The evaluation of Large Language Models (LLMs) faces a critical challenge in construct validity, where fragmented benchmarks and ad hoc metrics frequently conflate method variance, such as prompt sensitivity, with true latent capabilities. Concurrently, emerging research suggests that LLM capabilities and outputs can be modeled as continuous geometric manifolds. In this Systematization of Knowledge (SoK), we bridge these paradigms by proposing a generalized Multi-Trait Multi-Method (MTMM) framework for LLM evaluation. We formalize and unify nine evaluation metrics, including Paraphrase Instability, Drift Score, Overton Width, and Pluralism Score, interpreting them not as isolated scalar values but as geometric measurements within a shared latent coordinate space. This spatial unification factorizes model behavior into three orthogonal latent dimensions: (1) Instability and Sensitivity, (2) Position and Alignment, and (3) Coverage and Expressiveness. By systematically separating task-irrelevant perturbations from true capability spans, the framework provides a theoretically grounded and domain-agnostic taxonomy for robust and empirically stable benchmark design.
@article{arxiv.2605.08522,
title = {Coordinates of Capability: A Unified MTMM-Geometric Framework for LLM Evaluation},
author = {Adib Sakhawat and Tahsin Islam and Takia Farhin and Syed Rifat Raiyan and Hasan Mahmud and Md Kamrul Hasan},
journal= {arXiv preprint arXiv:2605.08522},
year = {2026}
}
Comments
The paper has mistake of undertaking political spaces to semantic dimensions. This needs to be removed because this is a fetal flaw in consideration. The initial hypothesis and premise needs to be rigorously formulated within the political landscape not generalizing the metrics. Hence a withdrawal for now is necessary