LIMIT-small-cyclic

LIMIT-small-cyclic is a self-produced dataset created for the reproduction of the paper On the Theoretical Limitations of Embedding-Based Retrieval.
The reproduction codebase is available at https://github.com/gabor-hosu/embedding_dimension_limit.

The dataset is derived from the name and attribute distribution of the original LIMIT dataset, while following the same underlying construction principles described in the paper.

Due to hardware constraints, the dataset size was scaled down compared to the original experimental setup. The released version contains 2,000 documents and 23 queries.

Dataset Generation

The dataset was generated using the following procedure.

First, a cyclic binary relevance matrix is constructed, defining which documents are relevant to which queries:

import numpy as np
from itertools import combinations

def cyclic_matrix(num_of_queries: int, k: int = 2) -> np.array:
    num_of_cols = (num_of_queries - 1) * (k - 1) + 1
    A = np.zeros((num_of_queries, num_of_cols), dtype=bool)

    rows = np.arange(num_of_queries).reshape(num_of_queries, 1)  # (N, 1)
    starts = (k - 1) * np.arange(num_of_queries).reshape(num_of_queries, 1)  # (N, 1)
    offsets = np.arange(k).reshape(1, k)  # (1, k)

    cols = (starts + offsets) % num_of_cols  # (N, k), via broadcasting

    A[rows, cols] = True
    return A

Next, the binary relevance structure is converted into a natural-language corpus, queries, and relevance judgments following the MTEB format:

import pandas as pd
import random

def generate_dataset(
    liked_items: list[str],
    names: list[str],
    qrel_matrix: np.ndarray,
    items_per_person: int = 20,
    total_num_of_docs: int = 2000,
    seed: int = 42,
):
    num_of_queries, num_of_docs = qrel_matrix.shape
    random.seed(seed)

    query_items = random.sample(liked_items, num_of_queries)
    remaining_items = list(set(liked_items) - set(query_items))
    
    doc_ids = np.array(random.sample(names, num_of_docs))
    remaining_doc_ids = list(set(names) - set(doc_ids))
    
    docs = {}
    qrels_data = []
    
    # fill up the binary qrel structure with natural language
    for query_idx, (mask, item) in enumerate(zip(qrel_matrix, query_items)):
        selected_doc_ids = doc_ids[mask]
        for doc_id in selected_doc_ids:
            doc = docs.get(doc_id)
            if doc is None:
                docs[doc_id] = []
                doc = docs[doc_id]

            doc.append(item)
            qrels_data.append({
                "query-id": f"query_{query_idx}",
                "corpus-id": doc_id,
                "score": 1
            })
    
    # add remaining items to the docs
    for doc_id in docs:
        num_new_items_per_docs = items_per_person - len(docs[doc_id])
        new_items = random.sample(remaining_items, num_new_items_per_docs)
        docs[doc_id].extend(new_items)
        
    num_new_docs = total_num_of_docs - len(docs)
    if num_new_docs > 0:
        new_doc_ids = random.sample(remaining_doc_ids, num_new_docs)
        docs |= {
            doc_id: random.sample(remaining_items, items_per_person)
            for doc_id in new_doc_ids
        }
    
    # build and return the proper mteb format
    corpus = pd.DataFrame(
        [
            {
                "_id": doc_id,
                "title": "",
                "text": f"{doc_id} likes {', '.join(random.sample(docs[doc_id], len(docs[doc_id])))}."
            }
            for doc_id in docs
        ]
    )

    queries = pd.DataFrame(
        [
            {
                "_id": f"query_{query_idx}",
                "text": f"Who likes {item}?"
            }
            for query_idx, item in enumerate(query_items)
        ]
    )
    
    qrels = pd.DataFrame(qrels_data)
    
    return corpus, queries, qrels

A = cyclic_matrix(num_of_queries=23)

corpus, queries, qrels = generate_dataset(
    liked_items=liked_items,
    names=names,
    qrel_matrix=A,
)

corpus.to_json("corpus.jsonl", orient="records", lines=True)
queries.to_json("queries.jsonl", orient="records", lines=True)
qrels.to_json("qrels.jsonl", orient="records", lines=True)

The resulting dataset consists of a synthetic natural-language corpus, corresponding queries, and dense relevance judgments designed to stress-test embedding-based retrieval under constrained dimensionality.