# When Can We Work in Embedding Space? What Text Embeddings Preserve

arXiv: https://arxiv.org/abs/2608.31059 · HTML: https://mlsanity.com/paper/2608.31059/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 47 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Inference for Regression with Variables Generated by AI or Machine Learning](https://mlsanity.com/paper/2402.15585/) (2024)
- [CAREER: A Foundation Model for Labor Sequence Data](https://mlsanity.com/paper/2202.08370/) (2022)
- [Adventures in Demand Analysis Using AI](https://mlsanity.com/paper/2501.00382/) (2024)
- [From Unstructured Data to Demand Counterfactuals: Theory and Practice](https://mlsanity.com/paper/2601.05374/) (2026)

## Abstract (arXiv)

When do text embeddings work as inputs to empirical analysis? Their use rests on an assumption: that we can trade text for its low-dimensional embedding, and lose little in doing so. I make that assumption precise under a generative model in which documents are mixtures of latent topics. I study two uses---clustering units in embedding space and controlling for high-dimensional text. A cluster of embeddings is a set of documents with similar topic mixtures; controlling for the embedding is equivalent to controlling for the topic mixture, so validity reduces to whether that mixture captures the confounding. In an application to 363 U.S. metropolitan areas, embedding-based clusters of LLM-generated economic descriptions recover interpretable economic archetypes and separate local employment dynamics more sharply than clustering on model residuals, or on a curated set of industry and demographic covariates.