# Variational Nested Dropout

arXiv: https://arxiv.org/abs/2101.11353 · HTML: https://mlsanity.com/paper/2101.11353/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 65 references that are in the map.
- First posted on arXiv 27 Jan 2021.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Slimmable Neural Networks](https://mlsanity.com/paper/1812.08928/) (2018)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Universally Slimmable Networks and Improved Training Techniques](https://mlsanity.com/paper/1903.05134/) (2019)
- [Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding](https://mlsanity.com/paper/1511.02680/) (2015)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)

## Built on by (most cited first, 4 of 4)

- [The Pitfalls and Promise of Conformal Inference Under Adversarial Attacks](https://mlsanity.com/paper/2405.08886/) (2024)
- [ReFusion: Improving Natural Language Understanding with Computation-Efficient Retrieval Representation Fusion](https://mlsanity.com/paper/2401.02993/) (2024)
- [Debiasing Machine Unlearning with Counterfactual Examples](https://mlsanity.com/paper/2404.15760/) (2024)
- [Probe with Participation Trophies: Random-Reward RL as a Probe of LLM Capability](https://mlsanity.com/paper/2610.01066/) (2026)

## Abstract (arXiv)

Nested dropout is a variant of dropout operation that is able to order network parameters or features based on the pre-defined importance during training. It has been explored for: I. Constructing nested nets: the nested nets are neural networks whose architectures can be adjusted instantly during testing time, e.g., based on computational constraints. The nested dropout implicitly ranks the network parameters, generating a set of sub-networks such that any smaller sub-network forms the basis of a larger one. II. Learning ordered representation: the nested dropout applied to the latent representation of a generative model (e.g., auto-encoder) ranks the features, enforcing explicit order of the dense representation over dimensions. However, the dropout rate is fixed as a hyper-parameter during the whole training process. For nested nets, when network parameters are removed, the performance decays in a human-specified trajectory rather than in a trajectory learned from data. For generative models, the importance of features is specified as a constant vector, restraining the flexibility of representation learning. To address the problem, we focus on the probabilistic counterpart of the nested dropout. We propose a variational nested dropout (VND) operation that draws samples of multi-dimensional ordered masks at a low cost, providing useful gradients to the parameters of nested dropout. Based on this approach, we design a Bayesian nested neural network that learns the order knowledge of the parameter distributions. We further exploit the VND under different generative models for learning ordered latent distributions. In experiments, we show that the proposed approach outperforms the nested network in terms of accuracy, calibration, and out-of-domain detection in classification tasks. It also outperforms the related generative models on data generation tasks.