In-Context Learning Operates as Concept Subspace Learning
Authors: Wei Tang, Xinyan Jiang, Fakhri Karray et al.
Summary
arXiv:2605. 18830v1 Announce Type: new Abstract: 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.
Relevance
Read next because In-Context Learning Operates as Concept Subspace Learning overlaps with clean result "LoRA persona trained on alone emits at 23.5% when a co-trained partner learns ..., vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)", clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)". Matching terms: text, rect, under, rate, control, without, full, leakage. Source: arxiv cs.LG (Machine Learning).
Abstract
arXiv:2605.18830v1 Announce Type: new Abstract: 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.