# Neural Networks Reduction via Lumping

arXiv: https://arxiv.org/abs/2209.07475 · HTML: https://mlsanity.com/paper/2209.07475/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 57 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 30 of 35)

- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [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)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [CoCa: Contrastive Captioners are Image-Text Foundation Models](https://mlsanity.com/paper/2205.01917/) (2022)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [HRank: Filter Pruning using High-Rank Feature Map](https://mlsanity.com/paper/2002.10179/) (2020)
- [Designing Neural Network Architectures using Reinforcement Learning](https://mlsanity.com/paper/1611.02167/) (2016)
- [A Comprehensive Survey of Neural Architecture Search: Challenges and Solutions](https://mlsanity.com/paper/2006.02903/) (2020)
- [NISP: Pruning Networks using Neuron Importance Score Propagation](https://mlsanity.com/paper/1711.05908/) (2017)
- [Network Trimming: A Data-Driven Neuron Pruning Approach towards Efficient Deep Architectures](https://mlsanity.com/paper/1607.03250/) (2016)

## Built on by (most cited first, 2 of 2)

- [Assessing Code Understanding in LLMs](https://mlsanity.com/paper/2504.00065/) (2025)
- [Neural Network Compression by Approximate Differential Equivalence](https://mlsanity.com/paper/2606.01402/) (2026)

## Abstract (arXiv)

The increasing size of recently proposed Neural Networks makes it hard to implement them on embedded devices, where memory, battery and computational power are a non-trivial bottleneck. For this reason during the last years network compression literature has been thriving and a large number of solutions has been been published to reduce both the number of operations and the parameters involved with the models. Unfortunately, most of these reducing techniques are actually heuristic methods and usually require at least one re-training step to recover the accuracy. The need of procedures for model reduction is well-known also in the fields of Verification and Performances Evaluation, where large efforts have been devoted to the definition of quotients that preserve the observable underlying behaviour. In this paper we try to bridge the gap between the most popular and very effective network reduction strategies and formal notions, such as lumpability, introduced for verification and evaluation of Markov Chains. Elaborating on lumpability we propose a pruning approach that reduces the number of neurons in a network without using any data or fine-tuning, while completely preserving the exact behaviour. Relaxing the constraints on the exact definition of the quotienting method we can give a formal explanation of some of the most common reduction techniques.