The imposters among us: function vectors that ace every check and do the wrong task (in search of circularity)
star2vec
Abstract
TL;DR: We extracted shift-by-k-months function vectors on Llama-3.2-3B from few-shot prompts that contained fewer distinct months (lower diversity). The vectors passed three classic checks: the behavioral gate, stability when extracting from disjoint halves of the prompt samples (cosine similarity ≥ 0.99 for the broken vectors, 0.98 for the full set), and the causal effect (where injection tripled zero-shot accuracy and the correct answer’s probability, including for the most broken vector). However, they encoded a completely different task: output a month adjacent to the queried one, while completely ignoring “k”. Margins ranged from -0.31 to -0.94 across the broken sets, with -1.000 for the most broken set, on the months included in the few-shot prompts. The culprit is the number of distinct example inputs. Lower diversity makes the model perform the few-shot task better (from 0.38 to 0.83) even though the function vector changes identity, so the checks actually favor the imposters. After a sweep across layers and strengths, no injection setting (0 out of 672) rescued the broken vectors. Thresholds calibrated on generated random data were wrong in both directions (145–156× too lo