arXiv:2603.03415v4 Announce Type: replace Abstract: In this work, we investigate how the internal representations of Large Language Models (LLMs) change with inputs of increasing difficulty. Although sparsity changes may not be obvious for individual samples, dataset-level results reveal a consistent statistical trend: as task difficulty increases (e.g., harder questions, longer contexts, or more answer choices), the last hidden states of LLMs become systematically sparser. In short, \textbf{the harder the task, the sparser the representation}. This sparsity--difficulty relation is observable across diverse models and domains, suggesting that harder inputs drive more concentrated activation patterns in the last hidden state. Through a series of controlled analyses and learning-dynamics experiments, we show that representational density is a learned property of data familiarity: models develop rich, distributed representations for mastered patterns, while unfamiliar inputs default to sparser activations. Our finding is also actionable. We illustrate this with Sparsity-Guided Curriculum In-Context Learning (SG-ICL), which uses sparsity to select few-shot demonstrations matched to the query's difficulty, outperforming standard CoT and Auto-CoT baselines on MATH-500. Our study provides new insights into how LLM representations reflect task difficulty and how this signal can be leveraged for inference. The source code is available at the URL: https://github.com/MingyuJ666/sparsityLLM.