Cosine Similarity & Angular Distance
Orientation-Invariant Proximity for High-Dimensional Sparse & Dense Vectors
#Linear Algebra#Vector Search#Embeddings#NLP#Information Retrieval
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STAGE 1 / 7— Anti-Pattern
Section 1: The LLM Anti-Pattern vs Right-Sized Model
The Naive Generative LLM Approach:
Sending pairs of document embeddings or text paragraphs to an LLM asking: "Rate how semantically similar these two passages are from 0 to 1".
Why It Fails in Production:
Costs 50,000x more compute, introduces prompt drift, takes seconds instead of nanoseconds, and fails to obey mathematical metric properties.
Targeted Algorithm (Cosine Similarity & Angular Distance)
Latency:0.002ms (AVX/SIMD)
Cost / 1M Ops:$0.00
Determinism:100% Deterministic
Generative LLM Alternative
Latency:1,800ms
Cost / 1M Ops:$5,000
Determinism:Subjective / Inconsistent