On the Theoretical Limitations of Embedding-based Retrieval

This repository contains the official resources for the paper "On the Theoretical Limitations of Embedding-based Retrieval". This work introduces the LIMIT dataset, designed to stress-test embedding models based on theoretical principles. We show that for any given embedding dimension d, there exists a combination of documents that cannot be returned by any query. We use this theory to instantiate the dataset LIMIT, finding that even state-of-the-art models struggle: highlighting a fundamental limitation of the current single-vector embedding paradigm.

Overview

• Data
• Code
• Evaluation
• Citation
• License and disclaimer

Data

The datasets used in our experiments are available in the data/ directory of this repository, formatted in MTEB style (i.e. json lines).

Each dataset contains:

• A queries.json file containing a line for each of the 1000 queries, each with an _id and the text field.
• A corpus.json file containing a line for each of the 50k (or 46 if using the small version) documents, each with an _id, text and empty title field.
• A qrels.json file containing rows for each of the 2000 relevant query->doc mappings, mapping query-id of the queries into the corpus-id in the documents, with score indicating relevance.

• Full Dataset (limit): The complete dataset, containing 50k documents.

  • Link to data/limit

• Small Sample (limit-small): A smaller version with only the 46 documents relevant to the queries.

  • Link to data/limit-small

Code

We provide code to generate the LIMIT style datasets, as well as to run the free embedding experiment in the code/ folder.

• Dataset Generation: To generate the dataset from scratch, you can use the Jupyter notebook located at code/generate_limit_dataset.ipynb. This contains all necessary steps and dependencies.

  • Link to code/generate_limit_dataset.ipynb

• Free Embedding Experiments: The script to run the free embedding experiments can be found in code/free_embedding_experiment.py.

  • Link to code/free_embedding_experiment.py

If you use the free embedding code, you'll need to install the following requirements.

Installation

We recommend using the uv package manager.

# Create a virtual environment
uv venv
source .venv/bin/activate

# Install dependencies
uv pip install -r https://raw.githubusercontent.com/google-deepmind/limit/refs/heads/main/code/requirements.txt

Loading with Huggingface Datasets

You can also load the data using the datasets library from Huggingface (LIMIT, LIMIT-small):

from datasets import load_dataset
ds = load_dataset("orionweller/LIMIT-small", "corpus") # also available: queries, test (contains qrels).

Evaluation

Evaluation was done using the MTEB framework. You can reproduce this only on the v2.0.0 branch (soon to be main). Note that the v2.0.0 branch is changing rapidly, so please install the version pinned in the requirements until it becomes main. An example is:

import mteb
from sentence_transformers import SentenceTransformer

# load the model using MTEB
model_name = "sentence-transformers/all-MiniLM-L6-v2"
model = mteb.get_model(model_name) # will default to SentenceTransformers(model_name) if not implemented in MTEB
# or using SentenceTransformers
model = SentenceTransformer(model_name)

# select the desired tasks and evaluate
tasks = mteb.get_tasks(tasks=["LIMITSmallRetrieval"]) # or use LIMITRetrieval for the full dataset
results = mteb.evaluate(model, tasks=tasks)

Please see their Github for more details.

Citation

If you use this work, please cite the paper as:

@article{weller2025theoretical,
  title={On the Theoretical Limitations of Embedding-Based Retrieval},
  author={Weller, Orion and Boratko, Michael and Naim, Iftekhar and Lee, Jinhyuk},
  journal={arXiv preprint arXiv:2508.21038},
  year={2025}
}

License and disclaimer

Copyright 2025 Google LLC

All software is licensed under the Apache License, Version 2.0 (Apache 2.0); you may not use this file except in compliance with the Apache 2.0 license. You may obtain a copy of the Apache 2.0 license at: https://www.apache.org/licenses/LICENSE-2.0

All other materials are licensed under the Creative Commons Attribution 4.0 International License (CC-BY). You may obtain a copy of the CC-BY license at: https://creativecommons.org/licenses/by/4.0/legalcode

Unless required by applicable law or agreed to in writing, all software and materials distributed here under the Apache 2.0 or CC-BY licenses are distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the licenses for the specific language governing permissions and limitations under those licenses.

This is not an official Google product.