metadata

language: en
license: cc-by-4.0
size_categories:
  - n<1K
task_categories:
  - text-ranking
tags:
  - retrieval
  - embeddings
  - theoretical-limitations
dataset_info:
  - config_name: default
    features:
      - name: query-id
        dtype: string
      - name: corpus-id
        dtype: string
      - name: score
        dtype: int64
    splits:
      - name: test
        num_examples: 2000
  - config_name: corpus
    features:
      - name: _id
        dtype: string
      - name: title
        dtype: string
      - name: text
        dtype: string
    splits:
      - name: corpus
        num_examples: 46
  - config_name: queries
    features:
      - name: _id
        dtype: string
      - name: text
        dtype: string
    splits:
      - name: queries
        num_examples: 1000
configs:
  - config_name: default
    data_files:
      - split: test
        path: qrels.jsonl
  - config_name: corpus
    data_files:
      - split: corpus
        path: corpus.jsonl
  - config_name: queries
    data_files:
      - split: queries
        path: queries.jsonl

LIMIT-small

A retrieval dataset that exposes fundamental theoretical limitations of embedding-based retrieval models. Despite using simple queries like "Who likes Apples?", state-of-the-art embedding models achieve less than 20% recall@100 on LIMIT full and cannot solve LIMIT-small (46 docs).

Introduction

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

Dataset Details

Queries (1,000): Simple questions asking "Who likes [attribute]?"

Examples: "Who likes Quokkas?", "Who likes Joshua Trees?", "Who likes Disco Music?"

Corpus (46 documents): Short biographical texts describing people and their preferences

Format: "[Name] likes [attribute1] and [attribute2]."
Example: "Geneva Durben likes Quokkas and Apples."

Qrels (2,000): Each query has exactly 2 relevant documents (score=1), creating nearly all possible combinations of 2 documents from the 46 corpus documents (C(46,2) = 1,035 combinations).

Format

The dataset follows standard MTEB format with three configurations:

default: Query-document relevance judgments (qrels), keys: corpus-id, query-id, score (1 for relevant)
queries: Query texts with IDs , keys: _id, text
corpus: Document texts with IDs, keys: _id, title (empty), and text

Purpose

Tests whether embedding models can represent all top-k combinations of relevant documents, based on theoretical results connecting embedding dimension to representational capacity. Despite the simple nature of queries, state-of-the-art models struggle due to fundamental dimensional limitations.

Sample Usage

Loading with Hugging Face Datasets

You can also load the data using the datasets library from Hugging Face:

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

Evaluation with MTEB

Evaluation was done using the MTEB framework on the v2.0.0 branch (soon to be main). An example is:

import mteb
from sentence_transformers import SentenceTransformer

model_name = "sentence-transformers/all-MiniLM-L6-v2"

# load the model using MTEB
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)
print(results)

Citation

@misc{weller2025theoreticallimit,
      title={On the Theoretical Limitations of Embedding-Based Retrieval}, 
      author={Orion Weller and Michael Boratko and Iftekhar Naim and Jinhyuk Lee},
      year={2025},
      eprint={2508.21038},
      archivePrefix={arXiv},
      primaryClass={cs.IR},
      url={https://arxiv.org/abs/2508.21038}, 
}

Datasets:

orionweller
/

LIMIT-small