48
56
59
60
62
Figure 16: Generated images from the codebook of a 6 bit SFVQ (N 64) trained on W space of StyleGAN2 pre-trained on the CIFAR10 datasct, when SFVQ is initialized by N 16 codewords.
A.2 StyleGAN2: universal interpretation of the AFHQ dataset
Similar to what is discussed in Sec. 5.1 of the paper, we apply the SFVQ to capture a universal morphology of the latent space, and we expect that subsequent codebook vectors in SFVQ refer to similar images. Hence, applied a 6 bit SFVQ on the W space of the StyleGAN2 model, which was pre-trained on the AFHQ dataset. Images corresponding to the SFVQ's codebook vectors are represented in Fig. 17. We can observe that similar animal species are typically located adjacent to one another. Tn addition, there are some other similarities among neighboring codebook vectors, such as change in rotation (from right to left) when moving from index 0 to index 10, change rolation (from left to right) when moving from index 26 to index 34, light-colored animals for indices 22-25, bi-colored animals for indices 26-29, and baby-aged cats for indices 61-62.
20
Figure 17: Generated images from the codebook of a bit SFVQ (N 64) trained W space of StyleGAN2 pre-trained on the AFHQ dataset.
20

---

Published in Transactions on Machine Learning Research (06/2025)
A.3 Class-agnostin directions for StyleGAN2 pre- tre-trained on the AFHQ dataset
According to what is discussed in Sec. 5.2 of the paper, in this section, we aim to test whether and how the discovered direc- tion of Bicolor (in Fig. 9 of the paper) is class-agnostic across different AFHQ animal classes. To this end, we applied this di- rection to all existing animal species in the AFHQ dataset and represented the results in Fig. 18. We observe that this direc- tion works well for the Cat and Dog classes because there is suf- ficient data (i.e., cats and dogs with bicolored faces) within the AFHQ dataset. Therefore, the learned latent space supports this transformation. In addition, this transformation more or less works for Wolf class, since Wolf looks like Siberian husky (which exists in AFHQ dataset), and this transformation leads Siberian husky. However,
Direction W6-W7
Cat 0=8
20
Rd
Wolf Dog 0=8
the Wolf class to become similar the Bicolor direction does not work for other animal classes of Foz, Leopard, Cheetah, Tiger, and Lion. The reason is that the learned latent space is constrained by the datasct bias of individual classes (Jahanian et al., 2019). In other words, the learned latent space does not support this transformation for them, as there are no images with a bicolored face from these animal classes within the AFHQ dataset. The value deter- mines the magnitude of the step we take toward the Bicolor direction. To make sure whether this direction works for these five animal classes, used larger value (bigger steps) for them. We observe that even with larger steps, not only is there no meaningful transformation effect in the desired direc- tion, but also, in the very last step (3r), the images become unrealistic due to the presence of artifacts.
0 10
== 13
Fox
Leopard
a -= 13
Cheetah == 18 18
Tiger
1=
Lion 0= 18
Figure 18: Applying Bicolor direction to different animal species of AFHQ datasct.
A.4 Class-agnostic directions for BigGAN pre-trained on the ImageNet dataset
As discussed in Sec. 5.3 of the paper, we find out that the discovered directions by SFVQ (in p(z) space of BigGAN) for the golden retriever class are class-agnostic. It means that the detected directions also work when applied to other data classes within the ImageNet dataset. To confirm this, we applied all five directions found for the golden retriever (in Fig. 9 of the paper) on the husky class, and we illustrated the results in Fig. 19. The image in the middle column (in red square) is the initial test image to which we apply the directions, such that we step along both sides direction. According to the figure, all five directions are valid for the husky class, resulting meaningful and expected transformations.
21

