To establish a basis for understanding how generative models represent and transform data is an essential problem in the field of deep learning interpretation. Although, the mechanistic interpretation of discriminative architectures (e.g., transformers) has produced substantial new insights about these types of systems, there has been relatively little work on mechanistic interpretation of variational autoencoders (VAEs). VAEs are widely used for representation learning; this paper presents the first general-purpose multilevel causal intervention framework for the mechanistic interpretation of VAEs. The framework includes four basic manipulation types: input manipulation, latent-space perturbation, activation-patching, and causal-mediation-analysis. This paper also defines three new quantitative metrics that measure various characteristics of VAE internal representations that are not measured by existing disentanglement metrics alone: CausalEffect-Strength (CES), intervention specificity, and circuit modularity. We conducted the largest empirical study to date of the causal mechanisms of six VAE architectures (standard VAE, β-VAE, FactorVAE, β-TC-VAE, DIP-VAE-II, and VQ-VAE) over five different benchmark datasets (dSprites, 3DShapes, MPI3D, CelebA, and SmallNORB) using three different random seeds per architecture and dataset pair, leading to a total of 90 independent training runs. Our empirical results reveal several new findings: (i) a consistent within-dataset negative correlation between CES and DCI disentanglement, which we refer to as the CES-DCI trade-off; (ii) that the KL reweighting mechanism of β-VAE can cause a capacity bottleneck for β-VAE when the number of generative factors in a model approaches its latent dimensionality, causing a degradation of disentanglement performance on complex datasets; (iii) that no single VAE architecture will be best for all of the five datasets tested -- the optimal choice of VAE architecture is dependent upon the structure of the dataset being modeled; and (iv) that CES-based metrics applied to discrete latent spaces (VQ-VAE) yield near zero values, indicating a critical limitation of continuousintervention methods for analyzing discrete latent spaces. These results provide both a theoretical foundation and empirical evaluations of the interpretation of generative models.

We propose TopDis (Topological Disentanglement), a method for learning disentangled representations via adding multi-scale topological loss term. Disentanglement is a crucial property of data representations substantial for the explainability and robustness of deep learning models and a step towards high-level cognition. The state-of-the-art method based on VAE minimizes the total correlation of the joint distribution of latent variables. We take a different perspective on disentanglement by analyzing topological properties of data manifolds. In particular, we optimize the topological similarity for data manifolds traversals. To the best of our knowledge, our paper is the first one to propose a differentiable topological loss for disentanglement. Our experiments have shown that the proposed topological loss improves disentanglement scores such as MIG, FactorVAE score, SAP score and DCI disentanglement score with respect to state-of-the-art results. Our method works in an unsupervised manner, permitting to apply it for problems without labeled factors of variation. Additionally, we show how to use the proposed topological loss to find disentangled directions in a trained GAN.

High-dimensional clinical data have become invaluable resources for genetic studies, due to their accessibility in biobank-scale datasets and the development of high performance modeling techniques especially using deep learning. Recent work has shown that low dimensional embeddings of these clinical data learned by variational autoencoders (VAE) can be used for genome-wide association studies and polygenic risk prediction. In this work, we consider multiple unsupervised learning methods for learning disentangled representations, namely autoencoders, VAE, beta-VAE, and FactorVAE, in the context of genetic association studies. Using spirograms from UK Biobank as a running example, we observed improvements in the number of genome-wide significant loci, heritability, and performance of polygenic risk scores for asthma and chronic obstructive pulmonary disease by using FactorVAE or beta-VAE, compared to standard VAE or non-variational autoencoders. FactorVAEs performed effectively across multiple values of the regularization hyperparameter, while beta-VAEs were much more sensitive to the hyperparameter values.

The use of well-disentangled representations offers many advantages for downstream tasks, e.g. an increased sample efficiency, or better interpretability. However, the quality of disentangled interpretations is often highly dependent on the choice of dataset-specific hyperparameters, in particular the regularization strength. To address this issue, we introduce DAVA, a novel training procedure for variational auto-encoders. DAVA completely alleviates the problem of hyperparameter selection. We compare DAVA to models with optimal hyperparameters. Without any hyperparameter tuning, DAVA is competitive on a diverse range of commonly used datasets. Underlying DAVA, we discover a necessary condition for unsupervised disentanglement, which we call PIPE. We demonstrate the ability of PIPE to positively predict the performance of downstream models in abstract reasoning. We also thoroughly investigate correlations with existing supervised and unsupervised metrics. The code is available at https://github.com/besterma/dava.

