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.

How can we detect when global events fundamentally reshape public discourse? This study introduces a topological framework for identifying structural change in media narratives using persistent homology. Drawing on international news articles surrounding major events - including the Russian invasion of Ukraine (Feb 2022), the murder of George Floyd (May 2020), the U.S. Capitol insurrection (Jan 2021), and the Hamas-led invasion of Israel (Oct 2023) - we construct daily co-occurrence graphs of noun phrases to trace evolving discourse. Each graph is embedded and transformed into a persistence diagram via a Vietoris-Rips filtration. We then compute Wasserstein distances and persistence entropies across homological dimensions to capture semantic disruption and narrative volatility over time. Our results show that major geopolitical and social events align with sharp spikes in both H0 (connected components) and H1 (loops), indicating sudden reorganization in narrative structure and coherence. Cross-correlation analyses reveal a typical lag pattern in which changes to component-level structure (H0) precede higher-order motif shifts (H1), suggesting a bottom-up cascade of semantic change. An exception occurs during the Russian invasion of Ukraine, where H1 entropy leads H0, possibly reflecting top-down narrative framing before local discourse adjusts. Persistence entropy further distinguishes tightly focused from diffuse narrative regimes. These findings demonstrate that persistent homology offers a mathematically principled, unsupervised method for detecting inflection points and directional shifts in public attention - without requiring prior knowledge of specific events. This topological approach advances computational social science by enabling real-time detection of semantic restructuring during crises, protests, and information shocks.

All knowledgeable referees have confirmed the novelty parts and contributions of this work. I recommend acceptance of this paper and suggest the authors refine the paper before publication. Particularly, the concerns and suggestions raised by R#4 & R#3 should be addressed. AC and SAC discussed this paper on the issues raised by R3 and converged to accept. The authors are encouraged to discuss whether CNN belongs to the models that can be explained by the method proposed.

Weaknesses: Weaknesses Evaluating feature interactions - I think the synthetic dataset experiment in Section 4.1 is a good step towards evaluating the efficacy of PID. Looking at the AUC numbers, the performance of PID, AG, and NID seems quite close. Given these are synthetic data results, and the testbed is quite controlled, I would encourage the authors to provide more insights on why the performance is similar/close. For instance, the authors note AG is "tree-based", but it is not immediately clear how or why this may the main reason PID to perform better in F5, F6, and F8. Furthermore, with NID being a similar (in spirit) baseline, I would expect more in-depth analysis and discussion on the benefits that PID brings comparatively.

Detecting statistical interactions between input features is a crucial and challenging task. Recent advances demonstrate that it is possible to extract learned interactions from trained neural networks. It has also been observed that, in neural networks, any interacting features must follow a strongly weighted connection to common hidden units. Motivated by the observation, in this paper, we propose to investigate the interaction detection problem from a novel topological perspective by analyzing the connectivity in neural networks. Specially, we propose a new measure for quantifying interaction strength, based upon the well-received theory of persistent homology.

Recently, deep learning (DL) approaches to vulnerability detection have gained significant traction. These methods demonstrate promising results, often surpassing traditional static code analysis tools in effectiveness. In this study, we explore a novel approach to vulnerability detection utilizing the tools from topological data analysis (TDA) on the attention matrices of the BERT model. Our findings reveal that traditional machine learning (ML) techniques, when trained on the topological features extracted from these attention matrices, can perform competitively with pre-trained language models (LLMs) such as CodeBERTa. This suggests that TDA tools, including persistent homology, are capable of effectively capturing semantic information critical for identifying vulnerabilities.

This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels. The proposed approach is lean enough to handle large scale datasets, and extensive numerical experiments back the intuition that it is more suitable for detecting global changes of correlation structures than existing methods. Some theoretical guarantees for quantization algorithms based on dependent time sequences are also provided.

The paper studies the topological changes from before and after cointegration, for the natural frequencies of the Z24 Bridge. The second natural frequency is known to be nonlinear in temperature, and this will serve as the main focal point of this work. Cointegration is a method of normalising time series data with respect to one another - often strongly-correlated time series. Cointegration is used in this paper to remove effects from Environmental and Operational Variations, by cointegrating the first four natural frequencies for the Z24 Bridge data. The temperature effects on the natural frequency data are clearly visible within the data, and it is desirable, for the purposes of structural health monitoring, that these effects are removed. The univariate time series are embedded in higher-dimensional space, such that interesting topologies are formed. Topological data analysis is used to analyse the raw time series, and the cointegrated equivalents. A standard topological data analysis pipeline is enacted, where simplicial complexes are constructed from the embedded point clouds. Topological properties are then calculated from the simplicial complexes; such as the persistent homology. The persistent homology is then analysed, to determine the topological structure of all the time series.

If you've heard of quantum computing, you might be excited about the possibility of applying it to machine learning applications. I work at Springboard, and we recently launched a machine learning bootcamp that includes a job guarantee. We want to make sure our graduates are exposed to cutting-edge machine learning applications -- so we put together this article as part of our research into the intersection of quantum computing and machine learning. Let's start by examining the difference between quantum computing and classical computing. In classical computing, your data is stored in physical bits and it is binary and mutually exhaustive: a bit is either in a 0 state or in a 1 state and it cannot be both at the same time.

We usually think of aerial drones as consumer technology or used by the military to fly pilot-less missions. But there is an entire industry dedicated to using drones in industrial settings like mining, construction, and insurance. The technology of industrial drones is fascinating and involves components such as ruggedized flight bodies, GPS, and LIDAR, in addition to cameras. These industrial drones combine data collection from a network of sensors with advanced image processing techniques and artificial intelligence. So I could learn more, public relations ninja, Laura Hoang, introduced me to George Mathew, CEO of industrial drone supplier, Kespry.