On Disentangled Representations Extracted from Pretrained GANs
Authors: Valentin Khrulkov
Leyla Mirvakhabova
Ivan Oseledets
Artem Babenko
Venue:  (2021)
Keywords: Disentanglement
representations
GANs

Abstract: Constructing disentangled representations is known to be a difficult task, especially in the unsupervised scenario. The dominating paradigm of unsupervised disentanglement is currently to train a generative model that separates different factors of variation in its latent space. This separation is typically enforced by training with specific regularization terms in the model's objective function. These terms, however, introduce additional hyperparameters responsible for the trade-off between disentanglement and generation quality. While tuning these hyperparameters is crucial for proper disentanglement, it is often unclear how to tune them without external supervision.

This paper investigates an alternative route to disentangled representations. Namely, we propose to extract such representations from the state-of-the-art GANs trained without disentangling terms in their objectives. This paradigm of post hoc disentanglement employs little or no hyperparameters when learning representations, while achieving results on par with existing state-of-the-art, as shown by comparison in terms of established disentanglement metrics, fairness, and the abstract reasoning task.
All our code and models are publicly available.

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ON DISENTANGLED REPRESENTATIONS EXTRACTED FROM PRETRAINED GANS
Anonymous authors Paper under double-blind review
ABSTRACT
Constructing disentangled representations is known to be difficult task, espe- cially the unsupervised scenario. The dominating paradigm of unsupervised disentanglement is currently to train generative model that separates different factors of variation in its latent space. This separation typically enforced by training with specific regularization terms in the model's objective function. These terms, however, introduce additional hyperparameters responsible for the trade-off between disentanglement and generation quality. While tuning these hyperparam- eters is crucial for proper disentanglement, is often unclear how to tune them without external supervision.
This paper investigates an alternative route to disentangled representations. Namely, propose to extract such representations from the state-of-the-art GANs trained without disentangling terms in their objectives. This paradigm of post hoc disentanglement employs little resentations, while achieving results on par with existing stat-oo-thhe-an as shown by comparison in terms of established disentanglement metrics, fairness, and the abstract reasoning task. All our code and models are publicly available'.
hyperparameters when learning rep-
INTRODUCTION
Unsupervised learning of disentangled representations is currently one of the most important chal- lenges in machine learning. Identifying and separating the factors of variation for the data at hand provides a deeper understanding of its internal structure and can bring new insights into the data gen- eration process. Furthermore, disentangled representations are shown benefit certain downstream tasks, e.g., faimess (Locatello et al., 2019a) and abstract reasoning (van Steenkiste et al., 2019). Since the seminal papers on disentanglement learning, such as InfoGAN (Chen et al., 2016) and 3-VAE (Higgins et al., 2017), large number of models were proposed, and this problem continues to attract much research attention (Alemi et al., 2016; Chen et al., 2018; Burgess et al., 2017: Kim & Mnih, 2018; Kumar et al., 2018; Rubenstein et al., 2018; Esmacili et al., 2019; Mathicu et al., 2019; Rolinek et al., 2019; Nie et al., 2020; Lin et al., 2020).
The existing models achieve disentanglement in their latent spaces via specific regularization terms in their training objectives. Typically, these terms determine the trade-off between disentanglement and generation quality. For example, for 3-VAE (Higgins al., 2017), one introduces the KL- divergence regularization term that constrains the VAE bottleneck's capacity. This term is weighted by the multiplier that enforces better disentanglement for 3 > 1 while resulting in worse recon- struction quality. Similarly, InfoGAN utilized regularization term approximating the mutual infor- mation between the generated image and factor codes. As has been shown in the large scale study Locatello et al. (2019b), hyperparameter values can critically affect the obtained disentanglement. In the unsupervised setting, the values of ground truth latent factors utilized by disentanglement metrics are unknown, and thus selection of correct hyperparameters becomes a nontrivial task.
In this paper, we investigate disentangled representations can be extracted from the pretrained non- disentangled GAN models, which currently provide the state-of-the-ant generation quality (Karras et al., 2020). These GANs are trained without disentanglement terms in their objectives; therefore, do not need tune the hyperparameters mentioned above. Our study is partially inspired by very recent line of works on controllable generation (Voynov & Babenko, 2020; Shen & Zhou, 2020;
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Härkönen et al., 2020; Peebles et al., 2020), which explore the latent spaces of pretrained GANs and identify the latent directions useful for image editing. The mentioned methods operate without ex- ternal supervision, therefore, are valid to in the unsupervised disentanglement. As shown by the comparison on the common benchmarks, the proposed post hoc disentanglement is competitive to the current state-of-the-art in terms of existing metrics, becoming an important alternative the established "end-to-end" disentanglement. Overall, our contributions are the following:
We investigate an alternative paradigm to construct disentangled representations by ex- tracting them from con-disentangled models. In this setting, one does not need tune hyperparameters for disentanglement regularizers.
We bridge the fields of unsupervised controllable generation and disentanglement learning by using the developments of the former benefit the latter. As separate technical contri- bution, we propose a new simple technique, which outperforms the existing prior methods of controllable generation.
We extensively evaluate all the methods on several popular benchmarks employing com- monly used metries. In most of the operating points, the proposed post hoc disentanglement successfully reaches competitive performance.
2 RELATED WORK
2.1 DISENTANGLED REPRESENTATIONS
Learning disentangled representation a long-standing goal in representation learning (Bengio et al., 2013) useful for variety of downstream tasks (LeCun et al., 2004; Higgins et al., 2018; Tschannen al., 2018; Locatello al., 2019a; van Steenkiste et al., 2019). While there is no strict definition of disentangled representation, we follow the one considered in (Bengio et al., 2013): disentangled representation is a representation where a change in one dimension corresponds to the change only in one factor of variation while leaving other factors invariant. Natural data is assumed to be generated from independent factors of variations, and well-learned disentangled representa- tions should separate these explanatory sources.
The most popular approaches so far were based on variational autoencoders (VAEs). Usually, to make representations "more disentangled", VAEs objectives are enriched with specific regularizers (Alemi et al., 2016; Higgins et al., 2017; Chen et al., 2018; Burgess et al., 2017; Kim & Mnih, 2018; Kumar al., 2018: Rubenstein et al., 2018: Esmacili al.. 2019; Mathieu al., 2019; Rolinek et al., 2019). The general idea behind these approaches is to enforce an aggregated posterior to be factorized, thus providing disentanglement.
