# Towards a More Complete Theory of Function Preserving Transforms

arXiv: https://arxiv.org/abs/2410.11038 · HTML: https://mlsanity.com/paper/2410.11038/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 14 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [Net2Net: Accelerating Learning via Knowledge Transfer](https://mlsanity.com/paper/1511.05641/) (2015)
- [Network Morphism](https://mlsanity.com/paper/1603.01670/) (2016)

## Built on by (most cited first, 1 of 1)

- [Squeeze-Release: Iterative Pruning with Exact Structural Minimization](https://mlsanity.com/paper/2606.14346/) (2026)

## Abstract (arXiv)

In this paper, we develop novel techniques that can be used to alter the architecture of a neural network, while maintaining the function it represents. Such operations are known as function preserving transforms and have proven useful in transferring knowledge between networks to evaluate architectures quickly, thus having applications in efficient architectures searches. Our methods allow the integration of residual connections into function preserving transforms, so we call them R2R. We provide a derivation for R2R and show that it yields competitive performance with other function preserving transforms, thereby decreasing the restrictions on deep learning architectures that can be extended through function preserving transforms. We perform a comparative analysis with other function preserving transforms such as Net2Net and Network Morphisms, where we shed light on their differences and individual use cases. Finally, we show the effectiveness of R2R to train models quickly, as well as its ability to learn a more diverse set of filters on image classification tasks compared to Net2Net and Network Morphisms.