Tri-CHEF: Complex-Hermitian Embedding Fusion for Korean Multimodal Retrieval

Tri-CHEF is a Korean multimodal retrieval system designed to run on a single consumer GPU (RTX 4070 Laptop, 8 GB VRAM). It assigns three pretrained encoders (SigLIP2, BGE-M3, DINOv2) to three orthogonal axes of a complex-valued embedding and combines them through a Hermitian-style modulus rather than a weighted sum. This design preserves each encoder's evidence axis and prevents any single channel from dominating the score. A per-domain absolute threshold is fitted from random non-matching query-document pairs, and a drift guard rejects any new muₙull that falls outside half-to-double of the previous value during incremental ingestion. A Korean-aware character-bigram lexical filter and SHA-256 content-addressed caches complete the pipeline across four domains: documents, images, video, and audio. We further extend the deployed system with a fifth domain (background music, BGM) via a deliberately decoupled CLAP+Chromaprint pipeline, demonstrating when not to fuse — a complementary design lesson to the Tri-CHEF Hermitian fusion. On the in-house corpus (2, 390 images, 34, 661 document pages, 205 video files, 117 audio files), the deployed system attains 77 ms p95 image latency, leave-one-out Doc R@5=96. 00% with MRR=0. 8893 (both dense+sparse at alphaIM=0. 20), and 93% Top-1 confidence on a 15-query Korean evaluation set. On the public MIRACL-ko benchmark (213 dev queries, 1. 486 M Wikipedia passages), the Im-axis sub-system achieves nDCG@10=77. 82%, surpassing the published BGE-M3 dense baseline by +7. 92 pp through exact FAISS IndexFlatIP search. A Korean translation is included as Tri-CHEFₚaperKorean. pdf for accessibility to Korean-language readers. Version 1. 1 (2026-05-06): Added a DOI/license footer to every page of both PDF files for standalone identification. Body content, figure/table layout, and pagination are byte-equivalent to v1. 0.