text: This research attempts to construct a network that can convert online and offline handwritten characters to each other. The proposed network consists of two Variational Auto-Encoders (VAEs) with a shared latent space. The VAEs are trained to generate online and offline handwritten Latin characters simultaneously. In this way, we create a cross-modal VAE (Cross-VAE). During training, the proposed Cross-VAE is trained to minimize the reconstruction loss of the two modalities, the distribution loss of the two VAEs, and a novel third loss called the space sharing loss. This third, space sharing loss is used to encourage the modalities to share the same latent space by calculating the distance between the latent variables. Through the proposed method mutual conversion of online and offline handwritten characters is possible. In this paper, we demonstrate the performance of the Cross-VAE through qualitative and quantitative analysis.
  @cite_4: We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.
  @cite_6: Autoencoders play a fundamental role in unsupervised learning and in deep architectures for transfer learning and other tasks. In spite of their fundamental role, only linear autoencoders over the real numbers have been solved analytically. Here we present a general mathematical framework for the study of both linear and non-linear autoencoders. The framework allows one to derive an analytical treatment for the most non-linear autoencoder, the Boolean autoencoder. Learning in the Boolean autoencoder is equivalent to a clustering problem that can be solved in polynomial time when the number of clusters is small and becomes NP complete when the number of clusters is large. The framework sheds light on the different kinds of autoencoders, their learning complexity, their horizontal and vertical composability in deep architectures, their critical points, and their fundamental connections to clustering, Hebbian learning, and information theory.
summary: Recently, there are two common approaches that have become popular which use neural networks to learn latent representations, Encoder-Decoders and Generative Adversarial Networks (GAN) @cite_4 . Encoder-Decoders, such as an Autoencoder @cite_6 , compress data by encoding the inputs into a latent vector which is then uncompressed by the decoder. The Autoencoder is trained by minimizes the difference between the input and the output of the decoder. GANs take the opposite approach and use a generator, similar to an encoder, then uses a discriminator to maximize the authenticity of the generated data. Where Encoder-Decoders learn the latent representations directly, GANs learn to construct data from random latent representations.