Another line of research disentangled representations is based on the InfoGAN model (Chen et al., 2016). InfoGAN is an unsupervised model, which adds an extra regularizer to GAN loss to maximize the mutual information between the small subset of latent variables (factor codes) and observations. In practice, the mutual information loss is approximated using an encoder network via Variational Information Maximization. RifoGAN-CR(LA)) et al., 2020) is a modification of In- foGAN that employs the so-called contrastive regularizer (CR), which forces the elements of the latent code proposed InfoStyleGAN model (Nie et al., 2020) incorporates similar ideas into the state-of-the-ar StyleGAN architecture, allowing for producing both disentangled representations and achieving ex- cellent visual quality of samples.
be visually perceptible and distinguishable between each other. A very recently
In contrast these approaches, we use no regularizers or additional loss functions and simply study state-of-the the-hht-r art GANs trained in a conventional manner.
2.2 CONTROLLABLE GENERATION
Based on rich empirical evidence, it is believed that the latent space of GANs can encode meaning- ful semantic transformations, such as orientation, appearance, generated images via vector arithmetic (Radford et al., 2016; Zhu et al., 2016; Bau et al., 2019; Chen et al., 2016). This means that for image produced by some latent code, such transformation can be obtained by simply shifting this latent code in a certain carefully constructed direction, indepen- dent from the chosen latent code. F.g., in the case of human faces, may have separate directions
presence of objects in scenes, of
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for such factors as hair color, age, gender. The main applications of this property have been in the field of controllable generation, ie., building software to allow a user to manipulate an image to achieve a certain goal while keeping the result photorealistic. Powerful generative models are an appealing tool for this task since the generated images lie on the image manifold by construction. To manipulate real image, the standard approach is to invert the generator, i.e., to compute latent code that approximately corresponds to the desired image, and then apply previously discovered directions (Shen al., 2020).
The discovery of directions that allow for interesting image manipulations is nontrivial task, which, however, can be performed in an unsupervised manner surprisingly efficiently (Voynov & Babenko, 2020; Shen & Zhou, 2020; Härkönen et al., 2020; Peebles et al., 2020). In the heart of these methods lies the idea that the deformations produced by these directions should be as distinguishable as much as possible, which is achieved via maximizing a certain generator-basee loss function or by training a separate regressor network attempting to differentiate between them. We thoroughly discuss these approaches further in the text. An important common feature of these methods is that they do not depend on sensitive hyperparameters or even do not have them at all, which makes them appealing for usage in unsupervised settings.
Contrary to previous applications of such interpretable directions, we attempt to show they allow us solve a more fundamental task of building disentangled representations, useful in variety of downstream tasks.
3 TWO-STAGE DISENTANGLEMENT USING PRETRAINED GANS
In this section, we discuss how disentangled representations of data can be learned with a two-step procedure. Briefly, it can be described as follows. First, we search for a of k orthogonal inter- pretable directions in the latent space of the pretrained GAN in an unsupervised manner. This step is performed via one of the methods of controllable generation described below. These directions can be considered as the first k vectors of a new basis in the latent space. By (virtually) completing it to full orthogonal set of vectors, we can obtain (presumably, disentangled) representations of synthetic points by simple change of bases and truncating all but the first k coordinates; this can be com- puted by single matrix multiplication. To obtain such representations for real data, we can now train an encoder on a synthetic dataset where targets are constructed using the procedure above. We stick to orthogonal directions for several reasons. Experimentally, it has been shown that this constraint does not significantly affect the quality of discovered directions and is imposed by construction in several further discussed methods. Additionally, it makes the formulas less cumbersome.
Reminder on style-based architectures. Traditionally, the generator network in GANs trans- forms latent code z E (0, 1) to an image x E RC* Contrary to this, style- genera- tors introduce a so-called style network, usually realized trainable MLP, which "preprocesses" random latent codes to the so-called "style vectors" (elements of the style space). The obtained style vectors are, in turn, fed into the convolutional layers of the generator. It has been shown (Karras et al., 2019) that direct manipulations over the style vectors, rather than latent codes themselves, leads to visually plausible image interpolations and image mixing results. Intuitively, the style net- work performs a "rectification" of the latent space so that the new latent codes are more interpretable and disentangled. In this paper, we work with the style-based generators and perform image edit- ing in the style space, denoted by W; its elements are denoted as w. Let us now discuss the steps mentioned above in more detail. Recall, that we are interested in finding directions n such that G(w") with w' + an performs certain interpretable deformation of the image G(w). We now thoroughly describe the existing approaches to obtaining them in an unsupervised manner as well as various hyperparameters one needs specify for each method.
3.1 DISCOVERING INTERPRETABLE DIRECTIONS
We consider several recently proposed methods: C1 closeFoor (Shen & Zhou, 2020), GANspace (Härkönen et al., 2020), LntentDi sooverccveyyy (Voynov & Babenko, 2020). Inspired by these meth- ods, we also propose another family of methods termed DeepSpectral.
ClosedForm (CF). The authors of the ClosedF orm method propose to move along the singular vectors of the first layer of generator. More specifically, for the transformation in the first layer given
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by the matrix A (e.g., this may be the weight in fully-connected or transposed convolutional layer), the direction n is found as
arg max (NER pmmm 1)
||
(1)
All local maximas of Equation (I) form the set of singular vectors of the matrix A, and the authors propose to choose & singular vectors, associated with the corresponding k highest singular values. For the byyle-baeey GANs, the matrix A is obtained by concatenating the style mapping layers of each convolutional block.
Hyperparameters: this method is hyperparameter- free and requires only pretrained GAN model.
GANspace (GS), This method searches for important, meaningful directions by performing PCA in the style space of StyleGAN. Specifically, these directions are found in the following manner: first, randomly sampled noise vectors 21:N E [O, 1) are converted into style vectors W1.N- The interpretable directions then correspond to principal axes of the set W1:N; in practice, consider top k directions according to the corresponding singular values.
Hyperparameters: for this approach, we only need to provide the number of sampled points which can be taken fixed and large, as well as a random seed for sampling.
is an unsupervised model-agnostic procedure for identifying interpretable directions in the GAN latent space. Informally speaking. this method searches for a set of directions that can be easily distinguished from one another. The resulting directions meant to represent independent factors of generated images and include human- interpretable representations.
LatentDiscovery (LD). DatentDiscoves
The trainable components are the following: matrix N Dxk and a reconstructor network R, which evaluates the pair (G(w), G(w + ((ces)) The reconstructor model aims to recover the shift in the latent space corresponding the given image transformation. These two components optimized jointly by minimizing the following objective function:
N R = arg min .k. T. L,,, R) = arg min E k.s (k, + (T, N,R
(2)
N.R
Here, .)) is a reconstructor classification loss (cross-entropy function), L,(:,)) regression term (mean absolute error). which forces shifts along found directions to be more continuous. This method utilizes number of hyperparameters: however, as was shown in Voynov & Babenko (2020), it is quite stable, and the default values provide good quality across various models and datasets. Hyperparameters: the hyperparameters include the number of latent directions and the multiplier of the reconstructor term x; additionally, we can select different architectures for the regressor, as well as different training hyperpurameters and random seed for initialization.
