# Scaling Laws for Embedding Dimension in Information Retrieval

arXiv: https://arxiv.org/abs/2602.05062 · HTML: https://mlsanity.com/paper/2602.05062/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Sparse, Dense, and Attentional Representations for Text Retrieval](https://mlsanity.com/paper/2005.00181/) (2020)
- [Overview of the TREC 2020 deep learning track](https://mlsanity.com/paper/2102.07662/) (2021)
- [RocketQAv2: A Joint Training Method for Dense Passage Retrieval and Passage Re-ranking](https://mlsanity.com/paper/2110.07367/) (2021)
- [Condenser: a Pre-training Architecture for Dense Retrieval](https://mlsanity.com/paper/2104.08253/) (2021)
- [Improving Efficient Neural Ranking Models with Cross-Architecture Knowledge Distillation](https://mlsanity.com/paper/2010.02666/) (2020)
- [A Comprehensive Survey and Experimental Comparison of Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2101.12631/) (2021)
- [SPLADE-v3: New baselines for SPLADE](https://mlsanity.com/paper/2403.06789/) (2024)
- [Seq vs Seq: An Open Suite of Paired Encoders and Decoders](https://mlsanity.com/paper/2507.11412/) (2025)
- [A Reasoning-Focused Legal Retrieval Benchmark](https://mlsanity.com/paper/2505.03970/) (2025)
- [Scaling Laws For Dense Retrieval](https://mlsanity.com/paper/2403.18684/) (2024)
- [Overview of the TREC 2021 deep learning track](https://mlsanity.com/paper/2507.08191/) (2025)
- [Scaling Sparse and Dense Retrieval in Decoder-Only LLMs](https://mlsanity.com/paper/2502.15526/) (2025)
- [Hypencoder: Hypernetworks for Information Retrieval](https://mlsanity.com/paper/2502.05364/) (2025)
- [Benchmarking Information Retrieval Models on Complex Retrieval Tasks](https://mlsanity.com/paper/2509.07253/) (2025)
- [Retrieval Capabilities of Large Language Models Scale with Pretraining FLOPs](https://mlsanity.com/paper/2508.17400/) (2025)

## Built on by (most cited first, 2 of 2)

- [Memory-Orchestrated Semantic System (MOSS): An Auditable Agentic Memory Architecture](https://mlsanity.com/paper/2607.04391/) (2026)
- [Semantically Similar, Logically Distinct: Diagnosing the Semantic-Answerability Gap in Table RAG](https://mlsanity.com/paper/2607.17742/) (2026)

## Abstract (arXiv)

Dense retrieval, which encodes queries and documents into a single dense vector, has become the dominant neural retrieval approach due to its simplicity and compatibility with fast approximate nearest neighbor algorithms. As the tasks dense retrieval performs grow in complexity, the fundamental limitations of the underlying data structure and similarity metric -- namely vectors and inner-products -- become more apparent. Prior recent work has shown theoretical limitations inherent to single vectors and inner-products that are generally tied to the embedding dimension. Given the importance of embedding dimension for retrieval capacity, understanding how dense retrieval performance changes as embedding dimension is scaled is fundamental to building next generation retrieval models that balance effectiveness and efficiency. In this work, we conduct a comprehensive analysis of the relationship between embedding dimension and retrieval performance. Our experiments include two model families and a range of model sizes from each to construct a detailed picture of embedding scaling behavior. We find that the scaling behavior fits a power law, allowing us to derive scaling laws for performance given only embedding dimension, as well as a joint law accounting for embedding dimension and model size. Our analysis shows that for evaluation tasks aligned with the training task, performance continues to improve as embedding size increases, though with diminishing returns. For evaluation data that is less aligned with the training task, we find that performance is less predictable, with performance degrading with larger embedding dimensions for certain tasks. We hope our work provides additional insight into the limitations of embeddings and their behavior as well as offers a practical guide for selecting model and embedding dimension to achieve optimal performance with reduced storage and compute costs.