# AnglE-optimized Text Embeddings

arXiv: https://arxiv.org/abs/2309.12871 · HTML: https://mlsanity.com/paper/2309.12871/

## Key facts

- Cited by 99 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 52 references that are in the map.
- First posted on arXiv 22 Sep 2023.

## Builds on (most cited first, 30 of 33)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [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)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Supervised Learning of Universal Sentence Representations from Natural Language Inference Data](https://mlsanity.com/paper/1705.02364/) (2017)
- [Skip-Thought Vectors](https://mlsanity.com/paper/1506.06726/) (2015)
- [SentEval: An Evaluation Toolkit for Universal Sentence Representations](https://mlsanity.com/paper/1803.05449/) (2018)
- [DeCLUTR: Deep Contrastive Learning for Unsupervised Textual Representations](https://mlsanity.com/paper/2006.03659/) (2020)
- [ConSERT: A Contrastive Framework for Self-Supervised Sentence Representation Transfer](https://mlsanity.com/paper/2105.11741/) (2021)
- [Whitening Sentence Representations for Better Semantics and Faster Retrieval](https://mlsanity.com/paper/2103.15316/) (2021)
- [DiffCSE: Difference-based Contrastive Learning for Sentence Embeddings](https://mlsanity.com/paper/2204.10298/) (2022)
- [Unsupervised Learning of Sentence Embeddings using Compositional n-Gram Features](https://mlsanity.com/paper/1703.02507/) (2017)
- [Learning Distributed Representations of Sentences from Unlabelled Data](https://mlsanity.com/paper/1602.03483/) (2016)
- [An Unsupervised Sentence Embedding Method by Mutual Information Maximization](https://mlsanity.com/paper/2009.12061/) (2020)
- [Scaling Sentence Embeddings with Large Language Models](https://mlsanity.com/paper/2307.16645/) (2023)
- [PromptBERT: Improving BERT Sentence Embeddings with Prompts](https://mlsanity.com/paper/2201.04337/) (2022)
- [Not All Negatives are Equal: Label-Aware Contrastive Loss for Fine-grained Text Classification](https://mlsanity.com/paper/2109.05427/) (2021)
- [Improved Universal Sentence Embeddings with Prompt-based Contrastive Learning and Energy-based Learning](https://mlsanity.com/paper/2203.06875/) (2022)
- [Whitening-based Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2305.17746/) (2023)

## Built on by (most cited first, 30 of 99)

- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [NV-Embed: Improved Techniques for Training LLMs as Generalist Embedding Models](https://mlsanity.com/paper/2405.17428/) (2024)
- [Improving Text Embeddings with Large Language Models](https://mlsanity.com/paper/2401.00368/) (2023)
- [PoisonedRAG: Knowledge Corruption Attacks to Retrieval-Augmented Generation of Large Language Models](https://mlsanity.com/paper/2402.07867/) (2024)
- [Generative Representational Instruction Tuning](https://mlsanity.com/paper/2402.09906/) (2024)
- [A Survey of Large Language Models in Medicine: Progress, Application, and Challenge](https://mlsanity.com/paper/2311.05112/) (2023)
- [Repetition Improves Language Model Embeddings](https://mlsanity.com/paper/2402.15449/) (2024)
- [FollowIR: Evaluating and Teaching Information Retrieval Models to Follow Instructions](https://mlsanity.com/paper/2403.15246/) (2024)
- [TrojanRAG: Retrieval-Augmented Generation Can Be Backdoor Driver in Large Language Models](https://mlsanity.com/paper/2405.13401/) (2024)
- [KAG: Boosting LLMs in Professional Domains via Knowledge Augmented Generation](https://mlsanity.com/paper/2409.13731/) (2024)
- [DeTeCtive: Detecting AI-generated Text via Multi-Level Contrastive Learning](https://mlsanity.com/paper/2410.20964/) (2024)
- [Multicalibration for Confidence Scoring in LLMs](https://mlsanity.com/paper/2404.04689/) (2024)
- [SUGARCREPE++ Dataset: Vision-Language Model Sensitivity to Semantic and Lexical Alterations](https://mlsanity.com/paper/2406.11171/) (2024)
- [BEAVER: An Enterprise Benchmark for Text-to-SQL](https://mlsanity.com/paper/2409.02038/) (2024)
- [GISTEmbed: Guided In-sample Selection of Training Negatives for Text Embedding Fine-tuning](https://mlsanity.com/paper/2402.16829/) (2024)
- [Towards Label-Only Membership Inference Attack against Pre-trained Large Language Models](https://mlsanity.com/paper/2502.18943/) (2025)
- [A Semantic Search Engine for Mathlib4](https://mlsanity.com/paper/2403.13310/) (2024)
- [BERGEN: A Benchmarking Library for Retrieval-Augmented Generation](https://mlsanity.com/paper/2407.01102/) (2024)
- [Simple Techniques for Enhancing Sentence Embeddings in Generative Language Models](https://mlsanity.com/paper/2404.03921/) (2024)
- [Label Supervised LLaMA Finetuning](https://mlsanity.com/paper/2310.01208/) (2023)
- [Aloe: A Family of Fine-tuned Open Healthcare LLMs](https://mlsanity.com/paper/2405.01886/) (2024)
- [FeB4RAG: Evaluating Federated Search in the Context of Retrieval Augmented Generation](https://mlsanity.com/paper/2402.11891/) (2024)
- [Recent advances in text embedding: A Comprehensive Review of Top-Performing Methods on the MTEB Benchmark](https://mlsanity.com/paper/2406.01607/) (2024)
- [Cost-Effective Hallucination Detection for LLMs](https://mlsanity.com/paper/2407.21424/) (2024)
- [ViCaS: A Dataset for Combining Holistic and Pixel-level Video Understanding using Captions with Grounded Segmentation](https://mlsanity.com/paper/2412.09754/) (2024)
- [NeoBERT: A Next-Generation BERT](https://mlsanity.com/paper/2502.19587/) (2025)
- [EnrichIndex: Using LLMs to Enrich Retrieval Indices Offline](https://mlsanity.com/paper/2504.03598/) (2025)
- [Rethinking Visual Prompting for Multimodal Large Language Models with External Knowledge](https://mlsanity.com/paper/2407.04681/) (2024)
- [Large language models as uncertainty-calibrated optimizers for experimental discovery](https://mlsanity.com/paper/2504.06265/) (2025)
- [Generative Adversarial Reviews: When LLMs Become the Critic](https://mlsanity.com/paper/2412.10415/) (2024)

## Abstract (arXiv)

High-quality text embedding is pivotal in improving semantic textual similarity (STS) tasks, which are crucial components in Large Language Model (LLM) applications. However, a common challenge existing text embedding models face is the problem of vanishing gradients, primarily due to their reliance on the cosine function in the optimization objective, which has saturation zones. To address this issue, this paper proposes a novel angle-optimized text embedding model called AnglE. The core idea of AnglE is to introduce angle optimization in a complex space. This novel approach effectively mitigates the adverse effects of the saturation zone in the cosine function, which can impede gradient and hinder optimization processes. To set up a comprehensive STS evaluation, we experimented on existing short-text STS datasets and a newly collected long-text STS dataset from GitHub Issues. Furthermore, we examine domain-specific STS scenarios with limited labeled data and explore how AnglE works with LLM-annotated data. Extensive experiments were conducted on various tasks including short-text STS, long-text STS, and domain-specific STS tasks. The results show that AnglE outperforms the state-of-the-art (SOTA) STS models that ignore the cosine saturation zone. These findings demonstrate the ability of AnglE to generate high-quality text embeddings and the usefulness of angle optimization in STS.