Coordinate Heterogeneity Governs Binary Quantization: From InfoNCE to Recall
This work addresses the inconsistent performance of binary quantization in embedding spaces, which excels in contrastive learning embeddings but degrades sharply in others, and resolves the lack of a unified theoretical foundation between the “random rotation” and “axis-aligned” quantization strategies. The study identifies the heterogeneity of coordinate-wise variances as the key factor governing quantization efficacy and establishes, for the first time, an analytical framework under a Gaussian structural assumption. This framework yields a closed-form solution for rank fidelity, quantitatively linking the information content of magnitude bits to variance heterogeneity, and unifies the conditions under which the two seemingly opposing strategies are optimal. Theoretical predictions are validated across 13 datasets and 6 embedding types, providing the first principled design guidelines for binary quantization systems.