Width-Induced Functional Redundancy in Large Language Models

Recent observations show that large language models (LLMs) often retain non-trivial functionality even after aggressive pruning, early-exit, sparse routing, or low-precision quantization. While these phenomena are individually well-documented, a unifying explanation remains under-articulated. This research note proposes a conceptual framework linking model width to functional redundancy, arguing that increasing width induces overlapping approximations of similar functions across parameters. As a result, partial removal or degradation of components does not immediately annihilate functionality but instead yields a low-resolution inference regime.We formalize this intuition through definitions, hypotheses, and testable predictions, and outline experimental designs to validate or falsify the framework.