Cognica Blog

Between models and hardware lies an invisible structural gap — a data layer that should exist but doesn't. We examine why the current AI infrastructure stack is fragmented, why this is a structural problem rather than a transitional one, and what conditions a proper solution must satisfy. We then present UQA and the Cognica engine as one concrete response to these conditions.

A cosine similarity of 0.85 tells you an angle, not a probability. We show how to transform vector similarity scores into calibrated relevance probabilities using distributional statistics that ANN indexes already compute — completing the probabilistic unification of text and vector retrieval.

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.

This article provides a technical analysis of why legal case search is challenging in the legal services market. We examine the structural characteristics of legal case data and the limitations of existing distributed architectures (RDB + ElasticSearch + Vector DB), and explain why integrated search based on a single database is necessary.

Explains how to build a natural language search service by applying vector search to a case law search demo using FTS.