DeepSpectral (DS). We propose a novel approach to finding interpretable directions in the GAN latent space. Our motivation is as follows. While CF and GS both produce decent results, they effectively ignore all the layers in the generator but the first few ones. We hypothesize that by study- ing outputs of deeper intermediate layers of the generator, one can obtain richer set of directions unavailable for these methods. Concretely, we propose the following simple approach. Let G (w) denote the output of the i-th hidden layer of the generator. In order to obtain directions in the latent space, we compute k singular vectors of Jam (w) with the highest singular values (at some fixed point w). Here, Jot denotes the Jacobian matrix of mapping. In way, our approach generalizes CF since linear map and its Jacobian coincide (when bias is zero). By using automatic differenti- ation and an iterative approach to computing Singular Value Decomposition (thus, we do not form the full Jacobian matrix), such directions can be found basically instantly (Khrulkov & Oseledets, 2018). The only hyperparameters in this approach are the choice of the layer and the choice of the base point w compute the Jacobian. We experimentally verify the benefits of DS by considering various intermediate layers in Section 4.
Hyperparameters: we need to specify the layer and the base point
Another recently proposed method (Peebles et al., 2020) searches for interpretable directions by utilizing the so-called Hessian penallty, penalizing the norm of the off -if-diagonal elements of the Hessian matrix of a network. However, in our implementation, we were not able to obtain convincing results; plan to analyze in the future with the authors' implementation when released.
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3.2 LEARNING DISENTANGLED REPRESENTATIONS
We now discuss our approach to learning disen- tangled representations of a real dataset X. We start by training GAN on X, and finding a of k interpretable orthogonal directions of unit length. We stack them vertically into a matrix N E IR Dxk obtained directions are already orthogonal; other methods can be augmented with this con- straint by performing the QR projection (Pee- bles et al., 2020) parametrizing N via the matrix exponential (Voynov & Babenko, 2020). The obtained directions span "disentangled subspace" of W, with the basis formed by the columns of N. By projecting latent code onto this space and finding its components in this basis, we obtain new representation of the latent code, where ideally each coordinate rep- resents an individual factor of variation. The resulting k-dimensional representation can be easily computed as w N, where we utilized orthogonality of N. Note that this procedure is equivalent to first completing to an arbitrary orthogonal basis in the entire space RRD, and after the change of coordinates omitting all but the first & informative components, in the spirit of the PCA projection.
W
G(w)
In several methods (DS, CF, GS)
B1
B(Giw): 0)
[n nal N
Figure I: A visualization of our algorithm in the case of two interpretable directions n, and n2.
To obtain such representations for real data, we perform the following step.
We start by constructing large synthetic dataset X Xgen {w;, G(w:)) with w, being style vectors. The k-dimensional disentangled codes representing the images G(w,, are then computed N. We now train encoder network E(x; 8) RCXHXX + I by minimizing the following loss function:
[()) Ex,.. ((G((w:); -w
(3)
This approach is similar in spirit to generator inversion (Abdal et al., 2019; Zhu al., 2020; Creswell & Bharath, 2018; Zhu et al., 2016), which is known to be challenging problem and typically re- quires sophisticated algorithms. sonably well without any particular tweaks, probably due to the fact that the modified latent codes wN represent informative image attributes that are easier to be inferred.
our experiments, however, we were able to train encoders rea-
Hyperparammetrs: to train the encoder, need to fix the network architecture and training pa- rameters; it is also affected by the random seed for initialization. We also need to choose the value of N and sample N training points.
Summary. Let briefly summarize the proposed procedure to obtain disentangled representa- tions of a dataset.
1. Train non-disentangled GAN generator G on the dataset.
2. Obtain set of l: interpretable orthogonal directions of unit length in the latent space with one of the previously described methods; assume that they are arranged matrix IR Dxk
3. Train encoder E' synthetic data to predict the mapping G(w) + WN.
EXPERIMENTS
In this section, we extensively evaluate the proposed paradigm in order to assess its quality and stability with respect to various method hyperparameters and stochasticity sources. To achieve this, perform extensive sweep of random seeds and controllable generation methods and evaluate the obtained encoders with respect to multiple metrics. All our code and models are available at https: / //bit. t. 1y/ pb6dW.
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4.1 EXPERIMENTAL SETUP
Datasets. We consider the following standard datasets: 3D Shapes consisting of 480, 000 im- ages with 6 factors of variations (Burgess & Kim, 2018), MPI3 consisting of 1, 036, 800 images with 7 factors (Gondal et al., 2019) (more specifically. we use the toy part of the dataset), Cars 17, 568 images with 3 factors (Fidler et al., 2012; Reed et al., 2015); we resize all images to 64 x 64 resolution. We also study the recently proposed Isаaс3D dataset (Nie et al., 2020) con- taining 737, 280 images with factors of variations; images are resized to 128 x 128 resolution.
Model. We the recently proposed StyleGAN 2 model (Karras al., 2020) and its open-source implementation in Pytorch from github². Importantly, we fix the architecture and only vary the random seed when training models. For all datasets, we use the same architecture with 512 filters in each convolutional layer and the style network with 3 FC layers. The latter value was chosen based on experiments in Nie et al. (2020). For Isaac3D, we perform a more of a proof-of-concept experiment by training a single GAN model and varying only random seeds and hyperparameters when training encoders. We employ truncation with a scale of 0.7 for Isaac3D and 0.8 for other datasets; we did not tune these values and selected them initially based the idea that more realistic looking samples are beneficial for training the encoder, and the fact that Isaac3D is a more chal- lenging dataset. In Appendices A and B provide specific values of remaining hyperparameters, architecture and optimization details.
Disentaglement methods. We consider the four previously discussed methods, namely, CF, GS, LD and DS. For a fair comparison with VAEs in Locatello et al. (2019b;a); van Steenkiste et al. (2019), we use
for each method, i.e., we learn 10-dimensional representations of data. We use the following hyperparameters for each method.
GS: We fix . = 20, 000 and sweep across random seeds for sampling.
LD: We use the authors' implementation available at github with default hyperparameters and backbone; train it for 5, 000 iterations and sweep across random seeds.
DS: We consider the outputs of first convolutional layers resolutions 32 and 64, and the output of the generator; we average the results obtained for each of these layers. For the base point, we decided simply fix it to the style vector we corresponding to 0 E Z.
