# Uncertainty Estimation of Transformers' Predictions via Topological Analysis of the Attention Matrices

arXiv: https://arxiv.org/abs/2308.11295 · HTML: https://mlsanity.com/paper/2308.11295/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 22 Aug 2023.

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

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [Revealing the Dark Secrets of BERT](https://mlsanity.com/paper/1908.08593/) (2019)
- [Learning Confidence for Out-of-Distribution Detection in Neural Networks](https://mlsanity.com/paper/1802.04865/) (2018)
- [Gradient-based Adversarial Attacks against Text Transformers](https://mlsanity.com/paper/2104.13733/) (2021)
- [Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change](https://mlsanity.com/paper/1605.09096/) (2016)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Revisiting Mahalanobis Distance for Transformer-Based Out-of-Domain Detection](https://mlsanity.com/paper/2101.03778/) (2021)
- [Understanding Softmax Confidence and Uncertainty](https://mlsanity.com/paper/2106.04972/) (2021)
- [Artificial Text Detection via Examining the Topology of Attention Maps](https://mlsanity.com/paper/2109.04825/) (2021)
- [Manifold Topology Divergence: a Framework for Comparing Data Manifolds](https://mlsanity.com/paper/2106.04024/) (2021)
- [GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes](https://mlsanity.com/paper/2003.07989/) (2020)
- [Mitigating Uncertainty in Document Classification](https://mlsanity.com/paper/1907.07590/) (2019)
- [Acceptability Judgements via Examining the Topology of Attention Maps](https://mlsanity.com/paper/2205.09630/) (2022)
- [A Differentiable Language Model Adversarial Attack on Text Classifiers](https://mlsanity.com/paper/2107.11275/) (2021)
- [ScaleFace: Uncertainty-aware Deep Metric Learning](https://mlsanity.com/paper/2209.01880/) (2022)

## Built on by (most cited first, 8 of 8)

- [Hallucination Detection in LLMs with Topological Divergence on Attention Graphs](https://mlsanity.com/paper/2504.10063/) (2025)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [Mapping the Multiverse of Latent Representations](https://mlsanity.com/paper/2402.01514/) (2024)
- [Topological Data Analysis Applications in Natural Language Processing: A Survey](https://mlsanity.com/paper/2411.10298/) (2024)
- [Correcting sampling biases via importance reweighting for spatial modeling](https://mlsanity.com/paper/2309.04824/) (2023)
- [Expert-aware uncertainty estimation for quality control of neural-based blood typing](https://mlsanity.com/paper/2407.11181/) (2024)
- [A Multi-target Bayesian Transformer Framework for Predicting Cardiovascular Disease Biomarkers during Pandemics](https://mlsanity.com/paper/2509.01794/) (2025)
- [Sound Probabilistic Safety Bounds for Large Language Models](https://mlsanity.com/paper/2607.20286/) (2026)

## Abstract (arXiv)

Transformer-based language models have set new benchmarks across a wide range of NLP tasks, yet reliably estimating the uncertainty of their predictions remains a significant challenge. Existing uncertainty estimation (UE) techniques often fall short in classification tasks, either offering minimal improvements over basic heuristics or relying on costly ensemble models. Moreover, attempts to leverage common embeddings for UE in linear probing scenarios have yielded only modest gains, indicating that alternative model components should be explored. We tackle these limitations by harnessing the geometry of attention maps across multiple heads and layers to assess model confidence. Our approach extracts topological features from attention matrices, providing a low-dimensional, interpretable representation of the model's internal dynamics. Additionally, we introduce topological features to compare attention patterns across heads and layers. Our method significantly outperforms existing UE techniques on benchmarks for acceptability judgments and artificial text detection, offering a more efficient and interpretable solution for uncertainty estimation in large-scale language models.