---

Published in Transactions on Machine Learning Research (06/2025)
Rotation ZO-ZO
-20
-10
10
20
Zoom In Z2-Z2
-30
-20
-10
10
l0
20
30
Lay Down| 72-72
10
D0
1a
20
3
Open Mouth Z6-Z6
:30
-0
-10
10
10
20
Add Grass Z4-Z4
-30
-20
-10
00
20
30
Figure 19: Class-agnostic directions; applying five SFVQ's discovered directions for the golden retriever class on the husky class using BigGAN pre-trained on the ImageNet dataset.
A.5 Subsidiary study: traveling salesman problem
Spaco-filling vector quantization (SFVQ) has some parallels with the classic traveling salesman problem (TSP) (Flood, 1956) in bringing order to set of codebook vectors. One could ask whether can achieve better codebook arrangement than SFVQ by applying ordinary vector quantization (VQ) and afterward, use one of the traveling salesman solutions to reorganize VQ codebook vectors. The scenario of TSP involves a list of cities (codebook vectors) and the distances between them, with the goal of discovering the shortest possible route to visit each city only once. TSP is an NP-hard problem to solve. We can interpret these citics as the codewords of a VQ codebook. If we Iearn an bit VQ as usual and intend to rearrange the codebook vectors to achieve the shortest route, then there are 256! possible permutations for rearrangement. This is astronomically large number (8.5 x 10506). It is thus practically infeasible to do an exhaustive search for all possible permutations in most relatively high-bitrate cases of VQ. Hence, it is recommended to use heuristic TSP solvers that have lower computational complexity, such as nearest neighbor (Johnson & McGeoch, 1997), greedy (Johnson & McGeoch, 1997), and Christofides (Christofides, 1976).
To compare the performance of TSP hcuristic solutions with the SFVQ, we examine their ability to model three sparse sample distributions of circles, moons, and spinal in 3D space. We chose the distributions be sparse because it makes the task more challenging. We trained ordinary VQ and SFVQ with 9 bit (with
22

---

Published in Transactions on Machine Learning Research (06/2025)
identical initialization and hyper-parameter settings). After training the VQ, rearranged its codebook vectors using the nearest neighbor (NN) and Christofides TSP heuristic solvers. Fig. 20 demonstrates the results such that the order in the space-filling line is shown with color coding (light to dark color = first to last codebook vector) for both methods of VQ+TSP and SFVQ. Since the training objective of SFVQ is different from VQ, SFVQ locates the codebook vectors such that the line connecting the subsequent. codebook vectors mainly desires fill up the distribution space. As a result, the line ends up landing inside the distribution space. To affirm this fact, compare the upper and lower parts of spiral dataset arranged by Chrissofoiiee and VQ+NN methods. VQ locates fewer codebook vectors for these two parts of the sptral data, and thus we observe narrow line that does not fill the distribution's space appropriately. Furthermore, we notice more unfavorable jumps (lines outside the distribution or lines breaking the arrangement) for VQ+TSP methods than the SFVQ due to their improper codebook arrangement. Therefore, we generally observe that the SFVQ achieves a much better codebook arrangement than VQ+TSP for all three distributions.
VQ+Christofides
VQ+NN
SFVQ
circles
VER
moons
spiral
Figure 20: Comparison of the codebook arrangement property of SFVQ with ordinary VQ which is post- processed by traveling salesman heuristic solvers over three sparse distributions.
23