Recall that CF does not require any hyperparameters. As a separate minor experiment, we provide examples interesting directions found with our DS method in latent spaces of various righ-resolution StyleGAN 2 models in Appendix E.
Encoders. For each set of directions discovered by each method, we train the encoder model as described in Section For the first set of datasets, we use the same four-block CNN considered in Locatello et al. (2019b); specific details are provided in Appendix A. For Isaac we consider ResNet18 backbone (He et al., 2016), followed by the same FC net as in the previous case. We use 500, 000 generated points as the train set and sweep across random seeds.
Disentanglement metrics. We compute the following metrics commonly used for evaluating the disentanglement representations learned by VAEs: Modularity (Ridgeway Mozer, 2018) and Mu- tual information gap (MIG) (Chen et al., 2018). We adapt the implementation of the aforementioned metries made by the authors of Locatello al. (2019b) and released at github". We use 10, 000 points for computing the Mutual Information matrix.
Modularity measures whether each code of learned representation depends only on one factor of variation by computing their mutual information. MIG computes the average normalized difference between the top two entries of the pairwise mutual information matrix for each factor variation.
Abstract reasoning. Motivated by large-scale experiments conducted in van Steenkiste et al. (2019), we also evaluate our method on the task of abstract reasoning.
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In abstract reasoning task, a learner is expected to distinguish abstract relations to subsequently re-apply it to another setting. More specifically, this task consists of completing a x 3 context panel by choosing its last element from 3 x 2 answer panel including forming Raven's Progressive Matrices (RPMs) (Raven, 1941).
right and five wrong answers
We conduct these experiments Steenkiste et al. (2019) to generate difficult task panels. An example of such task panel is depicted in Figure For this experiment we utilize the the open-source" implementation of Wild Relation Network (WReN) (Santoro et al., 2018) with default hyperparameters. The encoder is frozen and produces 10-dimensional representations, which in turn are fed into WReN.
the 3D Shapes dataset and use the same procedure in van
Fairness. Another downstream task, which could benefit from disentangled representation, is learning fair predictions (Locatello et al., 2019a). Machine learning models inherit specifics of data, which could be collected in such a way that it can be biased towards sensitive groups caus- ing discrimination of any type (Dwork et al., 2012: Zliobaite, 2015; Hardt et al., 2016; Zafar et al., 2017; Kusner et al., 2017; Kilbertus et al., 2017). Similarly to Locatello et al. (2019a), we evaluate unfairness score of learned representations, which is the average total variation of predictions made on data with the perturbed so-called sensitive factor value.
Random seeds. For each of the first three datasets, we train eight GANs by only varying the initial random seed; for Isaac3D train single model. For each generator, then evaluate each method for five initial random seeds.
4.2 KEY EXPERIMENTAL. RESULTS
Our key results are summarized in Figures 2 and 3 and Table For each dataset and each method, report the Modularity and MIG scores obtained using our approach. We compare our results with the results in the large scale study of disentanglement in VAEs (Locatello et al., 2019b, Fig- ure 13). Note that Locatello et al. (2019b) evaluate various models by fixing all the architecture and optimization details and only varying regularization strength for each method, as well as random seeds. Thus, the setup is close to ours. Results are provided there in the form of violing plots; the actual numerical values are available only for Ca CD. Detailed comparison on this dataset is provided at Figure
We observe that all the methods are able achieve disentanglement scores
Stopm
3
1/0-
0.95
Modularity
100+
0.90
030
0,90
0.25
0.99
03-
0.5
0.35
02-
0.-
MIG
03-
0.30
0.85
Figure 2: Modularity and MIG scores (higher is better) obtained for various encoders and datasets trained via the two-stage procedure as described in Section 3 for StyleGAN 2. We observe that a) average results are on par or outperform most of the VAE-based models (Locatello et al., 2019b) b), on the other hand, for many methods, approach provides smaller variance; the variance is due to random seeds in generators and encoders, see Section
competitive with the scores reported for VAE-based approaches, see Locatello et al. (2019b, Fig- ure 13). E.g., on Cars3D, the average score of CF in terms of MIG exceeds the highest average
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Cars3D
Total
Best mean
0.23
MIC
0.15
6.55
Fecoeble
Fastrrder
D8 -0--
(a) Ours
VAEs
A Aggregated
Figure 3: Comparison of our MIG scores on Cars with various VAE based approaches; numbers are provided by the authors of Locatello et (2019b). Total denotes the entire distribution of VAE scores with respect to the typerparameter/seed space; For Best mean for each VAE-based method, we select a single best hyperparameter according to the mean (over random seeds) MIG value and plot the distribution only with respect to seeds. For (c), we plot the distributions of MIG over all configurations (method, seed, hyperparameters).
Dataset
Method
Cars3D
3D Shapes
MPI3D
Isaac3D
GS
0.143 =0.029
0.188 #0.070
0.160 #0.022
0.190 =0.01
CF
0.137 20.017
0.216 40.073
0.198
0.448 10.005
DS
0.098 20.058
0.398 10.086
0.155 #0.053
0.352 =0.07
LD InfoStyleGAN
0.107 40.050
0.160 40.061
0.073 #0.039
0.140 =0.013
0.328 =0.05 00.057
InfoStyleGANs
0.404 =0.085
Table I: We provide mean and standard devations of MIG for each method and for each dataset. InfoStyleGAN and InfoStyleGAN* correspond to models of various capacity (large and small) as specified in (Nie et al., 2020). For the first three datasets randomness is due to random seed both in generators and encoders; for Is the generator is fixed and we only vary the random seed and hyperparameters when training encoders.
score for all the competitors. Notice that the variance due to randomness tends to be smaller than for VAEs, and we able to consistently obtain competitive disentanglement quality. CF and GS tend to be more stable on average, while DS is capable of achieving higher scores but is less stable. In many cases, VAEs underperform for a large portion of the hyperparameter/seed space. Figure 3 (c) also provides the distributions of MIG values aggregated over random seeds, hyperparameter val- and methods, demonstrating that scores achieved by the post-hoc disentanglement generally higher.
While the MPI3D was not studied in Locatello al. (2019b), note that our MIG values comparable with carefully tuned VAE models achieving the best results in "'NeurIPS 2019 disen- tanglement challenge"* We also note that our DS method performs reasonably well by achieving the highest possible results on all the datasets and the best average result on 3D Shapes. It appears that LD struggled reliably uncover factors of variations. One possible reason is that we searched only for 10 directions, while unlike other methods, it does not have appealing property allowing us to select top & directions with respect to some value, c.g., as in the PCA case. A possible solution to that might be discovering new approach of the unsupervised selection of the best directions from a large set of candidates.
