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This research identifies a fundamental mechanism in Large Language Models where increasing out-of-distribution difficulty triggers a shift toward sparser hidden states, effectively concentrating computation into specialized subspaces to stabilize reasoning. The authors validate this phenomenon across diverse domains and propose Sparsity-Guided Curriculum In-Context Learning (SG-ICL), which leverages this adaptive behavior to optimize few-shot demonstration scheduling for improved performance. These findings offer critical mechanistic insights into how models internally handle complexity, moving beyond empirical benchmarks to explain the structural dynamics of LLM adaptation under stress.
Farther the Shift, Sparser the Representation: Analyzing OOD Mechanisms in LLMs
arXiv:2603.03415v3 Announce Type: replace Abstract: In this work, we investigate how Large Language Models (LLMs) adapt their internal representations when encountering inputs of increasing difficulty, quantified as the degree of out-of-distribution (OOD) shift. We reveal a consistent and quantifiable phenomenon: as task difficulty increases, whether through harder reasoning questions, longer contexts, or adding answer choices, the last hidden states of LLMs become substantially sparser. In short, \textbf{\textit{the farther the shift, the sparser the representations}}. This sparsity--difficulty relation is observable across diverse models and domains, suggesting that language models respond to unfamiliar or complex inputs by concentrating computation into specialized subspaces in the last hidden state. Through a series of controlled analyses with a learning dynamic explanation, we demonstrate that this sparsity is not incidental but an adaptive mechanism for stabilizing reasoning under OOD. Leveraging this insight, we design \textit{Sparsity-Guided Curriculum In-Context Learning (SG-ICL)}, a strategy that explicitly uses representation sparsity to schedule few-shot demonstrations, leading to considerable performance enhancements. Our study provides new mechanistic insights into how LLMs internalize OOD challenges. The source code is available at the URL: https://github.com/MingyuJ666/sparsityLLM.
Abstract:In this work, we investigate how Large Language Models (LLMs) adapt their internal representations when encountering inputs of increasing difficulty, quantified as the degree of out-of-distribution (OOD) shift. We reveal a consistent and quantifiable phenomenon: as task difficulty increases, whether through harder reasoning questions, longer contexts, or adding answer choices, the last hidden states of LLMs become substantially sparser. In short, \textbf{\textit{the farther the shift, the sparser the representations}}. This sparsity--difficulty relation is observable across diverse models and domains, suggesting that language models respond to unfamiliar or complex inputs by concentrating computation into specialized subspaces in the last hidden state. Through a series of controlled analyses with a learning dynamic explanation, we demonstrate that this sparsity is not incidental but an adaptive mechanism for stabilizing reasoning under OOD. Leveraging this insight, we design \textit{Sparsity-Guided Curriculum In-Context Learning (SG-ICL)}, a strategy that explicitly uses representation sparsity to schedule few-shot demonstrations, leading to considerable performance enhancements. Our study provides new mechanistic insights into how LLMs internalize OOD challenges. The source code is available at the URL: this https URL.
Computation and Language (cs.CL); Artificial Intelligence (cs.AI)
arXiv:2603.03415 [cs.CL]
(or arXiv:2603.03415v3 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2603.03415 Focus to learn more arXiv-issued DOI via DataCite
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