Embeddings API Comparison: OpenAI vs Cohere vs Voyage vs Jina

Full Model Comparison Table

OpenAI Embeddings: text-embedding-3-small & large

The most widely used embedding API — supports Matryoshka dimension reduction for storage optimization.

from openai import OpenAI
import numpy as np

client = OpenAI()

# Standard embedding — 1536 dims
response = client.embeddings.create(
    model="text-embedding-3-small",
    input=["RAG combines retrieval with LLM generation",
           "Vector databases store high-dimensional embeddings"]
)
embeddings = [item.embedding for item in response.data]
print(f"Shape: {len(embeddings)} x {len(embeddings[0])} dims")

# Matryoshka dimension reduction — truncate to 512 dims (saves 66% storage)
response_small = client.embeddings.create(
    model="text-embedding-3-small",
    input=["Compact embedding for storage-optimized RAG"],
    dimensions=512    # reduce from 1536 to 512
)
print(f"Reduced dims: {len(response_small.data[0].embedding)}")

# Cosine similarity between two embeddings
def cosine_sim(a, b):
    a, b = np.array(a), np.array(b)
    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))

sim = cosine_sim(embeddings[0], embeddings[1])
print(f"Cosine similarity: {sim:.4f}")  # ~0.7-0.8 for related topics

Cohere Embed v3 & Voyage AI

Cohere requires specifying input_type for asymmetric retrieval. Voyage AI leads MTEB general retrieval benchmarks.

import cohere
import voyageai

# COHERE — asymmetric retrieval with input_type
co = cohere.Client("YOUR_COHERE_KEY")

# Embed documents at indexing time
doc_embeddings = co.embed(
    texts=["Qdrant supports sparse and dense hybrid search",
           "pgvector adds vector search to PostgreSQL"],
    model="embed-english-v3.0",
    input_type="search_document",   # use this for indexed documents
    embedding_types=["float"]        # float | int8 | uint8 | binary
).embeddings.float

# Embed queries at search time
query_embeddings = co.embed(
    texts=["how does hybrid vector search work?"],
    model="embed-english-v3.0",
    input_type="search_query",      # use this for user queries
    embedding_types=["float"]
).embeddings.float

print(f"Doc dims: {len(doc_embeddings[0])}")    # 1024

# VOYAGE AI — top MTEB general retrieval performance
vo = voyageai.Client(api_key="YOUR_VOYAGE_KEY")

result = vo.embed(
    texts=["Voyage AI achieves state-of-the-art retrieval accuracy",
           "MTEB benchmark measures embedding quality across 56 tasks"],
    model="voyage-3",
    input_type="document"           # "document" or "query"
)
voyage_embeddings = result.embeddings
print(f"Voyage dims: {len(voyage_embeddings[0])}")  # 1024
print(f"Total tokens used: {result.total_tokens}")

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