Disentangling Action Sequences: Discovering Correlated Samples

1 INTRODUCTION . The basis of artificial intelligence is to understand and reason about the world based on a limited set of observations . Unsupervised disentanglement learning is highly desirable due to its similarity with the way we as human think . For instance , we can infer the movement of a running ball based on a single glance . This is because the human brain is capable of disentangling the positions from a set of images . It has been suggested that a disentangled representation is helpful for a large variety of downstream tasks ( Schölkopf et al. , 2012 ; Peters et al. , 2017 ) . According to Kim & Mnih ( 2018 ) , a disentangled representation promotes interpretable semantic information . That brings substantial advancement , including but not limited to reducing the performance gap between humans and AI approaches ( Lake et al. , 2017 ; Higgins et al. , 2018 ) . Other instances of disentangled representation include semantic image understanding and generation ( Lample et al. , 2017 ; Zhu et al. , 2018 ; Elgammal et al. , 2017 ) , zero-shot learning ( Zhu et al. , 2019 ) , and reinforcement learning ( Higgins et al. , 2017b ) . Despite the advantageous of the disentangling representation approaches , there are still two issues to be addressed including the abstract notion and the weak explanations . Notion The conception of disentangling factors of variation is first proposed in 2013 . It is claimed in Bengio et al . ( 2013 ) that for observations the considered factors should be explanatory and independent of each other . The explanatory factors are however hard to formalize and measure . An alternative way is to disentangle the ground-truth factors ( Ridgeway , 2016 ; Do & Tran , 2020 ) . However , if we consider the uniqueness of the ground-truth factors , a question which arises here is how to discover it from multiple equivalent representations ? As a proverb “ one can not make bricks without straw ” , Locatello et al . ( 2019 ) prove the impossibility of disentangling factors without the help of inductive biases in the unsupervised setting . Explanation There are mainly two types of explanations for unsupervised disentanglement : information bottleneck , and independence assumption . The ground-truth factors affect the data independently , therefore , the disentangled representations must follow the same structure . The approaches , holding the independence assumption , encourage independence between the latent variables ( Schmidhuber , 1992 ; Chen et al. , 2018 ; Kim & Mnih , 2018 ; Kumar et al. , 2018 ; Lopez et al. , 2018 ) . However , the real-world problems have no strict constraint on the independence assumption , and the factors may be correlative . The other explanation incorporates information theory into disentanglement . Burgess et al . ; Higgins et al . ; Insu Jeon et al . ; Saxe et al . suggest that a limit on the capacity of the latent information channel promotes disentanglement by enforcing the model to acquire the most significant latent representation . They further hypothesize that the information bottleneck enforces the model to find the significant improvement . In this paper , we first demonstrate that instead of the ground-truth factors the disentangling approaches learn actions of translating based on the orientation of the images . We then propose the concept of disentangling actions which discover the commonalities between the images and categorizes them into sequences . We treat disentangling action sequences as a necessary step toward disentangling factors , which can capture the internal relationships between the data , and make it possible to analyze the inductive biases from the data perspective . Furthermore , the results on a toy example show that the significance of actions is positively correlated with the threshold of latent information . Then , we promote that conclusion to complex problems . Our contributions are summarized in the following : • We show that the significance of action is related to the capacity of learned latent information , resulting in the different thresholds of factors . • We propose a novel framework , fractional variational autoencoder ( FVAE ) to extracts explanatory action sequences step-by-step , and at each step , it learns specific actions by blocking others ’ information . We organize the rest of this paper as follows . Sec.2 describes the development of unsupervised disentanglement learning and the proposed methods based on VAEs . In Sec.3 , through an example , we show that the disentangled representations are relative to the data itself and further introduce a novel concept , i.e. , disentangling action sequences . Then , we investigate the inductive biases on the data and find that the significant action has a high threshold of latent information . In Sec.4 , we propose a step-bystep disentangling framework , namely fractional VAE ( FVAE ) , to disentangle action sequences . For the labelled and unlabelled tasks , we respectively introduce two methods to measure their thresholds . We then evaluate FVAE on a labelled dataset ( dSprites , Matthey et al . ( 2017 ) ) and an unlabelled dataset ( 3D Chairs , Aubry et al . ( 2014 ) ) . Finally , we conclude the paper and discuss the future work in Sec.5 2 UNSUPERVISED DISENTANGLEMENT LEARNING . We first introduce the abstract concepts and the basic definitions , followed by the explanations based on information theory and other related works . This article focuses on the explanation of information theory and the proposed models based on VAEs . 2.1 THE CONCEPT . Disentanglement learning is fascinating and challenging because of its intrinsic similarity to human intelligence . As depicted in the seminal paper by Bengio et al. , humans can understand and reason from a complex observation to the explanatory factors . A common modeling assumption of disentanglement learning is that the observed data is generated by a set of ground-truth factors . Usually , the data has a high number of dimensions ; hence it is hard to understand , whereas the factors have a low number of dimensions , thus simpler and easier to be understood . The task of disentanglement learning is to uncover the ground-truth factors . Such factors are invisible to the training process in an unsupervised setting . The invisibility of factors makes it hard to define and measure disentanglement ( Do & Tran , 2020 ) . Furthermore , it is shown in Locatello et al . ( 2019 ) that it is impossible to unsupervised disentangle the underlying factors for the arbitrary generative models without inductive biases . In particular , they suggest that the inductive biases on the models and the data should be exploited . However , they do not provide a formal definition of the inductive bias and such a definition is still unavailable . 