Traditional structured prediction models try to learn the conditional likelihood, i.e., p(y|x), to capture the relationship between the structured output y and the input features x. For many models, computing the likelihood is intractable. These models are therefore hard to train, requiring the use of surrogate objectives or variational inference to approximate likelihood. In this paper, we propose conditional Glow (c-Glow), a conditional generative flow for structured output learning. C-Glow benefits from the ability of flow-based models to compute p(y|x) exactly and efficiently. Learning with c-Glow does not require a surrogate objective or performing inference during training. Once trained, we can directly and efficiently generate conditional samples to do structured prediction. We evaluate this approach on different structured prediction tasks and find c-Glow's structured outputs comparable in quality with state-of-the-art deep structured prediction approaches.
Normalizing flows are neural networks constructed with fully invertible components. The invertibility of the resulting network provides various mathematical benefits. Normalizing flows have been successfully used to build likelihood-based deep generative models @cite_20 @cite_33 @cite_0 and to improve variational approximation @cite_19 @cite_15 . Autoregressive flows @cite_15 @cite_9 @cite_22 @cite_34 condition each affine transformation on all previous variables, so that they ensure an invertible transformation and triangular Jacobian matrix. Continuous normalizing flows @cite_25 @cite_32 define the transformation function using ordinary differential equations. While most normalizing flow models define generative models, developed radial flows to model univariate conditional probabilities. Most related to our approach are flow-based generative models for complex output. first proposed a flow-based model, NICE, for modeling complex high-dimensional densities. They later proposed Real-NVP @cite_33 , which improves the expressiveness of NICE by adding more flexible coupling layers. The Glow model @cite_0 further improved the performance of such approaches by incorporating new invertible layers. Most recently, Flow++ @cite_18 improved generative flows with variational dequantization and architecture design, and proposed new invertible layers for flow-based models.
@cite_18 @cite_33 @cite_22 @cite_9 @cite_32 @cite_0 @cite_19 @cite_15 @cite_34 @cite_25 @cite_20
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Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete random variables such as text, but directly applying normalizing flows to discrete sequences poses significant additional challenges. We propose a VAE-based generative model which jointly learns a normalizing flow-based distribution in the latent space and a stochastic mapping to an observed discrete space. In this setting, we find that it is crucial for the flow-based distribution to be highly multimodal. To capture this property, we propose several normalizing flow architectures to maximize model flexibility. Experiments consider common discrete sequence tasks of character-level language modeling and polyphonic music generation. Our results indicate that an autoregressive flow-based model can match the performance of a comparable autoregressive baseline, and a non-autoregressive flow-based model can improve generation speed with a penalty to performance. Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at this https URL The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed flow consists of a chain of invertible transformations, where each transformation is based on an autoregressive neural network. In experiments, we show that IAF significantly improves upon diagonal Gaussian approximate posteriors. In addition, we demonstrate that a novel type of variational autoencoder, coupled with IAF, is competitive with neural autoregressive models in terms of attained log-likelihood on natural images, while allowing significantly faster synthesis. The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed flow consists of a chain of invertible transformations, where each transformation is based on an autoregressive neural network. In experiments, we show that IAF significantly improves upon diagonal Gaussian approximate posteriors. In addition, we demonstrate that a novel type of variational autoencoder, coupled with IAF, is competitive with neural autoregressive models in terms of attained log-likelihood on natural images, while allowing significantly faster synthesis.