Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are dominated by graph-based proxies that quantify structural connectivity but do not clarify what constitutes high-quality reasoning; such abstractions can be overly simplistic for inherently complex processes. We introduce a topological data analysis (TDA)-based evaluation framework that captures the geometry of reasoning traces and enables label-efficient, automated assessment. In our empirical study, topological features yield substantially higher predictive power for assessing reasoning quality than standard graph metrics, suggesting that effective reasoning is better captured by higher-dimensional geometric structures rather than purely relational graphs. We further show that a compact, stable set of topological features reliably indicates trace quality, offering a practical signal for future reinforcement learning algorithms.

Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically models data as filtered cubical complexes from which we can extract discriminative features using persistence homology. Meanwhile, convolutional neural networks (CNNs) have been shown to be biased towards texture based local features. To address this limitation, we propose a TDA feature engineering pipeline and a simple method to integrate topological features with deep learning models on remote sensing classification. Our method improves the performance of a ResNet18 model on the EuroSAT dataset by 1.44% achieving 99.33% accuracy, which surpasses all previously reported single-model accuracies, including those with larger architectures, such as ResNet50 (2x larger) and XL Vision Transformers (197x larger). We additionally show that our method's accuracy is 1.82% higher than our ResNet18 baseline on the RESISC45 dataset. To our knowledge, this is the first application of TDA features in satellite scene classification with deep learning. This demonstrates that TDA features can be integrated with deep learning models, even on datasets without explicit topological structures, thereby increasing the applicability of TDA. A clean implementation of our method will be made publicly available upon publication.

The surge of data available on the internet has led to the adoption of various computational methods to analyze and extract valuable insights from this wealth of information. Among these, the field of Machine Learning (ML) has thrived by leveraging data to extract meaningful insights. However, ML techniques face notable challenges when dealing with real-world data, often due to issues of imbalance, noise, insufficient labeling, and high dimensionality. To address these limitations, some researchers advocate for the adoption of Topological Data Analysis (TDA), a statistical approach that discerningly captures the intrinsic shape of data despite noise. Despite its potential, TDA has not gained as much traction within the Natural Language Processing (NLP) domain compared to structurally distinct areas like computer vision. Nevertheless, a dedicated community of researchers has been exploring the application of TDA in NLP, yielding 87 papers we comprehensively survey in this paper. Our findings categorize these efforts into theoretical and non-theoretical approaches. Theoretical approaches aim to explain linguistic phenomena from a topological viewpoint, while non-theoretical approaches merge TDA with ML features, utilizing diverse numerical representation techniques. We conclude by exploring the challenges and unresolved questions that persist in this niche field. Resources and a list of papers on this topic can be found at: https://github.com/AdaUchendu/AwesomeTDA4NLP.

Recent advances in Large Language Models (LLMs) have enabled the generation of open-ended high-quality texts, that are non-trivial to distinguish from human-written texts. We refer to such LLM-generated texts as \emph{deepfake texts}. There are currently over 11K text generation models in the huggingface model repo. As such, users with malicious intent can easily use these open-sourced LLMs to generate harmful texts and misinformation at scale. To mitigate this problem, a computational method to determine if a given text is a deepfake text or not is desired--i.e., Turing Test (TT). In particular, in this work, we investigate the more general version of the problem, known as \emph{Authorship Attribution (AA)}, in a multi-class setting--i.e., not only determining if a given text is a deepfake text or not but also being able to pinpoint which LLM is the author. We propose \textbf{TopRoBERTa} to improve existing AA solutions by capturing more linguistic patterns in deepfake texts by including a Topological Data Analysis (TDA) layer in the RoBERTa model. We show the benefits of having a TDA layer when dealing with noisy, imbalanced, and heterogeneous datasets, by extracting TDA features from the reshaped $pooled\_output$ of RoBERTa as input. We use RoBERTa to capture contextual representations (i.e., semantic and syntactic linguistic features), while using TDA to capture the shape and structure of data (i.e., linguistic structures). Finally, \textbf{TopRoBERTa}, outperforms the vanilla RoBERTa in 2/3 datasets, achieving up to 7\% increase in Macro F1 score.