Alignment Is Not Separation: Two Geometric Axes of Cross-Lingual Sentiment Representation in a Multilingual LLM

Activation steering and refusal-direction interventions are increasingly proposed as lightweight, training-free tools for improving multilingual LLM behavior, yet their reliability varies sharply and unpredictably across languages. Prior work on cross-lingual refusal directions reports that safety-relevant interventions transfer well for some non-English, low-resource languages but fail unexplainably for others (e.g., Arabic), with the failure attributed only loosely to ``a geometric mismatch.'' We investigate this puzzle directly by extracting difference-of-means sentiment directions for six languages spanning two resourcedness/ tokenization-fragmentation categories (English; low-resource Yoruba, Igbo, Amharic; high-resource-but-heavily-fragmented Arabic, Hindi) from Qwen2.5-7B-Instruct, and measuring two distinct geometric properties: (1) directional alignment with the English sentiment direction (cosine similarity), and (2) within-language cluster separation quality (Silhouette score) between positive and negative sentiment activations. We find that these two properties are only moderately correlated ($r=0.79$, $n=5$, not significant) and diverge in informative ways: Igbo, despite low training-data resourcedness, achieves the best non-English cluster separation, while Arabic achieves the highest directional alignment with English yet only middling separation. This dissociation offers a candidate explanation for previously unexplained cross-lingual steering failures: high alignment alone does not guarantee that a language's internal representation is cleanly organized enough for a transplanted direction to act reliably. We release our full extraction and analysis pipeline and discuss concrete next steps for isolating the mechanism behind Arabic's specific vulnerability.