# Structured Ensembles: an Approach to Reduce the Memory Footprint of Ensemble Methods

arXiv: https://arxiv.org/abs/2105.02551 · HTML: https://mlsanity.com/paper/2105.02551/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 46 references that are in the map.
- First posted on arXiv 6 May 2021.

## Builds on (most cited first, 30 of 31)

- [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)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [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)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [Supermasks in Superposition](https://mlsanity.com/paper/2006.14769/) (2020)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [Why M Heads are Better than One: Training a Diverse Ensemble of Deep Networks](https://mlsanity.com/paper/1511.06314/) (2015)
- [Continual Learning via Neural Pruning](https://mlsanity.com/paper/1903.04476/) (2019)

## Built on by (most cited first, 5 of 5)

- [Wake-Sleep Consolidated Learning](https://mlsanity.com/paper/2401.08623/) (2023)
- [Continual Learning with Invertible Generative Models](https://mlsanity.com/paper/2202.05694/) (2022)
- [Centroids Matching: an efficient Continual Learning approach operating in the embedding space](https://mlsanity.com/paper/2208.02048/) (2022)
- [Class incremental learning with probability dampening and cascaded gated classifier](https://mlsanity.com/paper/2402.01262/) (2024)
- [Enhanced LFTSformer: A Novel Long-Term Financial Time Series Prediction Model Using Advanced Feature Engineering and the DS Encoder Informer Architecture](https://mlsanity.com/paper/2310.01884/) (2023)

## Abstract (arXiv)

In this paper, we propose a novel ensembling technique for deep neural networks, which is able to drastically reduce the required memory compared to alternative approaches. In particular, we propose to extract multiple sub-networks from a single, untrained neural network by solving an end-to-end optimization task combining differentiable scaling over the original architecture, with multiple regularization terms favouring the diversity of the ensemble. Since our proposal aims to detect and extract sub-structures, we call it Structured Ensemble. On a large experimental evaluation, we show that our method can achieve higher or comparable accuracy to competing methods while requiring significantly less storage. In addition, we evaluate our ensembles in terms of predictive calibration and uncertainty, showing they compare favourably with the state-of-the-art. Finally, we draw a link with the continual learning literature, and we propose a modification of our framework to handle continuous streams of tasks with a sub-linear memory cost. We compare with a number of alternative strategies to mitigate catastrophic forgetting, highlighting advantages in terms of average accuracy and memory.