Large Language Models (LLMs) are prone to critical failure modes, including \textit{intrinsic faithfulness hallucinations} (also known as confabulations), where a response deviates semantically from the provided context. Frameworks designed to detect this, such as Semantic Divergence Metrics (SDM), rely on identifying latent topics shared between prompts and responses, typically by applying geometric clustering to their sentence embeddings. This creates a disconnect, as the topics are optimized for spatial proximity, not for the downstream information-theoretic analysis. In this paper, we bridge this gap by developing a principled topic identification method grounded in the Deterministic Information Bottleneck (DIB) for geometric clustering. Our key contribution is to transform the DIB method into a practical algorithm for high-dimensional data by substituting its intractable KL divergence term with a computationally efficient upper bound. The resulting method, which we dub UDIB, can be interpreted as an entropy-regularized and robustified version of K-means that inherently favors a parsimonious number of informative clusters. By applying UDIB to the joint clustering of LLM prompt and response embeddings, we generate a shared topic representation that is not merely spatially coherent but is fundamentally structured to be maximally informative about the prompt-response relationship. This provides a superior foundation for the SDM framework and offers a novel, more sensitive tool for detecting confabulations.

Monitoring cattle health and optimizing yield are key challenges faced by dairy farmers due to difficulties in tracking all animals on the farm. This work aims to showcase modern data-driven farming practices based on explainable machine learning(ML) methods that explain the activity and behaviour of dairy cattle (cows). Continuous data collection of 3-axis accelerometer sensors and usage of robust ML methodologies and algorithms, provide farmers and researchers with actionable information on cattle activity, allowing farmers to make informed decisions and incorporate sustainable practices. This study utilizes Bluetooth-based Internet of Things (IoT) devices and 4G networks for seamless data transmission, immediate analysis, inference generation, and explains the models performance with explainability frameworks. Special emphasis is put on the pre-processing of the accelerometers time series data, including the extraction of statistical characteristics, signal processing techniques, and lag-based features using the sliding window technique. Various hyperparameter-optimized ML models are evaluated across varying window lengths for activity classification. The k-nearest neighbour Classifier achieved the best performance, with AUC of mean 0.98 and standard deviation of 0.0026 on the training set and 0.99 on testing set). In order to ensure transparency, Explainable AI based frameworks such as SHAP is used to interpret feature importance that can be understood and used by practitioners. A detailed comparison of the important features, along with the stability analysis of selected features, supports development of explainable and practical ML models for sustainable livestock management.