# To Boost or not to Boost: On the Limits of Boosted Neural Networks

arXiv: https://arxiv.org/abs/2107.13600 · HTML: https://mlsanity.com/paper/2107.13600/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 28 Jul 2021.

## Builds on (most cited first, 10 of 10)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [CatBoost: gradient boosting with categorical features support](https://mlsanity.com/paper/1810.11363/) (2018)
- [Why M Heads are Better than One: Training a Diverse Ensemble of Deep Networks](https://mlsanity.com/paper/1511.06314/) (2015)
- [Theory of Deep Learning III: explaining the non-overfitting puzzle](https://mlsanity.com/paper/1801.00173/) (2017)
- [Deep Incremental Boosting](https://mlsanity.com/paper/1708.03704/) (2017)
- [Gradient Boosting Machine: A Survey](https://mlsanity.com/paper/1908.06951/) (2019)

## Abstract (arXiv)

Boosting is a method for finding a highly accurate hypothesis by linearly combining many ``weak" hypotheses, each of which may be only moderately accurate. Thus, boosting is a method for learning an ensemble of classifiers. While boosting has been shown to be very effective for decision trees, its impact on neural networks has not been extensively studied. We prove one important difference between sums of decision trees compared to sums of convolutional neural networks (CNNs) which is that a sum of decision trees cannot be represented by a single decision tree with the same number of parameters while a sum of CNNs can be represented by a single CNN. Next, using standard object recognition datasets, we verify experimentally the well-known result that a boosted ensemble of decision trees usually generalizes much better on testing data than a single decision tree with the same number of parameters. In contrast, using the same datasets and boosting algorithms, our experiments show the opposite to be true when using neural networks (both CNNs and multilayer perceptrons (MLPs)). We find that a single neural network usually generalizes better than a boosted ensemble of smaller neural networks with the same total number of parameters.