Content and style (C-S) disentanglement intends to decompose the underlying explanatory factors of objects into two independent subspaces. From the unsupervised disentanglement perspective, we rethink content and style and propose a formulation for unsupervised C-S disentanglement based on our assumption that different factors are of different importance and popularity for image reconstruction, which serves as a data bias. The corresponding model inductive bias is introduced by our proposed C-S disentanglement Module (C-S DisMo), which assigns different and independent roles to content and style when approximating the real data distributions. Specifically, each content embedding from the dataset, which encodes the most dominant factors for image reconstruction, is assumed to be sampled from a shared distribution across the dataset. The style embedding for a particular image, encoding the remaining factors, is used to customize the shared distribution through an affine transformation. The experiments on several popular datasets demonstrate that our method achieves the state-of-the-art unsupervised C-S disentanglement, which is comparable or even better than supervised methods. We verify the effectiveness of our method by downstream tasks: domain translation and single-view 3D reconstruction. Project page at https://github.com/xrenaa/CS-DisMo.

This paper challenges the common assumption that the weight $\beta$, in $\beta$-VAE, should be larger than $1$ in order to effectively disentangle latent factors. We demonstrate that $\beta$-VAE, with $\beta < 1$, can not only attain good disentanglement but also significantly improve reconstruction accuracy via dynamic control. The paper removes the inherent trade-off between reconstruction accuracy and disentanglement for $\beta$-VAE. Existing methods, such as $\beta$-VAE and FactorVAE, assign a large weight to the KL-divergence term in the objective function, leading to high reconstruction errors for the sake of better disentanglement. To mitigate this problem, a ControlVAE has recently been developed that dynamically tunes the KL-divergence weight in an attempt to control the trade-off to more a favorable point. However, ControlVAE fails to eliminate the conflict between the need for a large $\beta$ (for disentanglement) and the need for a small $\beta$. Instead, we propose DynamicVAE that maintains a different $\beta$ at different stages of training, thereby decoupling disentanglement and reconstruction accuracy. In order to evolve the weight, $\beta$, along a trajectory that enables such decoupling, DynamicVAE leverages a modified incremental PI (proportional-integral) controller, and employs a moving average as well as a hybrid annealing method to evolve the value of KL-divergence smoothly in a tightly controlled fashion. We theoretically prove the stability of the proposed approach. Evaluation results on three benchmark datasets demonstrate that DynamicVAE significantly improves the reconstruction accuracy while achieving disentanglement comparable to the best of existing methods. The results verify that our method can separate disentangled representation learning and reconstruction, removing the inherent tension between the two.

Disentanglement is an enjoyable property in representation learning which increases the interpretability of generative models such as Variational Auto-Encoders (VAE), Generative Adversarial Models and their many variants. In the context of latent space models, this work presents a representation learning framework that explicitly promotes disentanglement thanks to the combination of an auto-encoder with Principal Component Analysis (PCA) in latent space. The proposed objective is the sum of an auto-encoder error term along with a PCA reconstruction error in the feature space. This has an interpretation of a Restricted Kernel Machine with an interconnection matrix on the Stiefel manifold. The construction encourages a matching between the principal directions in latent space and the directions of orthogonal variation in data space. The training algorithm involves a stochastic optimization method on the Stiefel manifold, which increases only marginally the computing time compared to an analogous VAE. Our theoretical discussion and various experiments show that the proposed model improves over many VAE variants along with special emphasis on disentanglement learning.

Recent state-of-the-art autoencoder based generative models have an encoder-decoder structure and learn a latent representation with a pre-defined distribution that can be sampled from. Implementing the encoder networks of these models in a stochastic manner provides a natural and common approach to avoid overfitting and enforce a smooth decoder function. However, we show that for stochastic encoders, simultaneously attempting to enforce a distribution constraint and minimising an output distortion leads to a reduction in generative and reconstruction quality. In addition, attempting to enforce a latent distribution constraint is not reasonable when performing disentanglement. Hence, we propose the variance-constrained autoencoder (VCAE), which only enforces a variance constraint on the latent distribution. Our experiments show that VCAE improves upon Wasserstein Autoencoder and the Variational Autoencoder in both reconstruction and generative quality on MNIST and CelebA. Moreover, we show that VCAE equipped with a total correlation penalty term performs equivalently to FactorVAE at learning disentangled representations on 3D-Shapes while being a more principled approach.

This report to our stage 1 submission to the NeurIPS 2019 disentanglement challenge presents a simple image preprocessing method for training VAEs leading to improved disentanglement compared to directly using the images. In particular, we propose to use regionally aggregated feature maps extracted from CNNs pretrained on ImageNet. Our method achieved the 2nd place in stage 1 of the challenge (AIcrowd, 2019).

The challenge of learning disentangled representation has recently attracted much attention and boils down to a competition using a new real world disentanglement dataset (Gondal et al., 2019). Various methods based on variational auto-encoder have been proposed to solve this problem, by enforcing the independence between the representation and modifying the regularization term in the variational lower bound. However recent work by Locatello et al. (2018) has demonstrated that the proposed methods are heavily influenced by randomness and the choice of the hyper-parameter. In this work, instead of designing a new regularization term, we adopt the FactorVAE but improve the reconstruction performance and increase the capacity of network and the training step. The strategy turns out to be very effective and achieve the 1st place in the challenge.