In-Context Learning Operates as Concept Subspace Learning
For mechanistic interpretability researchers, this work provides a concrete, testable hypothesis about how ICL works in large language models, though the findings are limited to structured task families and proxy models.
The paper shows that in-context learning (ICL) operates by inferring low-dimensional concept subspaces, where task-relevant information concentrates in a small fraction of the model's activation space. In Llama-3-8B, a 68-73 dimensional subspace (out of 4096) recovers 78.8% of the accuracy gap between clean and corrupted prompts, while the complementary subspace contributes 0%.
Regression and Bayesian accounts of in-context learning (ICL) explain how demonstrations can induce predictors, while mechanistic analyses often identify compact activation directions that steer prompted behavior. However, it remains unclear whether structured demonstrations induce low-dimensional concept inference. We study this question through a concept-subspace view of ICL, in which tasks vary only along intrinsic concept coordinates, although inputs are observed in a high-dimensional ambient space. For ridge and least-squares ICL proxies, prediction decomposes exactly into concept-coordinate regression and off-subspace leakage. Under block-diagonal or near-block-diagonal covariance assumptions, the leading estimation and nuisance-sensitivity terms scale with the dimension of the concept subspace, while residual effects are controlled by cross-subspace coupling. This separation gives a mechanistic prediction: recoverable task information should concentrate in a low-dimensional, task-aligned activation subspace. On CounterFact-derived multi-relation prompts with Llama-3-8B, a 68--73-dimensional subspace of the 4096-dimensional residual stream restores 78.8% of the clean--corrupted accuracy gap, whereas patching the complementary subspace restores 0%. Concept swaps redirect predictions toward injected relations, while random and cross-task matched-rank controls are largely ineffective. Additional experiments on Qwen2.5-7B and a controlled cross-lingual rule task show the same qualitative pattern. These results support concept subspaces as compact, task-aligned mediators of recoverable ICL behavior in structured task families, without implying full-circuit recovery.