arXiv:2610.29521v1 Announce Type: new Abstract: Multilingual patent prior-art retrieval requires identifying X-category references that are particularly relevant to the novelty or inventive step of a claimed invention, beyond topical similarity across languages and document views. We present X-Embedding, a two-stage framework that first learns patent-domain representations and then optimizes X-category retrieval relevance. The first stage aligns complementary sections within patents and corresponding sections across different-language patent-family members, learning from both patent structure and multilingual expressions. The second stage learns X-category relevance using examination-report X citations as positives and negatives drawn from retrieval candidates and A-category citations. Matryoshka representation learning (MRL) enables 64- and 1024-dimensional embeddings within one model. Evaluation on a common Chinese, English, and Japanese collection with four query views yields 89.09% overall macro Hit@100 at 64 dimensions, exceeding Qwen3-Embedding-0.6B and RoBERTa by 21.25 and 3.68 percentage points, respectively. Under the same second-stage training and evaluation conditions, two-stage training outperforms direct supervised fine-tuning by 3.19 points, with gains of 5.34 and 4.72 points for English and Japanese and higher scores in nine of twelve language-view combinations. Overall macro Hit@10 and Hit@20 also improve by 3.71 and 3.79 points, respectively. These results support sequential patent-domain and task adaptation for improving aggregate X-category retrieval on this multilingual collection.