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Improving Representation Learning in Autoencoders Via Multidimensional Interpolation and Dual Regularizations Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI-19) Improving Representation Learning in Autoencoders via Multidimensional Interpolation and Dual Regularizations Sheng Qian1∗ , Guanyue Li2∗ , Wen-Ming Cao3 , Cheng Liu4 , Si Wu2y and Hau San Wong3 1Huawei Device Company Limited 2School of Computer Science and Engineering, South China University of Technology 3Department of Computer Science, City University of Hong Kong 4Department of Computer Science, Shantou University [email protected], [email protected], fwenmincao2-c, [email protected], [email protected], [email protected] Abstract Autoencoders enjoy a remarkable ability to learn data representations. Research on autoencoders shows that the effectiveness of data interpolation can reflect the performance of representation learn- ing. However, existing interpolation methods in autoencoders do not have enough capability of traversing a possible region between datapoints on a data manifold, and the distribution of interpolated Figure 1: In ACAI (left), only one interpolation path (blue dashed latent representations is not considered. To address line) between two latent representations (red points) is considered. these issues, we aim to fully exert the potential However, our model (right) can traverse a possible region with many of data interpolation and further improve represen- more paths, thus the diversity of interpolated samples will increase. tation learning in autoencoders. Specifically, we In addition, the latent distribution is constrained to match with a propose a multidimensional interpolation approach prior (illustrated by a sphere). to increase the capability of data interpolation by setting random interpolation coefficients for each dimension of the latent representations. In addition, possess an effective capability of data interpolation. Recently, we regularize autoencoders in both the latent and several research works have paid attention to exploring data data spaces, by imposing a prior on the latent interpolation methods in autoencoders [Larsen et al., 2016; representations in the Maximum Mean Discrepan- Berthelot et al., 2019] and generative models [Radford et al., cy (MMD) framework and encouraging generated 2015; White, 2016]. The research has demonstrated that there datapoints to be realistic in the Generative Ad- is a close relationship between representation learning and versarial Network (GAN) framework. Compared data interpolation. In other words, the effectiveness of data to representative models, our proposed approach interpolation can reflect the performance of representation has empirically shown that representation learning learning to some extent. exhibits better performance on downstream tasks Inspired by the relationship between data interpolation and on multiple benchmarks. representation learning, there is a possibility to further im- prove representation learning through explicitly considering data interpolation in autoencoders. The recent work [Berth- 1 Introduction elot et al., 2019] proposes a generative adversarial regulariza- Among unsupervised learning frameworks of representation tion strategy referred to as Adversarially Constrained Autoen- learning, autoencoders (AEs) and variants [Vincent et al., coder Interpolation (ACAI). ACAI promotes high-quality 2010; Kingma and Welling, 2014; Srivastava et al., 2014; data interpolation by introducing regularization into the data Makhzani et al., 2016] have shown a remarkable ability to reconstruction process, and improves representation learning encode compressed latent representations by reconstructing for downstream tasks. However, as empirically shown datapoints. In particular, by decoding the interpolated la- in [White, 2016], generative models will generate inferior tent representation of two datapoints, an autoencoder can datapoints when performing linear interpolation, which may generate an interpolated datapoint which approximates these cause the distribution of interpolated latent representations to two datapoints semantically. This indicates that autoencoders diverge from a prior. Besides, linear interpolation does not have enough capability to traverse a possible region between ∗Equal contribution. two datapoints on a data manifold, and the distribution of yCorresponding author. the latent representations is not considered when performing 3268 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI-19) interpolation. Different from the above approaches, AEs are regularized To alleviate the above issues, we replace linear interpola- to explicitly match the distribution of the latent represen- tion with a more effective interpolation method, and explicitly tations with a predefined prior in the VAE-based and the take the distribution of the latent representations into consid- GAN-based cases. In the VAE-based case, VAE introduces eration. Specifically, we propose a new interpolation method an additional loss into the reconstruction loss. This loss referred to as multidimensional interpolation, and fuse dual measures the KL divergence between the distribution of regularizations in both the latent and data spaces, so that both the latent representations and the prior. Besides the KL data interpolation and representation learning in autoencoders divergence, MMD is also used to measure the distribution can be further improved. Briefly speaking, multidimensional divergence in [Tolstikhin et al., 2018]. Along with learning interpolation treats each dimension of the latent representa- continuous representations, vector-quantized VAE (VQVAE) tion differently, and sets random interpolation coefficients [van den Oord et al., 2017] applies the distributional regular- for each dimension. As a result, it will enhance the quality ization framework into learning discrete representations using and diversity of interpolation. Furthermore, we constrain the a learned quantized codebook. distribution of the latent representations to match with a prior In the GAN-based case, adversarial AE (AAE) [Makhzani using the MMD framework [Gretton et al., 2007], so that et al., 2016] introduces an auxiliary subnetwork referred to as interpolated representations can follow this prior. Then, data- a discriminator based on the GAN framework, and forces this points generated by performing interpolation and sampling discriminator to determine whether latent representations are from this prior are encouraged to be perceptually realistic inferred from the encoder or sampled from the prior. More- based on the GAN framework [Goodfellow et al., 2014]. In over, VAE-GAN [Larsen et al., 2016] fuses both the VAE other words, generated datapoints are expected to follow the and GAN frameworks in the autoencoder. In VAE-GAN, real data distribution. In Figure 1, we provide a comparison the traditional pixel-wise reconstruction loss is replaced by of interpolations between ACAI and our proposed model. an adversarial feature-wise reconstruction loss obtained from Overall, the main contributions of this work are as follows: the GAN’s discriminator. • We improve the ACAI model by extending linear inter- polation to multidimensional interpolation, such that the 2.2 Interpolation latent space can be better explored and thus the diversity In the latent space there are two basic types of interpola- of interpolation can be significantly increased. tions: linear interpolation and spherical interpolation. Linear • On the other hand, we incorporate MMD-based regu- interpolation combines latent representations linearly, which larization in the latent space with adversarial regular- is easily understood. Hence, it is frequently used to inspect ization in the data space to improve the realism of the the performance of representation learning [Larsen et al., interpolated datapoints. Compared with ACAI, the main 2016; Radford et al., 2015; Wu et al., 2016; Dumoulin advantage of this work lies in effective data generation et al., 2017]. When the latent space is high dimensional, from a prior. interpolated representations on the linear interpolation path always suffer from change of magnitude. To address this • Due to the aforementioned strategies, representation issue, [White, 2016] introduces the spherical interpolation by learning in autoencoders can be enhanced significantly. applying nonlinear interpolation based on a great circle path As a result, better performance can be achieved on on an n-dimensional hypersphere. Besides, [Laine, 2018] downstream tasks. proposes to perform interpolation along geodesics in the data space rather than in the latent space. [Agustsson et al., 2019] 2 Related Work designs several interpolation operations to reduce mismatch between the distribution of interpolated data and a prior. In this section, we briefly introduce some related works on autoencoder variants and data interpolation. 3 Background of ACAI 2.1 Autoencoders ACAI model aims to improve data interpolation and repre- Based on regularizations introduced into autoencoders, these sentation learning in autoencoders. Specifically, the network variants are generally divided into three categories: Normal- architecture of ACAI consists of an autoencoder and a dis- based, VAE-based and GAN-based (VAE refers to as vari- criminator. The former, in addition to serving as a basic ational AE [Kingma and Welling, 2014]). Specifically, in autoencoder, also forms a GAN with the discriminator to the Normal-based case, dropout AE (DoAE) [Srivastava et propel
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