VENICE: UNIVERSAL SPECTRAL RATE-DISTORTION QUANTIZATION FRAMEWORK FOR VECTOR SEARCH

High-dimensional vector embeddings impose severe memory and latency constraints in large-scale maximum inner product search. Vector quantization has emerged as the standard compression paradigm, where existing state-of-the-art methods perform effectively under classical assumptions of uncorrelated dimensions and isotropic energy distributions. Most real-world embeddings, however, exhibit a different geometry characterized by coordinate cross-correlations and anisotropic spectral decay, which we prove randomized Hadamard transforms redistribute rather than remove. To harness the benefits of non-uniform bit budgets, remove these cross-correlations, and correct inner product distortion, we present VENICE, a universal spectral framework that wraps arbitrary base quantizers as plug-and-play black boxes. Grounded in Shannon rate-distortion theory, VENICE transforms anisotropic embeddings into decoupled sub-vectors of uniform sensitivity through closed-form spectral decorrelation, water-filling rate allocation, and sensitivity equalization. This establishes the geometry downstream codecs were designed for, while norm restoration corrects the shrinkage of their output. We not only mathematically prove the foundational properties of VENICE, but also empirically validate its benefits across five benchmarks, wrapping six codecs of diverse nature. Across 4-, 2-, and 1-bit regimes, VENICE consistently improves both training-free and learned codecs on anisotropic spectra, cutting recall loss by up to 93% and rescuing ultra-low-bit quantizers from performance collapse.