# Extremal learning: extremizing the output of a neural network in regression problems

arXiv: https://arxiv.org/abs/2102.03626 · HTML: https://mlsanity.com/paper/2102.03626/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 6 Feb 2021.

## Builds on (most cited first, 6 of 6)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Learning Longer-term Dependencies in RNNs with Auxiliary Losses](https://mlsanity.com/paper/1803.00144/) (2018)

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

- [Quantum Extremal Learning](https://mlsanity.com/paper/2205.02807/) (2022)

## Abstract (arXiv)

Neural networks allow us to model complex relationships between variables. We show how to efficiently find extrema of a trained neural network in regression problems. Finding the extremizing input of an approximated model is formulated as the training of an additional neural network with a loss function that minimizes when the extremizing input is achieved. We further show how to incorporate additional constraints on the input vector such as limiting the extrapolation of the extremizing input vector from the original training data set. An instructional example of this approach using TensorFlow is included.