Update README.md

update README.md

README.md

@@ -61,6 +61,24 @@ When a user submits a query, the system enforces groundedness through a multi-l
    of the cited chunks. The similarity is calibrated to a 0–1 scale and averaged, producing a single
    groundedness score that is surfaced to the user with a visual indicator (green/yellow/red).
 
+## Similarity Metrics for Semantic Understanding - basics
+
+Cosine similarity measures how closely two vectors (representing data like words, images, or preferences) are aligned in a multi-dimensional space by calculating the cosine of the angle between them.
+
+Archetypical cosine scores range from -1 to 1. 
+
+1: Vectors point in the exact same direction (highly similar).
+0: Vectors are at a 90-degree angle (orthogonal/unrelated).
+-1: Vectors point in opposite directions.
+
+## Beyond Pure Cosine Similarity
+
+In 2025, V.S. Raghu Parupudi proposed two metrics: Overlap Similarity (OS) and Hyperbolic Tangent Similarity (HTS) as “more robust normalization schemes, [to] capture [holistic semantic similarity more effectively than traditional methods.”   Parupudi, V. S. R. (2025). Magnitude Matters: a Superior Class of Similarity Metrics for Holistic Semantic Understanding. arXiv:2509.19323. 
+
+Parupudi concluded that “for a wide range of… NLP applications… paraphrase detection, semantic search, and inference - practitioners can achieve… performance improvement by replacing Cosine Similarity with Overlap Similarity or Hyperbolic Tangent Similarity.”
+
+Both OS and HTS attempt to introduce, to varying degrees (and with varying efficacy) 1) relational normalization 2) numerical-stability improvement within a bounded range and 3) outlier suppression. 
+
 ## Design
 
 Two-package monorepo: