# Sylvester Normalizing Flows for Variational Inference

arXiv: https://arxiv.org/abs/1803.05649 · HTML: https://mlsanity.com/paper/1803.05649/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

## Built on by (most cited first, 30 of 72)

- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents](https://mlsanity.com/paper/2201.00308/) (2022)
- [Neural Flows: Efficient Alternative to Neural ODEs](https://mlsanity.com/paper/2110.13040/) (2021)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [A Dynamical System Perspective for Lipschitz Neural Networks](https://mlsanity.com/paper/2110.12690/) (2021)
- [Geometric Clifford Algebra Networks](https://mlsanity.com/paper/2302.06594/) (2023)
- [Explicitly Minimizing the Blur Error of Variational Autoencoders](https://mlsanity.com/paper/2304.05939/) (2023)
- [The Dark Machines Anomaly Score Challenge: Benchmark Data and Model Independent Event Classification for the Large Hadron Collider](https://mlsanity.com/paper/2105.14027/) (2021)
- [Invertible Tabular GANs: Killing Two Birds with OneStone for Tabular Data Synthesis](https://mlsanity.com/paper/2202.03636/) (2022)
- [MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retraining](https://mlsanity.com/paper/2110.08009/) (2021)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Invertible DenseNets with Concatenated LipSwish](https://mlsanity.com/paper/2102.02694/) (2021)
- [PU-Flow: a Point Cloud Upsampling Network with Normalizing Flows](https://mlsanity.com/paper/2107.05893/) (2021)
- [Challenges for Unsupervised Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2110.06948/) (2021)
- [Flow-based Recurrent Belief State Learning for POMDPs](https://mlsanity.com/paper/2205.11051/) (2022)
- [Invertible Rescaling Network and Its Extensions](https://mlsanity.com/paper/2210.04188/) (2022)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Cauchy-Schwarz Regularized Autoencoder](https://mlsanity.com/paper/2101.02149/) (2021)
- [Sparse Flows: Pruning Continuous-depth Models](https://mlsanity.com/paper/2106.12718/) (2021)
- [Improving Aleatoric Uncertainty Quantification in Multi-Annotated Medical Image Segmentation with Normalizing Flows](https://mlsanity.com/paper/2108.02155/) (2021)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [On Incorporating Inductive Biases into VAEs](https://mlsanity.com/paper/2106.13746/) (2021)
- [Path-Gradient Estimators for Continuous Normalizing Flows](https://mlsanity.com/paper/2206.09016/) (2022)
- [EigenVI: score-based variational inference with orthogonal function expansions](https://mlsanity.com/paper/2410.24054/) (2024)
- [Model Selection for Bayesian Autoencoders](https://mlsanity.com/paper/2106.06245/) (2021)
- [Jacobian Determinant of Normalizing Flows](https://mlsanity.com/paper/2102.06539/) (2021)
- [An Adaptive Orthogonal Convolution Scheme for Efficient and Flexible CNN Architectures](https://mlsanity.com/paper/2501.07930/) (2025)
- [Structured Dropout Variational Inference for Bayesian Neural Networks](https://mlsanity.com/paper/2102.07927/) (2021)
- [Universal Approximation of Residual Flows in Maximum Mean Discrepancy](https://mlsanity.com/paper/2103.05793/) (2021)

## Abstract (arXiv)

Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single-unit bottleneck from planar flows, making a single transformation much more flexible. We compare the performance of Sylvester normalizing flows against planar flows and inverse autoregressive flows and demonstrate that they compare favorably on several datasets.