NanoFlow: Scalable Normalizing Flows with Sublinear Parameter Complexity

Abstract

Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter complexity because of reduced expressiveness of bijective mapping, which renders the models prohibitively expensive in terms of parameters. We present an alternative of parameterization scheme, called NanoFlow, which uses a single neural density estimator to model multiple transformation stages. Hence, we propose an efficient parameter decomposition method and the concept of flow indication embedding, which are key missing components that enable density estimation from a single neural network. Experiments performed on audio and image models confirm that our method provides a new parameter-efficient solution for scalable NFs with significantly sublinear parameter complexity.Preprint. Under review.

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“…As shown in Figure2, we divide all flow steps (f 1 , f 2 , ..., f K ) into several groups and share the model parameters of N N (WaveNet-like network, see Appendix A.1) in the coupling layers among flow steps in a group. Our grouped parameter sharing mechanism is similar to the shared neural density estimator proposed in[12] with some differences that: 1) we simplify the model by removing the flow indication embedding since the unshared conditional projection layer in different flow steps can help the model to indicate the position of the step; 2) instead of sharing the parameters among all flow steps, we generalize the sharing mechanism by sharing the parameters among flow steps in a group, making it easier to adjust the number of trainable model parameters without changing the model architecture.…”