Spacy: How Foundational Knowledge is Applied

🔍 How Mathematics Powers Machine Learning in spaCy

🔢 1. Linear Algebra in spaCy

In spaCy, words, sentences, and documents are represented as vectors in a high-dimensional space. These vectors allow the model to capture semantic meaning and relationships between words.

• Vector Representation: Words like "apple" are represented as vectors in ℝⁿ:
  v_apple = [0.2, -0.1, 0.4, ..., 0.5]
• Cosine Similarity: Used to compute similarity between word vectors:
  cos(θ) = (v₁ ⋅ v₂) / (||v₁|| × ||v₂||)
  Example:

  
          import spacy
          nlp = spacy.load("en_core_web_md")
          doc1 = nlp("apple")
          doc2 = nlp("orange")
          print(doc1.similarity(doc2))
      

• Matrix Multiplication: Core operation in neural networks:
  h = W ⋅ x + b

🎲 2. Probability & Statistics in spaCy

spaCy uses statistical modeling for tasks like text classification and named entity recognition. Here's how the math fits in:

• Softmax Function: Converts raw output to probability distribution:
  P(yᵢ) = exp(zᵢ) / Σⱼ exp(zⱼ)
• Bayes’ Theorem: Foundation for many classification tasks:
  P(Class | Features) = (P(Features | Class) × P(Class)) / P(Features)
• Cross-Entropy Loss: Measures the difference between predicted and actual output:
  L = -Σ yᵢ log(ŷᵢ)

🧠 Summary Table