Many nonlinear iterative procedures generate high-dimensional trajectories whose early behavior is informative but difficult to compare directly. This paper studies a soft-computing representation problem: how to convert a short early trajectory segment into compact, interpretable, fixed-dimensional fuzzy coordinates that preserve information about subsequent convergence and trajectory geometry. The problem is investigated for iterated Pearson correlation matrices, a nonlinear matrix iteration historically connected with CONCOR-type blockmodeling and repeated-correlation methods. The proposed descriptor uses two logarithmic signals from the early post-transient regime: a step-size signal, measuring contraction magnitude, and a contraction-ratio signal, measuring local contraction evolution. Each signal is projected onto a three-node triangular fuzzy partition using zero-degree F-transform coefficients and one centered first-degree coefficient. This yields an eight-dimensional two-channel representation separating local level from local trend and contraction magnitude from contraction evolution. Across 22 matrix dimensions with 1000 trajectories per dimension, the descriptor is compared with raw trajectory samples, statistical summaries, and PCA-compressed raw features using Random Forest regression for convergence-length approximation. It achieves mean R^2 = 0.6480, close to raw trajectories (0.6518) and statistical summaries (0.6528), while improving over the step-size-only F-transform descriptor (0.5001). Repeated random-split and shifted-window experiments confirm stability. PCA and clustering further show reproducible low-dimensional organization, with the first two principal components explaining 84.26% of variance and k = 3 favored by the mean silhouette criterion.

We provide evidence that eigenanalysis of the empirical neural tangent kernel (eNTK) can surface the features used by trained neural networks. Across two standard toy models for mechanistic interpretability, Toy Models of Superposition (TMS) and a 1-layer MLP trained on modular addition, we find that the eNTK exhibits sharp spectral cliffs whose top eigenspaces align with ground-truth features. In TMS, the eNTK recovers the ground-truth features in both the sparse (high superposition) and dense regimes. In modular arithmetic, the eNTK can be used to recover Fourier feature families. Moreover, we provide evidence that a layerwise eNTK localizes features to specific layers and that the evolution of the eNTK spectrum can be used to diagnose the grokking phase transition. These results suggest that eNTK analysis may provide a practical handle for feature discovery and for detecting phase changes in small models.

Short text clustering is a known use case in the text analytics community. When the structure and content falls in the natural language domain e.g. Twitter posts or instant messages, then natural language techniques can be used, provided texts are of sufficient length to allow for use of (pre)trained models to extract meaningful information, such as part-of-speech or topic annotations. However, natural language models are not suitable for clustering transaction counterparties, as they are found in bank payment messaging systems, such as SWIFT. The manually typed tags are typically physical or legal entity details, which lack sentence structure, while containing all the variations and noise that manual entry introduces. This leaves a gap in an investigator or counter-fraud professional's toolset when looking to augment their knowledge of payment flow originator and beneficiary entities and trace funds and assets. A gap that vendors traditionally try to close with fuzzy matching tools. With these considerations in mind, we are proposing a hybrid string similarity, topic modelling, hierarchical clustering and rule-based pipeline to facilitate clustering of transaction counterparties, also catering for unknown number of expected clusters. We are also devising metrics to supplement the evaluation of the approach, based on the well-known measures of precision and recall. Testing on a real-life labelled dataset demonstrates significantly improved performance over a baseline rule-based ('keyword') approach. The approach retains most of the interpretability found in rule-based systems, as the former adds an additional level of cluster refinement to the latter. The resulting workflow reduces the need for manual review. When only a subset of the population needs to be investigated, such as in sanctions investigations, the approach allows for better control of the risks of missing entity variations.

Sparse autoencoders (SAEs) have shown promise in extracting interpretable features from complex neural networks. We present one of the first applications of SAEs to dense text embeddings from large language models, demonstrating their effectiveness in disentangling semantic concepts. By training SAEs on embeddings of over 420,000 scientific paper abstracts from computer science and astronomy, we show that the resulting sparse representations maintain semantic fidelity while offering interpretability. We analyse these learned features, exploring their behaviour across different model capacities and introducing a novel method for identifying ``feature families'' that represent related concepts at varying levels of abstraction. To demonstrate the practical utility of our approach, we show how these interpretable features can be used to precisely steer semantic search, allowing for fine-grained control over query semantics. This work bridges the gap between the semantic richness of dense embeddings and the interpretability of sparse representations. We open source our embeddings, trained sparse autoencoders, and interpreted features, as well as a web app for exploring them.

E-Commerce marketplaces support millions of daily transactions, and some disagreements between buyers and sellers are unavoidable. Resolving disputes in an accurate, fast, and fair manner is of great importance for maintaining a trustworthy platform. Simple cases can be automated, but intricate cases are not sufficiently addressed by hard-coded rules, and therefore most disputes are currently resolved by people. In this work we take a first step towards automatically assisting human agents in dispute resolution at scale. We construct a large dataset of disputes from the eBay online marketplace, and identify several interesting behavioral and linguistic patterns. We then train classifiers to predict dispute outcomes with high accuracy. We explore the model and the dataset, reporting interesting correlations, important features, and insights.