# Optimizing Loss Functions Through Multivariate Taylor Polynomial Parameterization

arXiv: https://arxiv.org/abs/2002.00059 · HTML: https://mlsanity.com/paper/2002.00059/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 3 of 3)

- [Efficient Activation Function Optimization through Surrogate Modeling](https://mlsanity.com/paper/2301.05785/) (2023)
- [Evolving GAN Formulations for Higher Quality Image Synthesis](https://mlsanity.com/paper/2102.08578/) (2021)
- [Optimizing Neural Networks through Activation Function Discovery and Automatic Weight Initialization](https://mlsanity.com/paper/2304.03374/) (2023)

## Abstract (arXiv)

Metalearning of deep neural network (DNN) architectures and hyperparameters has become an increasingly important area of research. Loss functions are a type of metaknowledge that is crucial to effective training of DNNs, however, their potential role in metalearning has not yet been fully explored. Whereas early work focused on genetic programming (GP) on tree representations, this paper proposes continuous CMA-ES optimization of multivariate Taylor polynomial parameterizations. This approach, TaylorGLO, makes it possible to represent and search useful loss functions more effectively. In MNIST, CIFAR-10, and SVHN benchmark tasks, TaylorGLO finds new loss functions that outperform functions previously discovered through GP, as well as the standard cross-entropy loss, in fewer generations. These functions serve to regularize the learning task by discouraging overfitting to the labels, which is particularly useful in tasks where limited training data is available. The results thus demonstrate that loss function optimization is a productive new avenue for metalearning.