We also discuss other relevant hyper-parameters. Finally, we provide additional results from the data domaindifferentthanimages. BackgroundandSetting For the convenience of the reader, we restate our notation here. We define two kinds of purity ofA on Sn. We first develop some notation. LetVd be the volume of the unit d-dimensional ball.

Nonnegative matrix factorization (NMF) is a widely used tool for learning parts-based, low-dimensional representations of nonnegative data, with applications in vision, text, and bioinformatics. In clustering applications, orthogonal NMF (ONMF) variants further impose (approximate) orthogonality on the representation matrix so that its rows behave like soft cluster indicators. Existing algorithms, however, are typically derived from optimization viewpoints and do not explicitly exploit the conic geometry induced by NMF: data points lie in a convex cone whose extreme rays encode fundamental directions or "topics". In this work we revisit NMF from this geometric perspective and propose Cone Collapse, an algorithm that starts from the full nonnegative orthant and iteratively shrinks it toward the minimal cone generated by the data. We prove that, under mild assumptions on the data, Cone Collapse terminates in finitely many steps and recovers the minimal generating cone of $\mathbf{X}^\top$ . Building on this basis, we then derive a cone-aware orthogonal NMF model (CC-NMF) by applying uni-orthogonal NMF to the recovered extreme rays. Across 16 benchmark gene-expression, text, and image datasets, CC-NMF consistently matches or outperforms strong NMF baselines-including multiplicative updates, ANLS, projective NMF, ONMF, and sparse NMF-in terms of clustering purity. These results demonstrate that explicitly recovering the data cone can yield both theoretically grounded and empirically strong NMF-based clustering methods.

Language models are often evaluated with scalar metrics like accuracy, but such measures fail to capture how models internally represent ambiguity, especially when human annotators disagree. We propose a topological perspective to analyze how fine-tuned models encode ambiguity and more generally instances. Applied to RoBERTa-Large on the MD-Offense dataset, Mapper, a tool from topological data analysis, reveals that fine-tuning restructures embedding space into modular, non-convex regions aligned with model predictions, even for highly ambiguous cases. Over $98\%$ of connected components exhibit $\geq 90\%$ prediction purity, yet alignment with ground-truth labels drops in ambiguous data, surfacing a hidden tension between structural confidence and label uncertainty. Unlike traditional tools such as PCA or UMAP, Mapper captures this geometry directly uncovering decision regions, boundary collapses, and overconfident clusters. Our findings position Mapper as a powerful diagnostic tool for understanding how models resolve ambiguity. Beyond visualization, it also enables topological metrics that may inform proactive modeling strategies in subjective NLP tasks.

Social media has reshaped political discourse, offering politicians a platform for direct engagement while reinforcing polarization and ideological divides. This study introduces a novel topic evolution framework that integrates BERTopic-based topic modeling with Moral Foundations Theory (MFT) to analyze the longevity and moral dimensions of political topics in Twitter activity during the 117th U.S. Congress. We propose a methodology for tracking dynamic topic shifts over time and measuring their association with moral values and quantifying topic persistence. Our findings reveal that while overarching themes remain stable, granular topics tend to dissolve rapidly, limiting their long-term influence. Moreover, moral foundations play a critical role in topic longevity, with Care and Loyalty dominating durable topics, while partisan differences manifest in distinct moral framing strategies. This work contributes to the field of social network analysis and computational political discourse by offering a scalable, interpretable approach to understanding moral-driven topic evolution on social media.

The task here is to predict the toxicological activity of chemical compounds based on the Tox21 dataset, a benchmark in computational toxicology. After a domain-specific overview of chemical toxicity, we discuss current computational strategies, focusing on machine learning and deep learning. Several architectures are compared in terms of performance, robustness, and interpretability. This research introduces a novel image-based pipeline based on DenseNet121, which processes 2D graphical representations of chemical structures. Additionally, we employ Grad-CAM visualizations, an explainable AI technique, to interpret the model's predictions and highlight molecular regions contributing to toxicity classification. The proposed architecture achieves competitive results compared to traditional models, demonstrating the potential of deep convolutional networks in cheminformatics. Our findings emphasize the value of combining image-based representations with explainable AI methods to improve both predictive accuracy and model transparency in toxicology.

Malware proliferation is increasing at a tremendous rate, with hundreds of thousands of new samples identified daily. Manual investigation of such a vast amount of malware is an unrealistic, time-consuming, and overwhelming task. To cope with this volume, there is a clear need to develop specialized techniques and efficient tools for preliminary filtering that can group malware based on semantic similarity. In this paper, we propose TrapNet, a novel, scalable, and unsupervised framework for malware fingerprinting and grouping. TrapNet employs graph community detection techniques for malware fingerprinting and family attribution based on static analysis, as follows: (1) TrapNet detects packed binaries and unpacks them using known generic packer tools. (2) From each malware sample, it generates a digest that captures the underlying semantics. Since the digest must be dense, efficient, and suitable for similarity checking, we designed FloatHash (FH), a novel numerical fuzzy hashing technique that produces a short real-valued vector summarizing the underlying assembly items and their order. FH is based on applying Principal Component Analysis (PCA) to ordered assembly items (e.g., opcodes, function calls) extracted from the malware's assembly code. (3) Representing malware with short numerical vectors enables high-performance, large-scale similarity computation, which allows TrapNet to build a malware similarity network. (4) Finally, TrapNet employs state-of-the-art community detection algorithms to identify dense communities, which represent groups of malware with similar semantics. Our extensive evaluation of TrapNet demonstrates its effectiveness in terms of the coverage and purity of the detected communities, while also highlighting its runtime efficiency, which outperforms other state-of-the-art solutions.

We thank the reviewers for their constructive feedback. We will improve the presentation according to the suggestions. Below we address some major concerns. Q1 [R1]: Does this work generalize to non-Euclidean domains with arbitrary distance measures? Q2 [R1]: In terms of the name, the proposed work is more "geometric" than "topological".

Cognitive maps provide a powerful framework for understanding spatial and abstract reasoning in biological and artificial agents. While recent computational models link cognitive maps to hippocampal-entorhinal mechanisms, they often rely on global optimization rules (e.g., backpropagation) that lack biological plausibility. In this work, we propose a novel cognitive architecture for structuring episodic memories into cognitive maps using local, Hebbian-like learning rules, compatible with neural substrate constraints. Our model integrates the Successor Features framework with episodic memories, enabling incremental, online learning through agent-environment interaction. We demonstrate its efficacy in a partially observable grid-world, where the architecture autonomously organizes memories into structured representations without centralized optimization. This work bridges computational neuroscience and AI, offering a biologically grounded approach to cognitive map formation in artificial adaptive agents.