$\mathbb{R}^{2k}$ is Theoretically Large Enough for Embedding-based Top-$k$ Retrieval

1. 1Apply the concept of Minimal Embeddable Dimension (MED) to determine the least dimension for embedding-based top-k retrieval
2. 2Run simulations to test the robustness of MED using different similarity metrics
3. 3Configure the embedding space to achieve a unit norm for all vectors
4. 4Test the effect of epsilon gap on the retrieval performance
5. 5Analyze the trade-off between dimensionality and retrieval accuracy

Data scientists and AI engineers working on information retrieval and recommendation systems can benefit from understanding the minimal embeddable dimension to optimize their models

💡 The minimal embeddable dimension is linear in k, making it efficient for large-scale retrieval tasks

💡 MED is Θ(k) for top-k retrieval, independent of m! #informationretrieval #embeddings