In Table we also provide results for Isaac3D, Interestingly, with the CF method, to achieve MIG competitive with InfoStyleGAN and outperform InfoStyleGAN, This suggests that auxiliary regularizers may not be necessary, and the latent space of StyleGANs is already disentan- gled to a high degree.
able
For the methods achieving the best results terms of MIG, we provide the corresponding Mutual Information matrix in Appendix D and visualize latent traversals in Appendix C.
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4.2.1 ABSTRACT REASONING AND FAIRNESS
We now verify whether the learned representations can be utilized for abstract reasoning tasks. We also verify the fairness of these representations, as previously discussed. See Figures and for the results. Note that our method allows for training abstract reasoning models with consistently high accuracy (e.g., mostly exceeding 95% in the case of CF). These results are competitive with VAE- based models van Steenkiste al. (2019, Figure 11); however, the difference is hard to estimate quantitatively the numerical results are not provided there. Similarly, we find that in terms of unfairness. our method finds the representations with the distribution of scores comparable those produced by VAEs, see Locatello al. (2019a, Figure 2): however, the variance for methods smaller in all the cases. On average, the VAE methods are slightly better on 3D Shapes and slightly worse Cars3D.
?
Figure 4: (Left) An example of the abstract reasoning task. The goal of the learner correctly choose the correct answer (marked with green in this example) from the answer panel, given the context panel. (Right) Accuracy obtained by training WReN with the (frozen) encoders obtained using one of the discussed methods. In most of the cases, we reliably obtain sufficiently high accuracy value.
Shapes
Cor33D
Aggregated
0.225
0.00
0.31
0.155
Unfairness
0.8
0.000
0.14
084
0.12
0.00
Figure 5: Distribution of unfairness scores (the lower, the better); we can observe that the scores are relatively low despite different hyperparameters and random seed setups.
Experiments on non-style-based GANs. The main bulk our experiments was conducted using StyleGANs. As proof of concept, we verify whether our method works for other non-style-based GANs, specifically, we consider ProGAN (Karras et al., 2018); all the details and experimental results covered in Appendix F. We compare DeepSpectral method to ClosedF and LatentDis wic.Diissveee scovery since these methods are the easiest to extend to non style-based GANs. The obtained results are slightly inferior StyleGAN 2, and attribute this behavior to the larger gap between real data and ProGAN samples compared to StyleGAN 2 samples. Since the encoder our scheme is trained the synthetic data, the quality of samples crucial.
CONCLUSION
In this work, we proposed new unsupervised approach to building disentangled representations of data. In a large scale experimental study, we analyzed many recently proposed controlled generation techniques and showed that: (i) Our approach allows for achieving disentanglement competitive with other state-of-the- may obstruct obtaining high quality disentangled representations in practice. A number of open questions, however, still remains. Firstly, the existence of directions in the GAN latent space almost perfectly correlated with exactly one of the factors of variations is quite surprising and requires further theoretical understanding, Additionally, there has been some evidence that linear shifts may perform subpar compared to more intricate non- con-linear deformations in a modified latent space. We leave this analysis for future work.
methods. (ii) We essentially get rid of critical hyperparameters, which

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A ARCHITECTURES
Here, we provide the model hyperparameters used in our study.
Mapping Network
(FC n.mip) latent dim x latent dim
Synthesis Network
(4x4 Conv) 3x3x width width
(4x4 Conv) 3x3x width width
(8x8 Conv) 3x3x width X width
(8x8 Conv) 3x3x width width
(16x 16 Conv) width x width
(16x16 Conv) 3x3x width width
(32x32 Conv) 3x3x width width
(32x32 Conv) 3x3x width x width
(64x64 Conv) 3x3 width width
664x64 Conv) 3x3x width X width
(a) Generator
(64x64 Conv) 3x3x width x width
(64x64 Conv) 3x3x width x width
(32x32 3onnw/333xxwitthhxwdhhhh
(32x32
(16x16 Conv) (ttp)//Xwxxxwwiwiidi..
(16x 16 (xnn))33x3xwiddhhxxidr
(8x8 3xnn)))33xxidt
(8 Conv) 3x3xwidthxwidth
(4x4 Conv) 3x3 x width x width
x4 Conv) 3x3 (width width
(4x4 FC) (16 -width) x width
(4x4 FC) widthxl
(b) Discriminator
Table 2: Generator and discriminator architectures for the StyleGAN 2 models for generating the
image of resolution 128 128. "FC xn_mlp" denotes numlp dense layers; "2* x 2 Conv" denotes the convolutional layers in the 2* resolution block. For resolution x 64, the first block in the discriminator and the last block in the generator are omitted.
Conv 4 x 4 x 3 x 32, stride=2
ReLU
Conv 4 x 4 x 32 x 32, stride22
ReLU
Conv 4 x 32 64, stride22
ReLU
Conv 4 4 64 64, stride=2
ReLU
FC 1024 f_size
ReLU
FC f.size x 10
Table 3: Encoder architecture used in our experiments. f fisize is 256 for 3D Shapes and MP M3D, and 512 for Cars3D and Tsaac3D. For Isaac3D the convolutional block is replaced with ResNet18 without the last classification layer.
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B HYPERPARAMETERS
Here,
we provide the training hyperparameters for StyleGAN 2, encoders and WReN.
Parameter
Value
iter
200000 for Isaac3D and 300000 for other datasets
batch
32
n_sample
64
size
128 for Isaac3D and 64 for other datasets
rl
10
path.regularize
2
path.batch.shrink
2
d reg every
16
g reg every
4
mixing
0.9
1r augment augment-p
0.002
False
0
ada.target
0.6
ada_length
500000
latent_dim
512
n_mpp
3
width
512
truncation
0.7 for Isaac3D and 0.8 for other datasets
mean_latent
4096
input.is.latent True
randomize.noize
False (for evaluation)
Table 4: Training hyperparameters of the StyleGAN model. Our implementation is based on modified it pass the
https: / //////tttttt tigttuub.... com/ ros http/rosiinallll iessinalitte ial Sereylegan2-pytee number of filters (width) for convolutional layers and the latent dimension as hyperparameters.
Table 5: Training hyperparameterrs for encoders. Table 6:
Training hyperparameters for WReN when solving the abstract reasoning tasks.
Parameter
Value
Batch size
128
Parameter
Value
Optimizer
Adam
Batch size
32
Adam: betal
0.9
Optimizer
Adam
Adam: beta2
0.999
Adam: betal
0.9
Adam: epsilon
1c - 8
Adam: beta2
0.999
Adam: learning rate
0.001
Adam: epsilon
le
Training epochs
20
Adam: learning rate
0.0001
Learning rate decay: step size
10
Training steps
100000
Learning rate decay: gamma
0.5
Learning rate decay: step size
10
Latent space dim:
10
Learning rate decay: gamma
0.5
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C LATENT TRAVERSALS
In this section, we visualize traversals of the latent space for the best model (in terms of MIG) on each dataset. Best viewed in color and zoomed.
