# BERTops: Studying BERT Representations under a Topological Lens

arXiv: https://arxiv.org/abs/2205.00953 · HTML: https://mlsanity.com/paper/2205.00953/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 46 references that are in the map.
- First posted on arXiv 2 May 2022.

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

- [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)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Quantifying Attention Flow in Transformers](https://mlsanity.com/paper/2005.00928/) (2020)
- [Universal Adversarial Triggers for Attacking and Analyzing NLP](https://mlsanity.com/paper/1908.07125/) (2019)
- [Is BERT Really Robust? A Strong Baseline for Natural Language Attack on Text Classification and Entailment](https://mlsanity.com/paper/1907.11932/) (2019)
- [Generating Natural Language Adversarial Examples](https://mlsanity.com/paper/1804.07998/) (2018)
- [TextBugger: Generating Adversarial Text Against Real-world Applications](https://mlsanity.com/paper/1812.05271/) (2018)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Visualizing and Measuring the Geometry of BERT](https://mlsanity.com/paper/1906.02715/) (2019)
- [To Tune or Not to Tune? Adapting Pretrained Representations to Diverse Tasks](https://mlsanity.com/paper/1903.05987/) (2019)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Predicting the Generalization Gap in Deep Networks with Margin Distributions](https://mlsanity.com/paper/1810.00113/) (2018)
- [A Tutorial on Kernel Density Estimation and Recent Advances](https://mlsanity.com/paper/1704.03924/) (2017)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology](https://mlsanity.com/paper/1812.09764/) (2018)
- [Visualizing and Understanding the Effectiveness of BERT](https://mlsanity.com/paper/1908.05620/) (2019)
- [Computing the Testing Error without a Testing Set](https://mlsanity.com/paper/2005.00450/) (2020)
- [Predicting Performance for Natural Language Processing Tasks](https://mlsanity.com/paper/2005.00870/) (2020)
- [Artificial Text Detection via Examining the Topology of Attention Maps](https://mlsanity.com/paper/2109.04825/) (2021)
- [Characterizing the Decision Boundary of Deep Neural Networks](https://mlsanity.com/paper/1912.11460/) (2019)
- [Few-Shot Learning on Graphs via Super-Classes based on Graph Spectral Measures](https://mlsanity.com/paper/2002.12815/) (2020)
- [Semi-Supervised Learning via Compact Latent Space Clustering](https://mlsanity.com/paper/1806.02679/) (2018)
- [On the Downstream Performance of Compressed Word Embeddings](https://mlsanity.com/paper/1909.01264/) (2019)

## Built on by (most cited first, 5 of 5)

- [Can BERT eat RuCoLA? Topological Data Analysis to Explain](https://mlsanity.com/paper/2304.01680/) (2023)
- [k* Distribution: Evaluating the Latent Space of Deep Neural Networks using Local Neighborhood Analysis](https://mlsanity.com/paper/2312.04024/) (2023)
- [Topological Data Analysis Applications in Natural Language Processing: A Survey](https://mlsanity.com/paper/2411.10298/) (2024)
- [Addressing caveats of neural persistence with deep graph persistence](https://mlsanity.com/paper/2307.10865/) (2023)
- [Cloud-ScPO: Hidden-State Geometry for Semi-Supervised Preference Optimization in LLM Reasoning](https://mlsanity.com/paper/2608.01014/) (2026)

## Abstract (arXiv)

Proposing scoring functions to effectively understand, analyze and learn various properties of high dimensional hidden representations of large-scale transformer models like BERT can be a challenging task. In this work, we explore a new direction by studying the topological features of BERT hidden representations using persistent homology (PH). We propose a novel scoring function named "persistence scoring function (PSF)" which: (i) accurately captures the homology of the high-dimensional hidden representations and correlates well with the test set accuracy of a wide range of datasets and outperforms existing scoring metrics, (ii) captures interesting post fine-tuning "per-class" level properties from both qualitative and quantitative viewpoints, (iii) is more stable to perturbations as compared to the baseline functions, which makes it a very robust proxy, and (iv) finally, also serves as a predictor of the attack success rates for a wide category of black-box and white-box adversarial attack methods. Our extensive correlation experiments demonstrate the practical utility of PSF on various NLP tasks relevant to BERT.