# On the Theoretical Limitations of Embedding-Based Retrieval

**Authors:** Orion Weller, Michael Boratko, Iftekhar Naim, Jinhyuk Lee  
**arXiv:** [2508.21038](https://arxiv.org/abs/2508.21038)  
**Date:** 2025-08-28  
**Summary page:** https://www.summarizepaper.com/en/paper/2508.21038v1/

## Key points

- Vector embeddings increasingly used for retrieval tasks
- Applications include reasoning, instruction-following, and coding
- Challenges in adapting to various queries and notions of relevance
- Theoretical limitations of vector embeddings highlighted in previous studies
- Recent study by Orion Weller et al. challenges assumption that challenges stem from unrealistic queries
- Number of top-k subsets retrievable constrained by dimensionality of embedding space
- Limitations persist even when focusing on k=2 subsets
- Introduction of new dataset called LIMIT to stress test models based on theoretical findings
- State-of-the-art models struggle on the LIMIT dataset despite its straightforward nature
- Need for future research to develop innovative methods addressing fundamental limitations in retrieval tasks

## Summary

In recent years, vector embeddings have been increasingly utilized for a wide range of retrieval tasks. These include reasoning, instruction-following, and coding. These new applications have pushed embeddings to adapt to various queries and notions of relevance. While previous studies have highlighted theoretical limitations of vector embeddings, there has been a prevailing belief that these challenges stem from unrealistic queries and can be overcome with improved training data and larger models. However, a recent study by Orion Weller et al. challenges this assumption by demonstrating that these theoretical limitations can manifest in realistic scenarios even with simple queries. By drawing connections to learning theory, the researchers show that the number of top-k subsets of documents retrievable for a given query is constrained by the dimensionality of the embedding space. Even when focusing on k=2 subsets, this limitation persists as evidenced through empirical testing with parameterized embeddings on test sets. To further investigate these constraints, the researchers introduce a new dataset called LIMIT designed to stress test models based on these theoretical findings. Surprisingly, state-of-the-art models struggle to perform well on this dataset despite its straightforward nature. This study sheds light on the boundaries of embedding models operating within the single vector paradigm and underscores the need for future research to develop innovative methods capable of addressing this fundamental limitation in retrieval tasks. In conclusion, highlights the intricate challenges faced by embedding models in handling diverse retrieval tasks and emphasizes of exploring novel approaches to overcome inherent limitations in current methodologies.