2.2 INFORMATION BOTTLENECK . Most of the dominant disentangling approaches are the variants of variational autoencoder ( VAE ) . The variational autoencoder ( VAE ) is a popular generative model , assuming that the latent variables obey a specific prior ( normal distribution in practice ) . The key idea of VAE is maximizing the likelihood objective by the following approximation : L ( θ , φ ; x , z ) =Eqφ ( z|x ) [ logpθ ( x|z ) ] −DKL ( qφ ( z|x ) ||p ( z ) ) , ( 1 ) which is known as the evidence lower bound ( ELBO ) ; where the conditional probabilityP ( x|z ) , Q ( z|x ) are parameterized with deep neural networks . Higgins et al . find that the KL term of VAEs encourages disentanglement and introduce a hyperparameter β in front of the KL term . They propose the β-VAE maximizing the following expression : L ( θ , φ ; x , z ) =Eqφ ( z|x ) [ logpθ ( x|z ) ] −βDKL ( qφ ( z|x ) ||p ( z ) ) . ( 2 ) β controls the pressure for the posterior Qφ ( z|x ) to match the factorized unit Gaussian prior p ( z ) . Higher values of β lead to lower implicit capacity of the latent information and ambiguous reconstructions . Burgess et al . propose the Annealed-VAE that progressively increases the information capacity of the latent code while training : L ( θ , φ ; x , z , C ) =Eqφ ( z|x ) [ logpθ ( x|z ) ] −γ|DKL ( qφ ( z|x ) ||p ( z ) ) −C| ( 3 ) where γ is a large enough constant to constrain the latent information , C is a value gradually increased from zero to a large number to produce high reconstruction quality . As the total information bottleneck gradually increasing , they hypothesize that the model will allocate the capacity of the most improvement of the reconstruction log-likelihood to the encoding axes of the corresponding factor . However , they did not exploit why each factor makes different contributions to the reconstruction log-likelihood . 2.3 OTHER RELATED WORK . The other dominant direction initiates from the prior of factors . They assume that the ground-truth factors are independent of each other , and a series of methods enforce the latent variables have the same structure as the factors . FactorVAE ( Kim & Mnih , 2018 ) applies a discriminator to approximately calculate the total correlation ( TC , Watanabe ( 1960 ) ) ; β-TCVAE ( Chen et al. , 2018 ) promotes the TC penelty by decomposing the KL term ; DIP-VAE ( Kumar et al. , 2018 ) identifies the covariance matrix of q ( z ) . 3 DISENTANGLING ACTION SEQUENCES . For machines and humans , disentangling the underlying factors is a challenging task . For instance , there are more than 1,400 breeds of dogs in the world , and it seems impossible for an ordinary person to distinguish all of them just by looking at their pictures . The challenge in disentangling the underlying factors is mainly due to the complexity of establishing relationships without supervision , where the corresponding models should contain some level of prior knowledge or inductive biases . However , it is possible to determine the differences without having extensive knowledge . For example , one may mistakenly identify the breed of a dog by looking at a picture but is almost impossible to misrecognize a dog as a cat . Therefore , in practice , discovering the differences or similarities is often a much easier task than that of uncovering the underlying factors , and it does not also need much prior knowledge . One may conclude that discovering the commonalities between things is an important step toward disentanglement . 3.1 ACTION SEQUENCES . Action The continuous set of images over a certain direction . The observed data consists of a set of actions such as rotation , translation , and scaling . Such actions are meaningful and underlying . Therefore , the goal of disentanglement learning is to separate the underlying actions of observation . Usually , the continuous actions are infeasible for the machine learning system , and we have to convert them into some discrete and consistent sequences . Given a dataset S , we assume it consists of parameterized action sequences , and each action sequence is a subset of the dataset . We can model a parameterized action sequence as : Si ( mj , j 6=i ) =Tmj , j 6=i ( { t } ) , ( 4 ) where Si∈S denotes an action sequence , i denotes the type of actions , m denotes a parameter vector , T denotes a transformation , t denotes the step of the action . The procedure is similar to the latent traversal in Higgins et al . ( 2017a ) . Differently , action sequences describe both the real observed data and the reconstructed data : For the real observed data , m is the ground-truth factor vector , and T is the generating function ; For the reconstructed data , m is the latent variable vector , andT is a neural network . For clarity , we denote generating actions as sequences of images controlled by the ground-truth factors and action sequences as the approximation of these actions generated by a neural network . However , the neural networks are flexible enough to approximate any actions , and it ’ s tricky to infer and learn the generating actions . The marvelous thing about disentanglement learning is that the models seem to learn these actions unsupervisedly . A popular view of disentanglement believes the ground-truth factors should be separated into independent latent variables Locatello et al . ( 2019 ) ; Chen et al . ( 2018 ) . That means the learned action sequences have to match the generating actions precisely . However , ( Rolinek et al. , 2019 ) shows that the VAEs conduct a PCA-like behavior , and the models prefer to extract the principal component . Hence , the models may select some action sequences having more considerable variations and learn the significant action sequences rather than the generating actions . Using VAEs , minimizing the objective increases the overlap between the posterior distributions across the dataset Burgess et al . ( 2018 ) , and it then leads to the learned action sequences showing some internal relationships . Although ( Locatello et al. , 2019 ) suggest that the inductive biases on the models and the data should be exploited , the current researches focus on the role of the models on disentanglement Burgess et al . ( 2018 ) ; Chen et al . ( 2018 ) ; Rolinek et al . ( 2019 ) .

Summary: This paper addresses the problem of disentangling representations using Variational Autoencoders. In particular, the authors introduce the concept of disentangling action sequences and propose the fractional variational autoencoder framework to disentangle them step-by-step. To this end, they analyze the inductive biases on the data and define latent information thresholds which are correlated with the significance of the actions.