# Robust Learning of Parsimonious Deep Neural Networks

arXiv: https://arxiv.org/abs/2205.04650 · HTML: https://mlsanity.com/paper/2205.04650/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 46 references that are in the map.
- First posted on arXiv 10 May 2022.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [Soft Filter Pruning for Accelerating Deep Convolutional Neural Networks](https://mlsanity.com/paper/1808.06866/) (2018)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Dynamic Network Surgery for Efficient DNNs](https://mlsanity.com/paper/1608.04493/) (2016)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Bayesian Compression for Deep Learning](https://mlsanity.com/paper/1705.08665/) (2017)
- [Provable Filter Pruning for Efficient Neural Networks](https://mlsanity.com/paper/1911.07412/) (2019)
- [SCOP: Scientific Control for Reliable Neural Network Pruning](https://mlsanity.com/paper/2010.10732/) (2020)
- [Lost in Pruning: The Effects of Pruning Neural Networks beyond Test Accuracy](https://mlsanity.com/paper/2103.03014/) (2021)
- [Data-Dependent Coresets for Compressing Neural Networks with Applications to Generalization Bounds](https://mlsanity.com/paper/1804.05345/) (2018)
- [Generalized Dropout](https://mlsanity.com/paper/1611.06791/) (2016)
- [A Scale Mixture Perspective of Multiplicative Noise in Neural Networks](https://mlsanity.com/paper/1506.03208/) (2015)

## Built on by (most cited first, 3 of 3)

- [Concurrent Training and Layer Pruning of Deep Neural Networks](https://mlsanity.com/paper/2406.04549/) (2024)
- [Complexity-Aware Training of Deep Neural Networks for Optimal Structure Discovery](https://mlsanity.com/paper/2411.09127/) (2024)
- [Online Training and Pruning of Deep Reinforcement Learning Networks](https://mlsanity.com/paper/2507.11975/) (2025)

## Abstract (arXiv)

We propose a simultaneous learning and pruning algorithm capable of identifying and eliminating irrelevant structures in a neural network during the early stages of training. Thus, the computational cost of subsequent training iterations, besides that of inference, is considerably reduced. Our method, based on variational inference principles using Gaussian scale mixture priors on neural network weights, learns the variational posterior distribution of Bernoulli random variables multiplying the units/filters similarly to adaptive dropout. Our algorithm, ensures that the Bernoulli parameters practically converge to either 0 or 1, establishing a deterministic final network. We analytically derive a novel hyper-prior distribution over the prior parameters that is crucial for their optimal selection and leads to consistent pruning levels and prediction accuracy regardless of weight initialization or the size of the starting network. We prove the convergence properties of our algorithm establishing theoretical and practical pruning conditions. We evaluate the proposed algorithm on the MNIST and CIFAR-10 data sets and the commonly used fully connected and convolutional LeNet and VGG16 architectures. The simulations show that our method achieves pruning levels on par with state-of the-art methods for structured pruning, while maintaining better test-accuracy and more importantly in a manner robust with respect to network initialization and initial size.