AC-Scoreq: Amplitude-Coupled Scalable Complex 2-bit Residual Quantization for Efficient Vector Retrieval

Efficient vector retrieval requires compact representations that balance storage, ranking quality, and search time. Successive low-bit phase-code applications compensate quantization residuals, but their shared block scales leave local magnitude differences that further phase refinement cannot directly represent. We propose AC-Scoreq, a fixed-codebook complex 2-bit residual quantizer that combines phase encoding, local amplitude adaptation, and cross-stage scale fitting. It applies a fixed four-direction phase codebook to successive residuals; the final application additionally selects a relative-amplitude shape for each pair of adjacent complex coordinates. The encoder alternates discrete-code refinement with joint fitting of the block scales, and each database vector is encoded independently without corpus-level codebook training or prior knowledge of queries. Varying the number of phase-code applications enables trade-offs among retrieval quality, search time, and compression ratio. Experimental results across multiple datasets and vector dimensionalities show that AC-Scoreq maintains competitive retrieval quality and low search latency while substantially reducing vector storage overhead. Its multi-application design further provides flexible accuracy compensation across compression ratios, demonstrating the method’s effectiveness, scalability, and practical deployment value.