State Of The Art Is One Index.

CALDEX was tested on three of the world’s hardest benchmarks, each chosen to break retrieval in a different place: LIMIT where search by meaning runs out, Cohere 1M where memory and speed decide what search costs, and GloVe 1.2M where graph indexes lose their way. One index leads on all three, on 4 cores.

Unlock more from your vector embeddings.

CALDEX lets you unlock maximum information from your data.

01 Google DeepMind

LIMIT

Paper and dataset

On the Theoretical Limitations of Embedding-Based Retrieval. (opens in a new tab)

documents
50,000
questions, two right answers each
1,000
systems from the paper
8
Table 1. Recall@2, the share of the true top 2 found.
SystemRecall@2 (%)
CALDEX One index · Zerivek 89.15, best in column
BM25 Keyword search 85.7
GTE-ModernColBERT Multi-vector model 23.1
Promptriever (Llama 3, 8B) Embedding model 3.2
GritLM 7B Embedding model 2.4
Gemini Embedding Embedding model 1.6
E5-Mistral 7B Embedding model 1.3
Qwen3 Embedding Embedding model 0.9
Arctic Embed L v2.0 Embedding model 0.4

Make your existing hardware intelligent.

One real-world retrieval benchmark CALDEX dominates.

02 VectorDBBench

Cohere 1M

Benchmark

One million Cohere embeddings of English Wikipedia.

vectors
1,000,000
dimensions
768
databases, each on its own machine
10
Figure 1. Recall@100, the share of the true top 100 found

Database Recall@100 (%) · more is better

  • CALDEX 4 cores · 16 GB · VectorDBBench 98.34%
  • Elastic Cloud 8 vCPUs · 60 GB · VectorDBBench 97.48%
  • Pinecone p2.x8 pod · VectorDBBench 92.62%
  • zvec 16 vCPUs · 64 GB · zvec’s own benchmark 91.64%
  • turbopuffer Serverless · VectorDBBench 89.93%
  • pgvector IVFFlat index · 2 vCPUs · 8 GB · VectorDBBench 88.98%
Figure 2. Time to convert raw vectors to searchable knowledge

System Seconds · less is better

  • CALDEX 4 cores · 16 GB · Single node 123.6 s
  • zvec 16 vCPUs · 64 GB 147.9 s 1.2× CALDEX’s
  • Milvus 16 vCPUs · 64 GB · HNSW 581.8 s 4.7× CALDEX’s
  • Milvus 16 vCPUs · 64 GB · SQ8 916.3 s 7.4× CALDEX’s
  • Zilliz Cloud 8 CU · performance 1,016 s 8.2× CALDEX’s
  • Pinecone p1.x1 pod 1,124 s 9.1× CALDEX’s
  • Pinecone s1.x1 pod 1,129 s 9.1× CALDEX’s
  • Pinecone p2.x1 pod · 8 nodes 1,210 s 9.8× CALDEX’s
  • Pinecone p1.x1 pod · 8 nodes 1,212 s 9.8× CALDEX’s
  • Pinecone s1.x1 pod · 2 nodes 1,451 s 11.7× CALDEX’s
  • Qdrant Cloud 16 vCPUs · 64 GB 1,500 s 12.1× CALDEX’s
  • Qdrant Cloud 4 vCPUs · 16 GB · 1 node 1,503 s 12.2× CALDEX’s
  • Pinecone p2.x1 pod 1,583 s 12.8× CALDEX’s
  • Qdrant Cloud 4 vCPUs · 16 GB · 5 nodes 1,648 s 13.3× CALDEX’s
  • Milvus 4 vCPUs · 16 GB · disk 1,782 s 14.4× CALDEX’s
  • Pinecone p2.x8 pod · 1 node 2,126 s 17.2× CALDEX’s
  • Milvus 2 vCPUs · 8 GB · HNSW 2,380 s 19.3× CALDEX’s
  • OpenSearch 16 vCPUs · 128 GB 3,572 s 28.9× CALDEX’s
  • Weaviate Cloud Standard tier 3,581 s 29.0× CALDEX’s
  • Weaviate Cloud Business Critical tier 3,674 s 29.7× CALDEX’s
  • OpenSearch 16 vCPUs · 128 GB · force merge 4,072 s 32.9× CALDEX’s
  • Elastic Cloud 8 vCPUs · 60 GB 4,463 s 36.1× CALDEX’s
  • Milvus 2 vCPUs · 8 GB · disk 6,004 s 48.6× CALDEX’s
  • Elastic Cloud 8 vCPUs · 60 GB · force merge 6,207 s 50.2× CALDEX’s
  • Zilliz Cloud 8,633 s 69.8× CALDEX’s
  • pgvector 2 vCPUs · 8 GB 10,250 s 82.9× CALDEX’s
  • Elastic Cloud up to 2.5 vCPUs · 8 GB 26,410 s 213.7× CALDEX’s
Figure 3. Memory and disk for a searchable index

