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zeekayandHanzo Dev
638fba4c90
Bylines, paper authorship, correspondence addresses and the founder blurb under each post named an individual. They name the organisation that published the work instead: the brand on posts and pages, the research byline on papers, and research@ in place of a personal address. Both are what these repositories already used elsewhere — nothing new was coined. Co-authors are untouched. Where a paper named someone else alongside, they stay named; only the one byline changed. Bibliography entries, running heads, PDF metadata and affiliations move with it, so a citation still resolves to whoever the cited paper names. Sample and fixture data uses the placeholder name these tests already use elsewhere, so no assertion changed meaning. Co-authored-by: Hanzo Dev <[email protected]>
70 lines
2.1 KiB
Lean4
70 lines
2.1 KiB
Lean4
/-
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Authors: Antje Worring, Zoo Labs Foundation Research
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Embedding Correctness (7680-dimensional)
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Vector embeddings for semantic search and RAG.
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Zoo uses 7680-dimensional embeddings for maximum resolution.
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Maps to:
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- zoo/papers/embedding-7680.tex: embedding specification
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- hanzo/engine: embedding inference
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- zoo/node: embedding storage
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Properties:
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- Dimensionality: 7680 dimensions (highest resolution)
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- Normalization: unit-length vectors for cosine similarity
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- Determinism: same input → same embedding
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- Batching: batch embeddings preserve individual results
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Author: Zoo Labs Foundation Research
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.List.Basic
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import Mathlib.Tactic
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namespace AI.Embedding
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def standardDim : Nat := 7680
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structure EmbeddingVector where
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dim : Nat
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hash : Nat -- content hash of the vector
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normalized : Bool -- unit length for cosine sim
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axiom embed : Nat → EmbeddingVector
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axiom embed_deterministic : ∀ (input : Nat), embed input = embed input
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/-- DIMENSIONALITY: Standard embedding is 7680-dim -/
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axiom embed_dim : ∀ (input : Nat), (embed input).dim = standardDim
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theorem dim_is_7680 : standardDim = 7680 := rfl
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/-- NORMALIZATION: Embeddings are unit-length -/
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axiom embed_normalized : ∀ (input : Nat), (embed input).normalized = true
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/-- DETERMINISM: Same input always produces same vector -/
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theorem deterministic (input : Nat) :
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embed input = embed input := rfl
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/-- BATCH: Batch embedding = individual embeddings -/
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noncomputable def batchEmbed (inputs : List Nat) : List EmbeddingVector :=
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inputs.map embed
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theorem batch_length (inputs : List Nat) :
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(batchEmbed inputs).length = inputs.length := by
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simp [batchEmbed]
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theorem batch_preserves (inputs : List Nat) (i : Fin inputs.length) :
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(batchEmbed inputs)[i]'(by simp [batchEmbed, i.isLt]) = embed inputs[i] := by
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simp [batchEmbed, List.getElem_map]
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/-- 7680 > 1536 (OpenAI ada-002) -/
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theorem higher_resolution : standardDim > 1536 := by simp [standardDim]
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/-- 7680 > 3072 (OpenAI text-embedding-3-large) -/
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theorem higher_than_openai : standardDim > 3072 := by simp [standardDim]
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end AI.Embedding
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