# Lottery Pools: Winning More by Interpolating Tickets without Increasing Training or Inference Cost

arXiv: https://arxiv.org/abs/2208.10842 · HTML: https://mlsanity.com/paper/2208.10842/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 61 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Builds on (most cited first, 30 of 42)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (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)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [The Lottery Ticket Hypothesis for Pre-trained BERT Networks](https://mlsanity.com/paper/2007.12223/) (2020)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Uniform convergence may be unable to explain generalization in deep learning](https://mlsanity.com/paper/1902.04742/) (2019)
- [Deconstructing Lottery Tickets: Zeros, Signs, and the Supermask](https://mlsanity.com/paper/1905.01067/) (2019)
- [Patching open-vocabulary models by interpolating weights](https://mlsanity.com/paper/2208.05592/) (2022)

## Built on by (most cited first, 11 of 11)

- [Dynamic Sparse No Training: Training-Free Fine-tuning for Sparse LLMs](https://mlsanity.com/paper/2310.08915/) (2023)
- [The Emergence of Essential Sparsity in Large Pre-trained Models: The Weights that Matter](https://mlsanity.com/paper/2306.03805/) (2023)
- [Sparsity May Cry: Let Us Fail (Current) Sparse Neural Networks Together!](https://mlsanity.com/paper/2303.02141/) (2023)
- [Ten Lessons We Have Learned in the New "Sparseland": A Short Handbook for Sparse Neural Network Researchers](https://mlsanity.com/paper/2302.02596/) (2023)
- [A Survey of Lottery Ticket Hypothesis](https://mlsanity.com/paper/2403.04861/) (2024)
- [Instant Soup: Cheap Pruning Ensembles in A Single Pass Can Draw Lottery Tickets from Large Models](https://mlsanity.com/paper/2306.10460/) (2023)
- [Sparse Model Soups: A Recipe for Improved Pruning via Model Averaging](https://mlsanity.com/paper/2306.16788/) (2023)
- [Domain-Generalizable Multiple-Domain Clustering](https://mlsanity.com/paper/2301.13530/) (2023)
- [Learning Scalable Model Soup on a Single GPU: An Efficient Subspace Training Strategy](https://mlsanity.com/paper/2407.03641/) (2024)
- [Sparse Weight Averaging with Multiple Particles for Iterative Magnitude Pruning](https://mlsanity.com/paper/2305.14852/) (2023)
- [SEVEN: Pruning Transformer Model by Reserving Sentinels](https://mlsanity.com/paper/2403.12688/) (2024)

## Abstract (arXiv)

Lottery tickets (LTs) is able to discover accurate and sparse subnetworks that could be trained in isolation to match the performance of dense networks. Ensemble, in parallel, is one of the oldest time-proven tricks in machine learning to improve performance by combining the output of multiple independent models. However, the benefits of ensemble in the context of LTs will be diluted since ensemble does not directly lead to stronger sparse subnetworks, but leverages their predictions for a better decision. In this work, we first observe that directly averaging the weights of the adjacent learned subnetworks significantly boosts the performance of LTs. Encouraged by this observation, we further propose an alternative way to perform an 'ensemble' over the subnetworks identified by iterative magnitude pruning via a simple interpolating strategy. We call our method Lottery Pools. In contrast to the naive ensemble which brings no performance gains to each single subnetwork, Lottery Pools yields much stronger sparse subnetworks than the original LTs without requiring any extra training or inference cost. Across various modern architectures on CIFAR-10/100 and ImageNet, we show that our method achieves significant performance gains in both, in-distribution and out-of-distribution scenarios. Impressively, evaluated with VGG-16 and ResNet-18, the produced sparse subnetworks outperform the original LTs by up to 1.88% on CIFAR-100 and 2.36% on CIFAR-100-C; the resulting dense network surpasses the pre-trained dense-model up to 2.22% on CIFAR-100 and 2.38% on CIFAR-100-C.