# Expressivity of Parameterized and Data-driven Representations in Quality Diversity Search

arXiv: https://arxiv.org/abs/2105.04247 · HTML: https://mlsanity.com/paper/2105.04247/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 10 May 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm](https://mlsanity.com/paper/1610.05729/) (2016)
- [Autonomous skill discovery with Quality-Diversity and Unsupervised Descriptors](https://mlsanity.com/paper/1905.11874/) (2019)

## Built on by (most cited first, 7 of 7)

- [Deep Surrogate Assisted Generation of Environments](https://mlsanity.com/paper/2206.04199/) (2022)
- [Covariance Matrix Adaptation MAP-Annealing](https://mlsanity.com/paper/2205.10752/) (2022)
- [COIL: Constrained Optimization in Learned Latent Space: Learning Representations for Valid Solutions](https://mlsanity.com/paper/2202.02163/) (2022)
- [Open-Ended Evolution for Minecraft Building Generation](https://mlsanity.com/paper/2209.03108/) (2022)
- [Full Domain Analysis in Fluid Dynamics](https://mlsanity.com/paper/2505.22275/) (2025)
- [Discount Model Search for Quality Diversity Optimization in High-Dimensional Measure Spaces](https://mlsanity.com/paper/2601.01082/) (2026)
- [Efficient Quality Diversity Optimization of 3D Buildings through 2D Pre-optimization](https://mlsanity.com/paper/2303.15896/) (2023)

## Abstract (arXiv)

We consider multi-solution optimization and generative models for the generation of diverse artifacts and the discovery of novel solutions. In cases where the domain's factors of variation are unknown or too complex to encode manually, generative models can provide a learned latent space to approximate these factors. When used as a search space, however, the range and diversity of possible outputs are limited to the expressivity and generative capabilities of the learned model. We compare the output diversity of a quality diversity evolutionary search performed in two different search spaces: 1) a predefined parameterized space and 2) the latent space of a variational autoencoder model. We find that the search on an explicit parametric encoding creates more diverse artifact sets than searching the latent space. A learned model is better at interpolating between known data points than at extrapolating or expanding towards unseen examples. We recommend using a generative model's latent space primarily to measure similarity between artifacts rather than for search and generation. Whenever a parametric encoding is obtainable, it should be preferred over a learned representation as it produces a higher diversity of solutions.