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      Semantics
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Cosine Similarity
= measures angle between 2 vectors
= S_{C}(A, B)
= \cos(\theta\)
= \frac{adjacent}{hypotenuse}
= \frac{A \cdot B}{\|A\| \, \|B\|}

\[ S_C(A, B) = \frac{A \cdot B}{\|A\| \, \|B\|} \]

  
    Cosine Similarity
   +1.0 = same meaning     = n-dim-parallel and same dir
   +0.0 = unrelated        = n-dim orthogonal
   -0.1 = opposite meaning = n-dim-parallel and oppo dir

  
    








Cosine similarity 
   Example in 3D 
      measures how aligned two 3D vectors are 
         the cosine of the angle between them    


Take two 3D vectors:
\[
A = (1, 2, 3) \\
B = (4, 5, 6)  
\]

1. Dot product:  
\[
A \cdot B = 1\cdot4 + 2\cdot5 + 3\cdot6 = 32
\]  

2. Norms (lengths):  
\[
\|A\| = \sqrt{1^2 + 2^2 + 3^2} = \sqrt{14}
\]  
\[
\|B\| = \sqrt{4^2 + 5^2 + 6^2} = \sqrt{77}
\]  

3. Cosine similarity:  
\[
\cos(\theta) = \frac{A \cdot B}{\|A\|\|B\|} = \frac{32}{\sqrt{14}\sqrt{77}} \approx 0.9746
\]   

So the cosine similarity between A and B in 3D 
  is approximately 0.9746
  meaning 
     the angle between them is small and 
     they point in a very similar direction

  

  
    Meaning
   Semantics
      Text
  

  
    RAG = Retrieval Augmented Generation

Data Modality  |    
   Text        |    
      Image    | OCR
         Video | VLM
      Audio    | ASR

  

  
    .csv
.xml
.json
  

  
    SQL
.py

OCR = Optical Character Recongnition

ASR = Automatic Speech Recognition

VLM = Vision Language Model

  
    Embeddings = Vector
           = List of Numbers
             Captures semantic meaning
             Dimensions x1000 
  

  
    .png, .jpg
.mp4
.wav
  

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