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Title: Hierarchical Adversarially Learned Inference

Paper content:
We propose a novel hierarchical generative model with a simple Markovian structure and a corresponding inference model.
Both the generative and inference model are trained using the adversarial learning paradigm.
We demonstrate that the hierarchical structure supports the learning of progressively more abstract representations as well as providing semantically meaningful reconstructions with different levels of fidelity.
Furthermore, we show that minimizing the Jensen-Shanon divergence between the generative and inference network is enough to minimize the reconstruction error.
The resulting semantically meaningful hierarchical latent structure discovery is exemplified on the CelebA dataset
.  There, we show that the features learned by our model in an unsupervised way outperform the best handcrafted features
. Furthermore, the extracted features remain competitive when compared to several recent deep supervised approaches on an attribute prediction task on CelebA.
Finally, we leverage the model's inference network to achieve state-of-the-art performance on a semi-supervised variant of the MNIST digit classification task.
Deep generative models represent powerful approaches to modeling highly complex high-dimensional data.
There has been a lot of recent research geared towards the advancement of deep generative modeling strategies, including Variational Autoencoders (VAE) BID16 , autoregressive models BID32 b) and hybrid models BID9 BID31 .
However, Generative Adversarial Networks (GANs) BID8 have emerged as the learning paradigm of choice across a varied range of tasks, especially in computer vision BID47 , simulation and robotics BID7 BID41 .
GANs cast the learning of a generative network in the form of a game between the generative and discriminator networks.
While the discriminator is trained to distinguish between the true and generated examples, the generative model is trained to fool the discriminator.
Using a discriminator network in GANs avoids the need for an explicit reconstruction-based loss function.
This allows this model class to generate visually sharper images than VAEs while simultaneously enjoying faster sampling than autoregressive models.Recent work, known as either ALI or BiGAN , has shown that the adversarial learning paradigm can be extended to incorporate the learning of an inference network.
While the inference network, or encoder, maps training examples x to a latent space variable z, the decoder plays the role of the standard GAN generator mapping from space of the latent variables (that is typically sampled from some factorial distribution) into the data space.
In ALI, the discriminator is trained to distinguish between the encoder and the decoder, while the encoder and decoder are trained to conspire together to fool the discriminator.
Unlike some approaches that hybridize VAE-style inference with GAN-style generative learning (e.g. BID20 , ), the encoder and decoder in ALI use a purely adversarial approach.
One big advantage of adopting an adversarial-only formalism is demonstrated by the high-quality of the generated samples.
Additionally, we are given a mechanism to infer the latent code associated with a true data example.One interesting feature highlighted in the original ALI work is that even though the encoder and decoder models are never explicitly trained to perform reconstruction, this can nevertheless be easily done by projecting data samples via the encoder into the latent space, copying these values across to the latent variable layer of the decoder and projecting them back to the data space.
Doing this yields reconstructions that often preserve some semantic features of the original input data, but are perceptually relatively different from the original samples.
These observations naturally lead to the question of the source of the discrepancy between the data samples and their ALI reconstructions.
Is the discrepancy due to a failure of the adversarial training paradigm, or is it due to the more standard challenge of compressing the information from the data into a rather restrictive latent feature vector?
BID44 show that an improvement in reconstructions is achievable when additional terms which explicitly minimize reconstruction error in the data space are added to the training objective.
BID23 palliates to the non-identifiability issues pertaining to bidirectional adversarial training by augmenting the generator's loss with an adversarial cycle consistency loss.In this paper we explore issues surrounding the representation of complex, richly-structured data, such as natural images, in the context of a novel, hierarchical generative model, Hierarchical Adversarially Learned Inference (HALI), which represents a hierarchical extension of ALI.
We show that within a purely adversarial training paradigm, and by exploiting the model's hierarchical structure, we can modulate the perceptual fidelity of the reconstructions.
We provide theoretical arguments for why HALI's adversarial game should be sufficient to minimize the reconstruction cost and show empirical evidence supporting this perspective.
Finally, we evaluate the usefulness of the learned representations on a semi-supervised task on MNIST and an attribution prediction task on the CelebA dataset.
In this paper, we introduced HALI, a novel adversarially trained generative model.
HALI learns a hierarchy of latent variables with a simple Markovian structure in both the generator and inference networks.
We have shown both theoretically and empirically the advantages gained by extending the ALI framework to a hierarchy.While there are many potential applications of HALI, one important future direction of research is to explore ways to render the training process more stable and straightforward.
GANs are well-known to be challenging to train and the introduction of a hierarchy of latent variables only adds to this.

assistant: text: Adversarially trained hierarchical generative model with robust and semantically learned latent representation.