---

Published in Transactions on Machine Learning Research (06/2025)
A.6 SeFa interpretable directions
There were annotations for SeFa (Shen & Zhou, 2021) in- terpretable directions for StyleGAN2, which was pre-trained on the FFHQ dataset. Therefore, we used the interactive tool provided in SeFa's GitHub repository and examined the first = 25 semantics of the StyleGAN2-FFFHG model. In the teractive tool, there were only three options available (WO-W1, 52-W5, W6-W13) to do the layer-wise edits and manipulate the latent. vector only for those layers. Hence, to obtain more precisc interpretable directions, we further scarched for the best layer-wise edits for each semantic (or interpretable direction). We provided the details of SeFa's interpretable directions in Table 3.
Table 3: SeFa (Shen & Zhou, 2021) inter-
pretable directions.
Direction
Semantic Index
StyleGA N2 Layers
Gender
2
[4-6]
Rotation
[0-2]
Eyeglasses
[0-1]
Race
[6-11]
Age
[3-4]
Bald
15
[4-5]
Hair Color
[7-8]
Smile
[4-5]
Beard
[8-9]
[2-5]
Makoup
[6-7]
A.7 Learned SFVQ codebooks for StyleGAN2 pre-trained the FFHQ dataset
As mentioned in Sec. 5.6, we provide the learned SFVQ curves trained on the W space of pre-trained StyleGAN2 on the FFHQ dataset here. Fig. 21 to Fig. 27 demonstrate the generated images from learned SFVQ codebooks with the bitrates from 2 to bit. We also provided similar figures for bitrates 9 to 12 bit in our GitHub repository. The learned SFVQ codebooks and their corresponding generated images for pro-trained StyleGAN2 on the FFHQ, AFHQ, and LSUN Cars for bitrates ranging from 2 bit are available in GitHub repository.
3
Figure 21: Codebook of 2 bit. SFVQ trained W space of StyleGAN2 pre-trained the FFHQ dataset.
Figure 22: Codebook of a 3 bit SFVQ trained on W space of StyleGAN2 pre-trained on the FFHQ dataset.
24

---

Published in Transactions on Machine Learning Research (06/2025)
Figure 23: Codebook of 4 bit SFVQ trained W space of StyleGAN2 pre-trained the FFHQ dataset.
18
14
15
20
Figure 24: Codebook of a 5 bit SFVQ trained W space of StyleGAN2 pre-trained the FFHQ dataset.
18
32
AHD
49
47
Figure 25: Codebook of a 6 bit SFVQ trained on W space of StyleGAN2 pre-trained on the FFHQ dataset.
LL
125
Figure 26: Codebook of a 7 bit SFVQ trained on W space of StyleGAN2 pre-trained on the FFHQ dataset.
25

---

Published in Transactions on Machine Learning Research (06/2025)
M12
IES
LIG
INT
126
TAT
RS
10
HTO
ISON
HS
GIS
23T
22
230
24
US
Figure 27: Codebook of a 8 bit SFVQ trained on W space of StyleGAN2 pre-trained on the FFHQ dataset.
26

---

Published in Transactions on Machine Learning Research (06/2025)
A.8 SFVQ is not sensitive to training syper-parameters
As discussed in Sec. 4, training of SFVQ and its interpretation ability is not sensitive to the training hyper- parameters. To prove this claim, we trained the SFVQ on the intermediate latent space (W) of StyleGAN2 pre-trained on the CIFAR10 dataset over different SFVQ bitrates {6, 7, 8), batch sizes {32, 64, 128), and learning rates (5.5e- le "1. After learning the SFVQ codebook over these different settings, we plotted the generated images corresponding to the learned codebook in the figures from Fig. 28 to Fig. 45. Apart from the generated images, we also plotted the heatmap of distances between different SFVQ codebook entries. According to all these figures, we see a clear arrangement in the SFVQ codebook over all different settings, as there is an obvious order and distinction between different CIFAR10 data classes, both in the generated imagos and the heatmaps. In other words, images from an identical data class are organized into groups in both generated images and heatmap plots.
Codebook Vector
70
22
16
Codebook
Figure 28: (a) Generated images from codebook of 6 bit SFVQ trained on W space of StyleGAN2 pre-
trained on the CIFARIO dataset when batch size=32 and learning rate=5.5e (b) Heatmap of Eu- clidean distances between all codebook vectors.
(b)
16
Codebook Vector
24
32
20
60
16 24 at 5o
Cadebook Vector Index
Figure 29: (a) Generated images from codebook of 6 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFARIO dataset when batch size=64 and learning rate=5.5e 1, clidean distances between all codebook vectors.
(b) Heatmap of Eu-
56 Codcbook Vector Index
16
24
26
27
30
82
40
20
58
59
16 24
Codebook Voctor Index
Figure 30: (a) Generated images from codebook of a 6 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFAR10 dataset when batch size=128 and learning rate=5.5e 4 (b) Heatmap of Euclidean distances between all codebook vectors.
27

