# Rescaling CNN through Learnable Repetition of Network Parameters

arXiv: https://arxiv.org/abs/2101.05650 · HTML: https://mlsanity.com/paper/2101.05650/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 14 Jan 2021.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Data-free parameter pruning for Deep Neural Networks](https://mlsanity.com/paper/1507.06149/) (2015)
- [Compressing Neural Networks using the Variational Information Bottleneck](https://mlsanity.com/paper/1802.10399/) (2018)
- [Structured Pruning of Neural Networks with Budget-Aware Regularization](https://mlsanity.com/paper/1811.09332/) (2018)
- [ShaResNet: reducing residual network parameter number by sharing weights](https://mlsanity.com/paper/1702.08782/) (2017)
- [Training highly effective connectivities within neural networks with randomly initialized, fixed weights](https://mlsanity.com/paper/2006.16627/) (2020)
- [Deep Anchored Convolutional Neural Networks](https://mlsanity.com/paper/1904.09764/) (2019)

## Abstract (arXiv)

Deeper and wider CNNs are known to provide improved performance for deep learning tasks. However, most such networks have poor performance gain per parameter increase. In this paper, we investigate whether the gain observed in deeper models is purely due to the addition of more optimization parameters or whether the physical size of the network as well plays a role. Further, we present a novel rescaling strategy for CNNs based on learnable repetition of its parameters. Based on this strategy, we rescale CNNs without changing their parameter count, and show that learnable sharing of weights itself can provide significant boost in the performance of any given model without changing its parameter count. We show that small base networks when rescaled, can provide performance comparable to deeper networks with as low as 6% of optimization parameters of the deeper one. The relevance of weight sharing is further highlighted through the example of group-equivariant CNNs. We show that the significant improvements obtained with group-equivariant CNNs over the regular CNNs on classification problems are only partly due to the added equivariance property, and part of it comes from the learnable repetition of network weights. For rot-MNIST dataset, we show that up to 40% of the relative gain reported by state-of-the-art methods for rotation equivariance could actually be due to just the learnt repetition of weights.