# Block Neural Autoregressive Flow

@article{DeCao2019BlockNA, title={Block Neural Autoregressive Flow}, author={Nicola De Cao and Ivan Titov and W. Aziz}, journal={ArXiv}, year={2019}, volume={abs/1904.04676} }

Normalising flows (NFS) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural autoregressive flow (NAF) which is a universal approximator for density functions. Their flow is a neural network (NN) whose parameters are predicted by another NN. The latter grows quadratically with the size of the former and thus an efficient technique for…

## 70 Citations

Cubic-Spline Flows

- MathematicsICML 2019
- 2019

This work stacks a new coupling transform, based on monotonic cubic splines, with LU-decomposed linear layers, which retains an exact one-pass inverse, can be used to generate high-quality images, and closes the gap with autoregressive flows on a suite of density-estimation tasks.

Sinusoidal Flow: A Fast Invertible Autoregressive Flow

- MathematicsACML
- 2021

The Sinusoidal Flow is proposed, a new type of normalising flows that inherits the expressive power and triangular Jacobian from fully autoregressive flows while guaranteed by Banach fixed-point theorem to remain fast invertible and thereby obviate the need for sequential inversion typically required in fully autOREgressive flows.

Gradient Boosted Flows

- Computer ScienceArXiv
- 2020

Gradient Boosted Flows (GBF) model a variational posterior by successively adding new NF components by gradient boosting so that each new NF component is fit to the residuals of the previously trained components.

Unconstrained Monotonic Neural Networks

- Computer ScienceBNAIC/BENELEARN
- 2019

This work proposes the Unconstrained Monotonic Neural Network (UMNN) architecture based on the insight that a function is monotonic as long as its derivative is strictly positive and demonstrates the ability of UMNNs to improve variational inference.

Neural Spline Flows

- MathematicsNeurIPS
- 2019

This work proposes a fully-differentiable module based on monotonic rational-quadratic splines, which enhances the flexibility of both coupling and autoregressive transforms while retaining analytic invertibility, and demonstrates that neural spline flows improve density estimation, variational inference, and generative modeling of images.

ELF: Exact-Lipschitz Based Universal Density Approximator Flow

- Computer Science, MathematicsArXiv
- 2021

A new Exact-Lipschitz Flow (ELF) is introduced that combines the ease of sampling from residual flows with the strong performance of autoregressive flows, and achieves state-of-the-art performance on multiple largescale datasets.

Learning Likelihoods with Conditional Normalizing Flows

- Computer ScienceArXiv
- 2019

This work provides an effective method to train continuous CNFs for binary problems and applies them to super-resolution and vessel segmentation tasks demonstrating competitive performance on standard benchmark datasets in terms of likelihood and conventional metrics.

Density estimation on low-dimensional manifolds: an inflation-deflation approach

- Computer Science, Mathematics
- 2020

This paper inflates the data manifold by adding noise in the normal space, trains an NF on this inflated manifold and, finally, deflates the learned density, which allows using this method for approximating arbitrary densities on non-flat manifolds provided that the manifold dimension is known.

Quasi-Autoregressive Residual (QuAR) Flows

- Computer ScienceArXiv
- 2020

This paper introduces a simplification to residual flows using a Quasi-Autoregressive (QuAR) approach, which retains many of the benefits of residual flows while dramatically reducing the compute time and memory requirements, thus making flow-based modeling approaches far more tractable and broadening their potential applicability.

Stochastic Neural Network with Kronecker Flow

- Computer ScienceAISTATS
- 2020

This work presents the Kronecker Flow, a generalization of the KrOnecker product to invertible mappings designed for stochastic neural networks, and applies this method to variational Bayesian neural networks on predictive tasks, PAC-Bayes generalization bound estimation, and approximate Thompson sampling in contextual bandits.

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