---

Published in Transactions on Machine Learning Research (06/2025)
16
Codchook Vector
24
2l6
28
15
21
24 32
68
Codebook Vector Index
Figure 31: (a) Generated images from codebook of 6 bit SFVQ trained on W space of StyleGAN2 pre-
trained on the CIFARIO dataset when batch size=32 and learning rate=le- (b) Heatmap of Euclidean distances between all codebook vectors.
(b)
Codebook Vector
32
Codebook
Figure 32: (a) Generated images from codebook of 6 bit SFVQ trained on W space of StyleGAN2 pre- trained the CIFARIO dataset when batch size=64 and learning rate=le- 3 (b) Heatmap of Fuclidean distances between all codebook vectors.
Codebook Vector Index
8
16
24
22
30
Codebook Vector Index
Figure 33: (a) Generated images from codebook of a 6 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFAR10 dataset when batch sizc=128 and lcarning rate=le 3 (b) Hcatmap Eu- clidean distances between all codebook vectors.
Codehook Index
80
20
Codebook
Vector Index
Figure 34: (a) Generated images from codebook of 7 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFAR10 dataset when batch size=32 and learning rate=5.5e 55-4 (b) Heatmap of Fu- clidean distances between all codebook vectors.
28

---

Published in Transactions on Machine Learning Research (06/2025)
Codebook Vector Index
20
Codebook Voctor Index
Figure 35: (a) Generated images from codebook of 7 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFARIO dataset when batch size=64 and learning rate=5.5e (b) Heatmap of Eu- clidean distances between all codebook vectors.
Codebook Vector Index
64
80
90
20
Codebook Vector Index
Figure 36: (a) Cenerated images from codebook of a 7 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFAR1O dataset when batch size=128 and learning rate=5.5e 4, (b) Heatmap of Euclidean distances between all codebook vectors.
Codehook Vector Index
16
64
80
20
Codebook
Vector Index
Figure 37: (a) Generated images from codebook of a 7 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFAR10 dataset when batch size=32 and learning rate=le 3 (b) Heatmap of Euclidean distances between all codebook vectors.
(b)
Codebook Vector Index
64
80
Codebook
Voctor Index
Figure 38: (a) Generated images from codebook of 7 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFAR10 dataset when batch size=64 and learning rate=le 3 (b) Heatmap of Euclidean distances wet all codebook vectors.
29

---

Published in Transactions on Machine Learning Research (06/2025)
Codebook Vector
Codebook Index
Figure 39: (a) Generated images from codebook of 7 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFARI0 dataset when batch size=128 and learning rate=le 3 (b) Heatmap of Eu- clidean distances between all codebook vectors.
Codibook
160
192
224
Codebook Vector Index
Figure 40: (a) Generated images from codebook a 8 bit SFVQ trained on W space of StyleGAN2 pre-
trained on the CIFARIO dataset when batch size=32 and learning rate=5.5e 4 (b) Heatmap of Eu- clidean distances between all codebook vectors.
(b)
129
Codkboook
100
256
150
Codebook Voctor Index
Figure 41: (a) Generated images from codebook of 8 bit SFVQ trained on W space of StyleGAN2 pre-
trained the CIFARIO dataset when batch size=64 and learning rate=5.5e (b) Heatmap of Eu- clidean distances between all codebook vectors.
Codcbook Victor Index
64
192
20
Codebook Vector Index
Figure 42: (a) Generated images from codebook of 8 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFAR10 dataset when batch size=128 and learning 5. (b) Heatmap of Euclidean distances between all codebook vectors.
30

