Cognica Blog

Sigmoid is not a design choice — it is a mathematical theorem. We show why the sigmoid function is the unique valid transform for converting BM25 scores to probabilities, completing Robertson's Probability Ranking Principle after 50 years.

Modern search systems struggle to combine lexical matching with semantic understanding. We explore how we built a probabilistic ranking framework in Cognica Database that transforms BM25 scores into calibrated probabilities, enabling principled fusion of text and vector search results.