# Be Careful What You Backpropagate: A Case For Linear Output Activations & Gradient Boosting

arXiv: https://arxiv.org/abs/1707.04199 · HTML: https://mlsanity.com/paper/1707.04199/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2017.

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

- [Collective Decision of One-vs-Rest Networks for Open Set Recognition](https://mlsanity.com/paper/2103.10230/) (2021)
- [Cluster Flow: how a hierarchical clustering layer make allows deep-NNs more resilient to hacking, more human-like and easily implements relational reasoning](https://mlsanity.com/paper/2304.14081/) (2023)

## Abstract (arXiv)

In this work, we show that saturating output activation functions, such as the softmax, impede learning on a number of standard classification tasks. Moreover, we present results showing that the utility of softmax does not stem from the normalization, as some have speculated. In fact, the normalization makes things worse. Rather, the advantage is in the exponentiation of error gradients. This exponential gradient boosting is shown to speed up convergence and improve generalization. To this end, we demonstrate faster convergence and better performance on diverse classification tasks: image classification using CIFAR-10 and ImageNet, and semantic segmentation using PASCAL VOC 2012. In the latter case, using the state-of-the-art neural network architecture, the model converged 33% faster with our method (roughly two days of training less) than with the standard softmax activation, and with a slightly better performance to boot.