Figure 6: Latent space traversal for 3D Shapes. We observe that all directions are almost perfectly disentangled, except for shape (6th row) and scale (5th row).
Figure 7: Latent space traversal for Cars3D. In principle, all the factors of variation (two rotations and car model) were captured, however, we can observe some entaglement.
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3
3
8
8
8
8
8
3
Figure 8: Latent space traversal for MP I3D. We observe that samples are of excellent visual quality, and found directions reasonably disentangled, except for shape and scale (5th row), and camera height and shape (Ist row).
Figure 9: Latent space traversals for Iseac3D (selected directions). appears that texture varia- tions, e.g., lighting, color, shape are easier to be inferred than 'physical" directions, such as the robot handle rotations.
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D WHICH FACTORS MODELS LEARN?
Let us now briefly analyze what factors of variations seem to be the easiest for our models to infer. For this plot the Mutual Information matrices obtained for the best of our models. It seems that the texture-based factors are easier to learn, while the discovery of physical features is more challenging.
CarclD
Figure 10: Mutual information matrices for various methods and datasets obtained for the model with highest overal MIG score; a higher value indicates stronger mutual information.
2
Figure 11: Mutual information matrix for the best method on the Isaac3D dataset.
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E LATENT TRAVERSALS FOR LARGE SCALE MODELS
In this section, we visually inspect the interesting directions found by our method on the high-resolution GAN models. We checkpoints available https: /tt:://ggttbbb// com/ justinpinkney/ hawerney/awwsoeeeeeee http://wwwweeeeeeeeeeeeeeeeee "pretrained" styleegn2s from top to bottom the datasets are: LSUN Church, FFHO, Anime portraits.
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2
2
2
2
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F EXPERIMENTS ON PROGAN
In this section we briefty describe our experiments with the non-style based GAN model, namely, study ProGAN. We conduct experiments on the 3D Shapes dataset. We used the code available at https: : / /ggitub....// com/a cww/akooocnnaaeaa /tt///aaniiaappxpaaaaaaa wwaaiima/proogaa__pppee ppo._gan_pytorrc.. We trained the default model for 2 epochs resolutions 16, 32 and for 4 epochs resolution 64 (this was sufficient for model to converge since the dataset is extremely large); we used batch size 128. We consider three methods, most easily adapted the non-style generators: CF, DS and LD. For CF used the first ConvT r ransposedd layer, and for DS we considered the outputs of convolutional blocks at resolutions 16, 32 and 64. LD works with this setup out of the box. Results are provided in Table 7. We see that the best obtained MIG score for this model roughly matches the average result of the CF, GS and LD methods for StyleGAN models, however, outperformed by the DS in many cases.
Metrics
Method
MIG
Modularity
DS
0.138 #0.009
0.900 =0.018
CF
0.110 10.009
0.927 10.017
LD
0.106 10.026
0.940 10.032
Table 7: The experimental results for Shapes dataset with the ProGAN model.
21


Reviews:
[{"review_id": "ut55ugwtFsA", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper proposes a method to learn disentangled representations. The idea is to use an existing GAN generator and use an existing controllable generation algorithm (such as ClosedForm or GANspace) to find a set of “important” directions in the latent space. These subspaces spanned by these directions could already represent disentangled factors of variation.  The main contribution of the paper is to propose learning a mapping from input to this subspace (that inverts the generator). \n\nPro:\n\nThe empirical evaluation shows that the unsupervised controlled generation methods are able to find a set of directions in the latent space that represent disentangled factors of variation and can achieve on-par performance on standard disentanglement benchmark datasets. \n\nThe experiments are fairly comprehensive (with multiple datasets, and several controllable generation methods)\n\nCon:\n\nThe success of the approach depends on whether the original algorithm (such as Closedform or GANspace) is able to find disentangled subspaces. If I understand correctly the paper only proposes to invert the generation process from the disentangled subspace (which is learned by existing methods) to the image. This somewhat limits the novelty. (Though I think the empirical finding that existing controllable generation algorithms also work well for disentanglement is also interesting) \n\nThe writing seems fairly unpolished. For example, it took some effort to understand that the authors are defining a new basis with columns of A, and the vectors w_i are defined under the coordinate system of the basis. These should be formally defined and clearly stated to avoid ambiguity. As another example, it is unclear what “sources of randomness” means. Sometimes this refers to hyper-parameters, while other times this refers to the randomly sampled variables used in the algorithm. \n", "extra_scores": {}, "extra_text": {}}, {"review_id": "tbHfSI_mCIB", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "### Summary\n\nThis paper proposes a non-conventional approach to learning disentangled representations through finding interpretable directions in the latent space of a pre-trained Style-GAN (Karras et al., 2018). To find these directions, several existing techniques from the recent literature on controllable image generation are considered. To apply this technique to existing (real) images, an encoder network is trained on the generated images to learn a mapping  from images to disentangled representations.\n\nAs the main contribution it is shown how this approach allows one to recover disentangled representations on several standard datasets, which perform similar to conventional techniques for learning disentangled representations based on VAEs. Nonetheless, the paper argues that this approach is preferred since it does not rely on hyper-parameter tuning using ground-truth factors, which is typically necessary for conventional approaches (Locatello et al., 2018). Finally, the paper also contributes its own approach for discovering interpretable latent directions, but which is a simple heuristic derived from the “ClosedForm” method proposed by Shen & Zhou (2020). \n\n### Pro’s / Con’s / Justification\n\nThe paper is reasonably well written, although I should note that it violates the required style guide for formatting paragraphs. By my count this paper would otherwise have exceeded the page limit of 8 pages by about 22 lines and I have previously reached out to the AC about this. \n\nI am somewhat conflicted about the significance of the contribution. On the one hand, I like the approach as an alternative to VAE-based approaches and I think that it is valuable to connect the field of disentangled representation learning with the field of controllable image generation. On the other hand, the insight that there is a correspondence between interpretable latent directions and disentangled factors of variation is not new as is evident from the recent literature cited here. Indeed, I would argue that the main contribution is simply the application of these techniques to a standard benchmark for learning disentangled representations. Here I also note that the proposed approach for going from disentangled representations for generated images to disentangled representations for real image is trivial. Nonetheless I would still consider the application itself to be a significant contribution. However, the current experiments are incomplete and have several other issues, which I will comment on next. \n\nFirst, I note that while the paper claims to investigate an alternative route to learning disentangled representations based on “state-of-the-art GANs”, only two variations of Style-GAN are considered. This is problematic, since it leaves it unclear to what extent the evaluated approach applies to other GANs. For example, were it found that the same techniques do not yield disentangled representations for other GANs, one would end up in the very same situation as when using conventional (VAE-based) approaches, namely by having to use ground-truth factors of variation to perform model-selection. Since this is the main argument as to why the proposed approach is preferred it is vital that this is investigated.