# Topological Data Analysis for Speech Processing

arXiv: https://arxiv.org/abs/2211.17223 · HTML: https://mlsanity.com/paper/2211.17223/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [HuBERT: Self-Supervised Speech Representation Learning by Masked Prediction of Hidden Units](https://mlsanity.com/paper/2106.07447/) (2021)
- [VoxCeleb: a large-scale speaker identification dataset](https://mlsanity.com/paper/1706.08612/) (2017)
- [SUPERB: Speech processing Universal PERformance Benchmark](https://mlsanity.com/paper/2105.01051/) (2021)
- [W2v-BERT: Combining Contrastive Learning and Masked Language Modeling for Self-Supervised Speech Pre-Training](https://mlsanity.com/paper/2108.06209/) (2021)
- [Speech Model Pre-training for End-to-End Spoken Language Understanding](https://mlsanity.com/paper/1904.03670/) (2019)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Probing Pretrained Language Models for Lexical Semantics](https://mlsanity.com/paper/2010.05731/) (2020)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)
- [ASVspoof 2019: spoofing countermeasures for the detection of synthesized, converted and replayed speech](https://mlsanity.com/paper/2102.05889/) (2021)
- [Artificial Text Detection via Examining the Topology of Attention Maps](https://mlsanity.com/paper/2109.04825/) (2021)
- [Acceptability Judgements via Examining the Topology of Attention Maps](https://mlsanity.com/paper/2205.09630/) (2022)
- [Understanding Self-Attention of Self-Supervised Audio Transformers](https://mlsanity.com/paper/2006.03265/) (2020)
- [SepTr: Separable Transformer for Audio Spectrogram Processing](https://mlsanity.com/paper/2203.09581/) (2022)
- [Speaker Normalization for Self-supervised Speech Emotion Recognition](https://mlsanity.com/paper/2202.01252/) (2022)
- [The Topological BERT: Transforming Attention into Topology for Natural Language Processing](https://mlsanity.com/paper/2206.15195/) (2022)
- [Learning Rate Curriculum](https://mlsanity.com/paper/2205.09180/) (2022)
- [Dialogue Term Extraction using Transfer Learning and Topological Data Analysis](https://mlsanity.com/paper/2208.10448/) (2022)
- [Towards Emotion Recognition: A Persistent Entropy Application](https://mlsanity.com/paper/1811.09607/) (2018)

## Built on by (most cited first, 9 of 9)

- [Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts](https://mlsanity.com/paper/2306.04723/) (2023)
- [AI-generated text boundary detection with RoFT](https://mlsanity.com/paper/2311.08349/) (2023)
- [Hallucination Detection in LLMs with Topological Divergence on Attention Graphs](https://mlsanity.com/paper/2504.10063/) (2025)
- [TOPFORMER: Topology-Aware Authorship Attribution of Deepfake Texts with Diverse Writing Styles](https://mlsanity.com/paper/2309.12934/) (2023)
- [Topological Data Analysis Applications in Natural Language Processing: A Survey](https://mlsanity.com/paper/2411.10298/) (2024)
- [Topological data analysis of human vowels: Persistent homologies across representation spaces](https://mlsanity.com/paper/2310.06508/) (2023)
- [The Density of Cross-Persistence Diagrams and Its Applications](https://mlsanity.com/paper/2603.11623/) (2026)
- [Topology-enhanced machine learning for speech signal processing](https://mlsanity.com/paper/2311.15210/) (2023)
- [CodeTD: Topology of Attention Detects Hallucinations in Code LLMs](https://mlsanity.com/paper/2609.07779/) (2026)

## Abstract (arXiv)

We apply topological data analysis (TDA) to speech classification problems and to the introspection of a pretrained speech model, HuBERT. To this end, we introduce a number of topological and algebraic features derived from Transformer attention maps and embeddings. We show that a simple linear classifier built on top of such features outperforms a fine-tuned classification head. In particular, we achieve an improvement of about 9% accuracy and 5% ERR on four common datasets; on CREMA-D, the proposed feature set reaches a new state of the art performance with accuracy 80.155. We also show that topological features are able to reveal functional roles of speech Transformer heads; e.g., we find the heads capable to distinguish between pairs of sample sources (natural/synthetic) or voices without any downstream fine-tuning. Our results demonstrate that TDA is a promising new approach for speech analysis, especially for tasks that require structural prediction. Appendices, an introduction to TDA, and other additional materials are available here - https://topohubert.github.io/speech-topology-webpages/