---

Published in Transactions on Machine Learning Research (06/2025)
Codlebook Vector Index
160
192
Codebook Vector Index
Figure 43: (a) Generated images from codebook a 8 bit SFVQ trained on W space of StyleGAN2 pre- trained on the CIFARIO dataset when batch size=32 and learning rate=le-9 3 (b) Heatmap of Euclidean distances between all codebook vectors.
128
100
250
Figure 44: (a) Generated images from codebook of 8 bit SFVQ trained on W space of StyleGAN2 pre- trained the CIFARIO dataset when batch size=64 and learning rate=le (b) Healmap of Euclidean distances between all codebook vectors.
80
60
224
250
250
Codeboak Vector Index
Figure 45: (a) Generated images from codebook of 8 bit SFVQ trained on W space of StyleGAN2 pre-
trained on the CIFAR10 dataset when batch size=128 and learning rate=le 3 (b) Heatmap of Eu- clidcan distances between all codebook vectors.
31


Reviews:
[{"review_id": "M3FgSNLXBO", "reviewer": "Reviewer_JnQ1", "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": "**Strengths:**\n\n1. This paper aims to interpret the latent spaces of GANs, which is an interesting and challenging problem.\n2. It seems that the proposed method achieves superior results than previous methods.\n3. Both qualitative and quantitative experiments have been conducted to evaluate the performance of the proposed method.\n\n**Weaknesses:**\n\n1. The related works and baselines presented in this paper are all from before 2023. Has there been no further research on this topic in recent years?\n\n2. The authors chose StyleGAN2 and BigGAN as the backbones to evaluate the performance of their proposed method. However, StyleGAN2 and BigGAN are from 2020 and 2018, respectively, and are outdated to some extent. Why not experiment on more state-of-the-art GAN models?\n\n3. Currently, diffusion models have significantly surpassed GANs in generative capabilities. Can the method proposed in this paper be applied to diffusion models? Is there a way to interpret the latent spaces of diffusion models?\n\n4. This paper does not include a related work section, which results in an insufficient and unclear presentation of the development and summary of related research.\n\n5. This paper is not well-organized and needs further improvement and refinement.", "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 presents a novel approach to interpreting the latent spaces of GANs using space-filling vector quantization (SFVQ). The proposed method introduces a modification to traditional vector quantization that captures the underlying structure of the latent space, making it more interpretable. Experimental results on pretrained StyleGAN2 and BigGAN models across various datasets demonstrate the effectiveness of the proposed method.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please address the issues raised in **Weaknesses**.", "broader_impact_concerns": "The paper does not have any apparent ethical issues.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "0x6gPvUZTz", "reviewer": "Reviewer_LTZ1", "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": "Strengths:\n\n- The images generated from the SFVQ codebooks offer insightful visualizations of the latent space structure, revealing clear clustering based on semantic attributes.\n- The lines connecting SFVQ codebook vectors correspond to interpretable directions for image manipulation, enabling controlled image generation.\n- The method identifies joint interpretable directions that affect multiple attributes simultaneously, which is a notable contribution.\n- Leveraging the SFVQ curve for data augmentation is a novel and promising approach.\n\nWeaknesses:\n\n- The core modifications to SFVQ appear incremental. Initializing codebook vectors using the mean of sorted latent vectors, and employing a convex combination (e.g., 0.99 and 0.01) for codebook expansion to address outlier issues, are practical but not substantial methodological advancements. The paper relies heavily on prior work and lacks significant theoretical contributions.\n- Although qualitative comparisons with existing methods are provided, they are largely subjective and lack rigorous evaluation metrics. The quantitative comparisons, while utilizing standard metrics, are limited in scope and do not fully substantiate the claimed improvements. The reported commutativity error is also of limited value, given the linear nature of the transformations. A more robust evaluation—including user studies for subjective assessments and a broader set of quantitative metrics—would strengthen the analysis.\n- The paper would benefit from clearer explanations of the proposed modifications and their practical impact. The connection between space-filling curves and the proposed method should be more thoroughly explained. Additionally, some visualizations, particularly the heatmaps, could be enhanced for better clarity and readability.\n- While the paper claims that SFVQ is not sensitive to hyperparameters, this is not convincingly demonstrated. A more thorough sensitivity analysis, especially of the bitrate and other training parameters, would help validate this claim.