Steering beyond Language: Improving Multilingual Training-Free Text Embeddings via Paired-Residual Subspace Removal· 超越语言：通过配对残差子空间移除改善多语言无训练文本嵌入

While deriving text embeddings directly from frozen LLMs has emerged as a promising direction, existing methods focus almost exclusively on English, leaving multilingual settings largely unexplored. In this work, we present the first systematic study of multilingual training-free text embeddings in LLMs. Our analysis reveals a language-conditioned embedding geometry in which semantically equivalent sentences remain misaligned across languages. We hypothesize that language-specific variation can be disentangled from semantic content to improve embedding quality. To this end, we propose Paired-Residual Subspace Removal (PRSR), a training-free inference-time intervention that steers LLM representations toward a more language-invariant semantic space. PRSR first constructs paired residuals fro