Rules Amortize, Pairings Don't: Linguistic Structure Determines What Latent Task Representations Can Replace In-Context Learning

Gunmay Jhingran

In-context learning (ICL) can be amortized into latent objects (task vectors, function vectors, context vectors) that recover few-shot behavior at zero-shot inference cost, but recent theory shows a static vector acts as a single synthetic demonstration and must fail on high-rank mappings such as word-level bijections. We ask a linguistic version of this question: which linguistic operations can be amortized out of the prompt? We train a 2.6M-parameter network that reads the geometry of a few-shot support set (centroid, principal subspace, spectrum, computed once and cached) and produces an input-conditioned additive update to the query's residual stream at a mid-depth layer of a frozen GPT-2-large/XL. Across eight inflectional directions and one lexical relation, under a canonical split that bars inverted-pair leakage between directions, three regimes emerge. On forward inflection, where 10-shot ICL is strong (0.67-0.89) and extracted task vectors collapse (<=0.06), the transform matches ICL at strictly zero-shot per-query cost. On lemmatization directions, which frozen GPT-2 can execute but 10 demonstrations systematically fail to convey (ICL 0.13-0.48 at 1.5B), the transform…