\n- The exclusive focus on StyleGAN2 and BigGAN limits the generalizability of the method. Evaluating its performance on a wider range of GAN architectures would enhance the applicability and relevance of the approach.", "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 using a modified Space-Filling Vector Quantization (SFVQ) for interpreting the latent spaces of pre-trained GANs like StyleGAN2 and BigGAN. The core modifications to SFVQ lie in the initialization and codebook expansion strategies. While the overall goal is interesting and the results visually compelling, the paper suffers from several weaknesses that limit its contribution and impact. The key contribution lies in improving SFVQ through changes to its initialization and code expansion process—specifically, by using convex averaging of codebook vectors instead of simple averaging. This refinement allows the SFVQ curve to more effectively capture the morphological structure of the latent space, making it easier to understand and control. Applied to pretrained GAN models like StyleGAN2 and BigGAN, the method provides a general, unsupervised approach for discovering interpretable directions in latent space, supporting intelligible image transformations and controllable data augmentation. Compared to other techniques, the modified SFVQ is claimed to offer better consistency and interpretability, while remaining architecture-agnostic and broadly applicable across data types.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "* Explore more substantial modifications to SFVQ or develop theoretical justifications for the proposed changes. In particular, the motivation behind the current choice of codebook initialization and its effect is missing. Also in regards to codebook expansion, the motivation behing the choice of the individual weights and their actual effect was not considered. \n* In multiple places, authors mention that the proposed method keeps the identity of the test image. However, these is no indept analysis of this aspect? In particular, it would be interesting to test if the convex averaging weights are responsible for this? Alternatively, is there an optimal weights for a specific task, while preserving the identitiy of the test image? \n* Further development of a theoretical understansing to analyze the properties of the modified SFVQ and its effectiveness in capturing the latent space structure would be useful. \n* Instead of relying solely on correlation, explore other metrics for quantifying interpretability, such as mutual information between latent codes and attributes, or disentanglement scores. Consider using established benchmarks like the DCI Disentanglement metric.\n* Investigate Hyperparameter Sensitivity by performing a thorough sensitivity analysis of the bitrate and training parameters, e.g., why in Figure 3 out of 64 codevectors, the horses are overrepresented?", "broader_impact_concerns": "There are no major concerns regarding the ethical implications of this work. The proposed method focuses on improving the interpretability of GAN latent spaces through a technical modification of the SFVQ algorithm. While enhanced control over generative models can raise general concerns about misuse, the paper does not introduce any new risks beyond those already associated with standard GAN technologies. Therefore, a Broader Impact Statement is not strictly necessary.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "aHKQE2jBZI", "reviewer": "Reviewer_pv2x", "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": "I am not that familiar with the task that the paper is studying.\n\nIn terms of strengths, compared with the previous methods for obtaining interpretable directions, the proposed method is conceptually simple, yet able to achieve good results. The SFVQ is also shown to enable a general interpretation of the latent space.\n\nIn terms of weaknesses, the paper is largely empirical, without theoretical justifications. I briefly glanced through the previous works on interpretations of GANs' latent space that the authors cited. It appears the previous methods typically involve optimization schemes specifically tailored to obtain interpretable directions, through PCA, contrastive learning, etc. As such, in the current form, it is unclear to me why the proposed method should be able to outperform the previous methods.", "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 paper considers the problem of learning meaningful directions in the latent space of a GAN. The paper utilizes the space-filling vector quantization (SFVQ) and fits the curve to the space, presenting techniques to improve the training of SFVQ. After the SFVQ is trained, the directions can be read off from the spline. Empirical evidences are provided to demonstrate the effectiveness of the proposed method on pre-trained GANs including StyleGAN2 and BigGAN. It was shown that SFVQ curve provides us with a mechanism to interpret the latent space of the GAN.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Can the authors elaborate on why the proposed method outperforms the previous ones, despite the model is not explicitly trained to obtain interpretable directions? Can the authors elaborate on why the proposed method is able to yield interpretable latent space in general?", "broader_impact_concerns": "Not applicable", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)