Compressing large language models (LLMs), often consisting of billions of parameters, provides faster inference, smaller memory footprints, and enables local deployment. The standard compression techniques are pruning and quantization, with the former eliminating redundant connections in model layers and the latter representing model parameters with as little as 4 bits. The key tradeoff is between the degree of compression and the impact on the quality of the compressed model. Existing research on LLM compression primarily focuses on performance in terms of general metrics like perplexity or downstream task accuracy. More fine-grained metrics, such as those measuring parametric knowledge, remain significantly underexplored. To help bridge this gap, we present a comprehensive analysis across multiple model families using the LAMA and LM-Harness benchmarks in order to systematically quantify the effect of commonly employed compression techniques on model performance. A particular focus is on tradeoffs involving parametric knowledge, with the goal of providing practitioners with practical insights to make informed decisions on compression.

Knowledge graph (KG) embeddings learn low- dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention- based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.