\n\nSecond, and related to this, is the quality of the provided comparison to VAE-based approaches. The reader is required to compare the boxplot in Figure 1 to the violin plots in Figure 13 in Locatello et al. (2018). Other than this being far from ideal and only allowing for a rough comparison, it is not clear to me that these results can be compared since Locatello et al. (2018) reports an average that additionally includes six different regularization strengths for the VAE-based methods. While it can be argued that this is a limitation of the VAE-based approach (i.e. having to consider multiple regularization strengths) it is not clear to what extend the style-based generators, the choice of encoder, and the hyper-parameters of the various techniques for discovering latent directions considered (such as the number of latent directions to search for) here are already “optimal” for these problems (in which case they should also be varied to allow for a fair comparison). Moreover, the results for “DeepSpectral” are reported separately for each choice of layer, while they should be aggregated into a single score to allow for a fair comparison. I note that in that case, the results don’t look all that convincing. “GS” works well on some datasets, but worse on others, “DS” has large variance on all datasets and performs average, “CF” has large variance and mixed results for MIG across data sets, and “LD” generally tends to perform bad. Can it really be argued that the GAN-based approach is more stable and does not require model-selection from these results? Certainly there is no clear best method for interpretable latent discovery. It is also not clear how the size of the interval for the regularization parameter in Locatello et al. (2018) compares to that explored for DS. To facilitate a better comparison I would argue that a comparison of various VAEs having the _optimal_ regularization strength, to the reported results when using pre-trained GANs is needed. I would also like to see the authors aggregate results across methods for interpretable latent discovery and compare that to an aggregate over possible VAEs (and regularization strengths). Based on the reported results I would expect the variance to be equally large in both cases, which would leave it unclear whether this pre-trained GAN-based approach is preferred.\n\nMy final concern regarding the experimental evaluation is concerned with the results presented in section 4.2.1, where the learned representations using the approach presented here are applied to abstract visual reasoning tasks and to a fairness task. These tasks were used to demonstrate the benefits of representations that are disentangled, but here they are used to validate the learned representation. For example, Figure 2 is compared to Figure 11 in van Steenkiste et al. (2019) and it is observed that the representations acquired from pre-trained GANs are better than VAE-based representations by comparing the spread. However, the “pre-trained” line in Figure 11 in van Steenkiste et al. (2019) only contains a random selection of representations learned by VAEs _without_ considering their disentanglement. Hence, it is not clear what can be concluded from this other than that more disentangled representations perform better on this task, but this was already observed in  van Steenkiste et al. (2019).\n\nThe remaining contribution that is “DeepSpectral” currently feels ad-hoc and more of a heuristic, even though there is a correspondence to GS in the linear case. One reason for this is that it performs about average in all cases and has relatively large variance (if averaging across the main hyper-parameter). Perhaps this part of the contribution can be strengthened by providing additional analysis, why this is a reasonable approach, i.e. by analyzing its behavior in the linear case where there is a correspondence. It could also be useful to see whether the number of layers can be chosen dynamically based on some internal statistic, but that does not require ground-truth disentanglement factors. \n  \n\n### Detailed comments\n\n* The title is too broad and not very informative. Please narrow it down to using pre-training GANs and methods for latent direction discovery\n\n* It is often claimed that by using the latent-discovery approach one gets rid of essentially all critical hyper-parameters. However, there is not enough evidence provided that the remaining hyper-parameter values chosen do not affect the quality of the discovered representations. For example, the base point in GS is always fixed. Similarly, for LD only default hyper-parameters are used and the effect of the regularization parameter is not explored.\n\n* W is sometimes used to refer to weights (eg. in the first layer of the transformation) and other times to the latent space learned by style GAN from which interpretable directions are recovered. I think in the “ClosedForm” paper they use A in place of W for the network weights, which may be more clear. \n\n* In general, please report the full experimental details used, even though they are the “default values”. For example, currently it is unclear to me how many training steps were sed to obtain the results in Figure 2.\n\n* Please take a moment to go through the references and correctly cite papers that have been published.\n\n### Post Rebuttal\n\nI have read the other reviews and the author's response. I also had another look at the revision. While I appreciate the work that was put in the revision, my main concerns remain:\n\n* This paper proposes an alternative to VAE-based approaches to learning disentangled representations, which are known to require hyper-parameter selection based on ground-truth factors (as pointed out in Locatello et al., 2019). Hence, to improve over VAEs in this regard, it is crucial that the proposed framework does not suffer from this same issue or least consistently performs better compared to VAEs. Unfortunately this is simply not the case: across Figure 2 and Table 1 there is no variation (among CF, GS, DS, LD) that consistently performs well or consistently outperforms VAEs. Similarly in Figure 3c it can be seen how the GAN-based approach and VAE-based approach perform similarly (especially if the outliers on the top would be included in the mean). Similar fluctuations can essentially be observed across all figures and which does not take into account yet the choice of GAN or other hyper-parameters that were kept fixed (as per my initial review). Further, notice how in Table 7 (when using ProGAN as opposed to StyleGAN), the best performing variation (DS) now performs more than 50% worse according to MIG -- which is not factored in the comparison to VAEs.\n* The abstract visual reasoning experiment is flawed, since the comparison to van Steenkiste et al. (2019) figure 11 considers a random selection of pre-trained VAEs for which it is unclear whether they were disentangled or not.\n* DS is a simple heuristic that generally does not outperform other approaches. Indeed, notice how not reporting the results for DS separate for each layer (as was done previously) now results in large fluctuations. In particular, for the four datasets considered in Figure 1 DS outperforms other methods only on 3D shapes. Further, although the authors in their rebuttal argue that DS is not a simple heuristic since they “build [DS] on the intuition that singular vectors of the Jacobian provide a set of locally ``independent directions with respect to the perceptual metric”, there is no evidence provided that this intuition is correct. I had suggested ways according to which this part of the contribution could be strengthened (i.e. by analyzing it in the linear case, or attempting to automatically select a good layer) but this was not further explored.\n\nI do think that there is significant value in a systematic analysis of GAN-based approaches applied for disentanglement in this way, as it could serve as a useful benchmark for existing (VAE-based) approaches to compare against. However, the current set-up falls short at this as it is not sufficiently systematic and certain variations remain insufficiently unexplored (like other kinds of GANs). Further, this is not how this work is currently motivated in the paper or how the comparisons are performed.