# Redundancy, Isotropy, and Intrinsic Dimensionality of Prompt-based Text Embeddings

arXiv: https://arxiv.org/abs/2506.01435 · HTML: https://mlsanity.com/paper/2506.01435/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 76 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 30 of 36)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Unsupervised Cross-lingual Representation Learning at Scale](https://mlsanity.com/paper/1911.02116/) (2019)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [NV-Embed: Improved Techniques for Training LLMs as Generalist Embedding Models](https://mlsanity.com/paper/2405.17428/) (2024)
- [Sentence-T5: Scalable Sentence Encoders from Pre-trained Text-to-Text Models](https://mlsanity.com/paper/2108.08877/) (2021)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [Supervised Learning of Universal Sentence Representations from Natural Language Inference Data](https://mlsanity.com/paper/1705.02364/) (2017)
- [LLM2Vec: Large Language Models Are Secretly Powerful Text Encoders](https://mlsanity.com/paper/2404.05961/) (2024)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Nomic Embed: Training a Reproducible Long Context Text Embedder](https://mlsanity.com/paper/2402.01613/) (2024)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Generative Representational Instruction Tuning](https://mlsanity.com/paper/2402.09906/) (2024)
- [All-but-the-Top: Simple and Effective Postprocessing for Word Representations](https://mlsanity.com/paper/1702.01417/) (2017)
- [Whitening Sentence Representations for Better Semantics and Faster Retrieval](https://mlsanity.com/paper/2103.15316/) (2021)
- [The Multilingual Amazon Reviews Corpus](https://mlsanity.com/paper/2010.02573/) (2020)
- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [NV-Retriever: Improving text embedding models with effective hard-negative mining](https://mlsanity.com/paper/2407.15831/) (2024)
- [WhiteningBERT: An Easy Unsupervised Sentence Embedding Approach](https://mlsanity.com/paper/2104.01767/) (2021)
- [Baseline Needs More Love: On Simple Word-Embedding-Based Models and Associated Pooling Mechanisms](https://mlsanity.com/paper/1805.09843/) (2018)
- [IsoScore: Measuring the Uniformity of Embedding Space Utilization](https://mlsanity.com/paper/2108.07344/) (2021)
- [Making a MIRACL: Multilingual Information Retrieval Across a Continuum of Languages](https://mlsanity.com/paper/2210.09984/) (2022)
- [I Wish I Would Have Loved This One, But I Didn't -- A Multilingual Dataset for Counterfactual Detection in Product Reviews](https://mlsanity.com/paper/2104.06893/) (2021)

## Built on by (most cited first, 11 of 11)

- [Randomly Removing 50% of Dimensions in Text Embeddings has Minimal Impact on Retrieval and Classification Tasks](https://mlsanity.com/paper/2508.17744/) (2025)
- [Learn Before Represent: Bridging Generative and Contrastive Learning for Domain-Specific LLM Embeddings](https://mlsanity.com/paper/2601.11124/) (2026)
- [Unveiling Intrinsic Dimension of Texts: from Academic Abstract to Creative Story](https://mlsanity.com/paper/2511.15210/) (2025)
- [Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch](https://mlsanity.com/paper/2605.03346/) (2026)
- [When Is 0.1% Enough? Analyzing the Combined Effects of Dimensionality Reduction and Quantization on Text Embedding Compression](https://mlsanity.com/paper/2606.01074/) (2026)
- [Representing Beauty: Towards a Participatory but Objective Latent Aesthetics](https://mlsanity.com/paper/2510.02869/) (2025)
- [Information-driven Fusion of Pathology Foundation Models for Enhanced Disease Characterization](https://mlsanity.com/paper/2512.11104/) (2025)
- [To MRL or not to MRL: Text Embeddings are Robust to Truncation Without Matryoshka Learning, Except In Heavy Truncation Scenarios](https://mlsanity.com/paper/2605.16608/) (2026)
- [Isotropy Cliffs: The Geometric Signature of Decision-Making in Large Language Models](https://mlsanity.com/paper/2608.00828/) (2026)
- [LSEAD: A Privacy-Preserving LLM-Based Speech Analysis Framework for Early Alzheimer's Disease Screening](https://mlsanity.com/paper/2608.07378/) (2026)
- [Geometric Structure Predicts Per-Example Neighborhood Loss Under PCA Truncation](https://mlsanity.com/paper/2610.17742/) (2026)

## Abstract (arXiv)

Prompt-based text embedding models, which generate task-specific embeddings upon receiving tailored prompts, have recently demonstrated remarkable performance. However, their resulting embeddings often have thousands of dimensions, leading to high storage costs and increased computational costs of embedding-based operations. In this paper, we investigate how post-hoc dimensionality reduction applied to the embeddings affects the performance of various tasks that leverage these embeddings, specifically classification, clustering, retrieval, and semantic textual similarity (STS) tasks. Our experiments show that even a naive dimensionality reduction, which keeps only the first 25% of the dimensions of the embeddings, results in a very slight performance degradation, indicating that these embeddings are highly redundant. Notably, for classification and clustering, even when embeddings are reduced to less than 0.5% of the original dimensionality the performance degradation is very small. To quantitatively analyze this redundancy, we perform an analysis based on the intrinsic dimensionality and isotropy of the embeddings. Our analysis reveals that embeddings for classification and clustering, which are considered to have very high dimensional redundancy, exhibit lower intrinsic dimensionality and less isotropy compared with those for retrieval and STS.