# Quantization vs Pruning: Insights from the Strong Lottery Ticket Hypothesis

arXiv: https://arxiv.org/abs/2508.11020 · HTML: https://mlsanity.com/paper/2508.11020/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 14 Aug 2025.

## Builds on (most cited first, 14 of 14)

- [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)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask](https://mlsanity.com/paper/1905.01067/) (2019)
- [Proving the Lottery Ticket Hypothesis: Pruning is All You Need](https://mlsanity.com/paper/2002.00585/) (2020)
- [Optimal Lottery Tickets via SubsetSum: Logarithmic Over-Parameterization is Sufficient](https://mlsanity.com/paper/2006.07990/) (2020)
- [Pruning from Scratch](https://mlsanity.com/paper/1909.12579/) (2019)
- [Logarithmic Pruning is All You Need](https://mlsanity.com/paper/2006.12156/) (2020)
- [Multi-Prize Lottery Ticket Hypothesis: Finding Accurate Binary Neural Networks by Pruning A Randomly Weighted Network](https://mlsanity.com/paper/2103.09377/) (2021)
- [Most Activation Functions Can Win the Lottery Without Excessive Depth](https://mlsanity.com/paper/2205.02321/) (2022)
- [A General Framework For Proving The Equivariant Strong Lottery Ticket Hypothesis](https://mlsanity.com/paper/2206.04270/) (2022)
- [Convolutional and Residual Networks Provably Contain Lottery Tickets](https://mlsanity.com/paper/2205.02343/) (2022)
- [On Expressive Power of Quantized Neural Networks under Fixed-Point Arithmetic](https://mlsanity.com/paper/2409.00297/) (2024)
- [On the Sparsity of the Strong Lottery Ticket Hypothesis](https://mlsanity.com/paper/2410.14754/) (2024)

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

- [A Unified Framework for Quantized and Continuous Strong Lottery Tickets](https://mlsanity.com/paper/2607.03860/) (2026)

## Abstract (arXiv)

Quantization is an essential technique for making neural networks more efficient, yet our theoretical understanding of it remains limited. Previous works demonstrated that extremely low-precision networks, such as binary networks, can be constructed by pruning large, randomly-initialized networks, and showed that the ratio between the size of the original and the pruned networks is at most polylogarithmic. The specific pruning method they employed inspired a line of theoretical work known as the Strong Lottery Ticket Hypothesis (SLTH), which leverages insights from the Random Subset Sum Problem. However, these results primarily address the continuous setting and cannot be applied to extend SLTH results to the quantized setting. In this work, we build on foundational results by Borgs et al. on the Number Partitioning Problem to derive new theoretical results for the Random Subset Sum Problem in a quantized setting. Using these results, we then extend the SLTH framework to finite-precision networks. While prior work on SLTH showed that pruning allows approximation of a certain class of neural networks, we demonstrate that, in the quantized setting, the analogous class of target discrete neural networks can be represented exactly, and we prove optimal bounds on the necessary overparameterization of the initial network as a function of the precision of the target network.