\n\nThese concerns are irrespective of whether the reader needs to perform a manual comparison to Locatello et. al (2019). Although I noted in my review that this is far from ideal, I can understand how this may be necessary if Locatello et al. (2019) can not provide a smaller range of hyper-parameters. In that sense, I believe that the authors did a good job incorporating VAE results at such short notice.", "extra_scores": {}, "extra_text": {}}, {"review_id": "PcgyaVdEX7g", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "[Summary]\nThis paper proposes a new approach to learn disentangled representations from Generative models that were trained without a loss that explicitly enforces disengagement. The motivation behind this work is to address the computational time cost regarding hyperparameter tuning that is typically required for VAEs trained with a disentangled loss. The proposed approach can be summarized in 3 steps: (1) Training a GAN (in an unsupervised way) (2) Find  ‘k’ new basis vectors in ‘W’ space (3) Train a new encoder on the synthetic dataset {(z,G(z))} with loss that encourages the encodings to correspond to the subspace spanned by the basis vectors. Furthermore, the authors propose a new approach for identifying meaningful basis vectors which the authors claim that it is the generalized version of ClosedFrom. For evaluation, the authors then perform a set of experiments involving disentanglement, abstract reasoning, fairness on a variety of datasets such as 3Dshapes, MPI, and Cars3D. \n\n[Clarity]\nOverall, I think the paper reads well. I would however encourage the authors to add a background section that maybe explains a bit more regarding disentanglement, controllable generation, and in particular the style gan generator. The related work section touches on some of these, but not enough in my opinion.  \nAs an example, I am personally not familiar with the GAN literature including the architecture of StyleGan decoder so I had to go and read [1] to see what is the difference between Z-space and W-space and what is the mapping. \n\nClarification on notation: In the related work section, the vector arithmetic is written as “z’ = z + a * n”. In the methodology, it is written as “w’ = w + a * n”. Is this just a change in notation, or ‘w’ here corresponds to the W-space? (If this is the case, why ‘w’ is later referred to as sample noise vectors. Also this doesn’t match the methodology Section in [2]). \n\n[Main Comment]\nOverall, I find the idea behind this paper quite interesting. While it is relatively simple and straightforward to implement, the idea of learning a disentangled representation from an entangled latent  is novel and makes sense.\n\nRegarding the experiments section,  I applaud the authors for doing the fairness and abstract reasoning experiments in addition to reporting standard disentanglement metrics. I would however encourage the authors to directly compare with disentangled VAE baselines. While the caption Fig 1 claims that the results are better, the VAE results are not reported here. (I had to double check the results in [3] to make sure the results are indeed better). \n\nOne key weakness of their approach is that it relies on training the encoder based on ‘generated’ samples. This could mean that the proposed approach might not be very effective for models where the latent space might be reasonably disentangled, but the generated samples don’t look good (maybe blurry), given that the encoders job will presumnaly get harder as sample quality gets worse. However, as the authors state, this approach certainly can be applied for existing GANs that are known to generate high fidelity images. \n\n\n[Questions]\n- As far as I can see, this approach is not specific to GANs and can be applied to the latent space of VAEs as well. I’m wondering about the results from applying this approach to a trained VAE with a style gan decoder. Could the authors explain the focus on GANs?\n- Could the authors elaborate on the proposed approach with the impossibility result in [1]. While the results suggest that we indeed were successful in learning a disentangled representation, it is not clear to me what inductive bias (or supervision) are we imposing here that encourages disentanglement. Is it simply the empirical evidence regarding controllable generation on GANs?\n- It is unclear to me how the authors computed singular vectors at the deeper convolutional layers. Computing the Jacobian does not sound like an easy computation, and heavily depending on the base point in this case. Could the authors elaborate on this? \n\n[References]\n[1] Karras, Tero, Samuli Laine, and Timo Aila. \"A style-based generator architecture for generative adversarial networks.\" Proceedings of the IEEE conference on computer vision and pattern recognition. 2019.\n[3] Shen, Yujun, and Bolei Zhou. \"Closed-Form Factorization of Latent Semantics in GANs.\" arXiv preprint arXiv:2007.06600 (2020).\n[3] Locatello, Francesco, et al. \"Challenging common assumptions in the unsupervised learning of disentangled representations.\" international conference on machine learning. 2019.\n\n\n-------------\nUPDATE\n-------------\n\nI thank the authors for their response. The revised version certainly looks better. I'm still happy to recommend this paper for acceptance. \n", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper evaluates the extent to which disentangled representations can be recovered from pre-trained GANs with style-based generators by finding an orthogonal basis in the space of style vectors, and then training an encoder to map images to coordinates in the resulting latent space. To construct the orthogonal basis, the authors consider 3 recently proposed methods for controllable generation, along with a newly developed generalization of one of these methods. The authors evaluate metrics for disentanglement for 4 datasets, consider an abstract visual reasoning task, and compute unfairness scores.

Reviewers expressed diverging opinions on this paper. R2 is in support of acceptance,  R3 finds the paper borderline but is leaning towards acceptance, whereas R4 is critical. R2 and R4 engaged in a relatively detailed discussion, but maintained their scores. 

Having read the paper, the metareviewer feels this submission indeed has strengths and weaknesses. On the one hand, the main results are notable; it is worth reporting that disentangled representations can be recovered from pretrained GANs is a relatively straightforward manner. In this context, the metareviewer feels that some comments by R4 are more critical than is warranted. The authors do not necessarily have to show that GAN-based methods uniformly improve upon VAE-based methods, either in terms of disentanglement metrics or in terms of sensitivity to hyperparameters. The main claim in this submission is that GAN-based methods are mostly comparable to VAE-based methods, and this claim is both sufficiently notable and sufficiently supported by experimental results. 

At the same time, this submission is not without flaws.  The writing is on the rough side, and as R4 notes the authors have removed all white space between paragraphs. The metareviewer also feels it is not satisfactory to show a box plot for GAN-based methods in Figure 2 and ask the reader to compare these plots to the violin plots for VAE-based methods in the Locatello paper. The authors need to find a way to make a more direct comparison here. R4's comments about the comparison in the abstract-reasoning setting are also well-taken –– here the baseline employs standard (entangled) models, so it is unclear what conclusions we should draw from this experiment. Similarly the unfairness results once again appeal to an indirect comparison to results in the  Locatello paper on this topic.

On balance, the metareviewer is inclined to say that this submission, in its current form, falls just below the threshold for acceptance. These results are clearly of note to the community and worth reporting, but the presentation has enough flaws that another round of reviews is warranted based on a revised manuscript. The metareviewer hopes to see this paper appear a conference in the (near) future. 
Decision: Reject