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Research11 min read

Why Sigmoid? The Mathematical Inevitability Behind Bayesian BM25

by Jaepil Jeong | February 23, 2026

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.

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Tech15 min read

Building a Probabilistic Search Engine: Bayesian BM25 and Hybrid Search

by Jaepil Jeong | February 1, 2026

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.

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