Index Memory + disk, relative to the raw vectors

  • CALDEX 0.62× 1.6× smaller
  • HNSW-SQ8 1.68× 2.7× CALDEX’s
  • Elasticsearch 2.04× 3.3× CALDEX’s
  • hnswlib 2.16× 3.5× CALDEX’s
  • pgvector ≥ 2.19× ≥ 3.5× CALDEX’s
  • Weaviate ≥ 2.21× ≥ 3.6× CALDEX’s
Figure 4. Queries per second against published results

Database Queries/second · more is better

  • CALDEX 4 cores · 16 GB · VectorDBBench 2,398
  • Qdrant Cloud 16 vCPUs · 64 GB · VectorDBBench 1,242
  • Pinecone p2.x8 pod · VectorDBBench 1,147
  • turbopuffer Serverless · VectorDBBench 798
  • Weaviate Cloud Business Critical tier · VectorDBBench 68
  • pgvector 2 vCPUs · 8 GB · VectorDBBench 11

Less memory. More accuracy.

CALDEX solves the hardest of the graph problems with ease.

03 ann-benchmarks

GloVe 1.2M

Dataset

Stanford’s GloVe word vectors, every index built by Zerivek.

vectors
1,183,514
dimensions
100
other graph indexes
6
Table 2. Memory, disk and accuracy comparison, CALDEX vs Existing solutions
IndexAccuracy (%)In memoryOn diskMemory + disk
Raw vectors 100 dimensions at 32 bits, the vectors alone, no graph — — 1.00× —
Reach 95% of the true top 10
CALDEX One index 96.05, best in column 0.98× 0.79× 1.77×, best in column
Below 95% in this run
FAISS HNSW-SQ8 8-bit vectors 94–95 1.00× 2.00× 3.00×
hnswlib 32-bit vectors 92–94 1.65× 1.65× 3.30×
HNSW-Flat 32-bit vectors 89.4 1.96× 1.96× 3.92×
USearch 8-bit vectors 83.69 0.69× 1.69× 2.38×
HNSW-PQ Product-quantised vectors 78.5 0.84× 1.84× 2.68×
USearch 32-bit vectors 75.7 1.65× 1.65× 3.30×
Table 3. Queries per second on single thread
SystemQueries/second
CALDEX 4 cores · 16 GB · on a single thread 1,395, best in column
Redis r6i.16xlarge · one CPU · ann-benchmarks 1,264
Vespa r6i.16xlarge · one CPU · ann-benchmarks 628
Weaviate r6i.16xlarge · one CPU · ann-benchmarks 456
Lucene r6i.16xlarge · one CPU · ann-benchmarks 277
Qdrant r6i.16xlarge · one CPU · ann-benchmarks 197
pgvector r6i.16xlarge · one CPU · ann-benchmarks 69

Every result, with the exact place it came from.

CALDEX returns the file, the exact place and the passage itself. Go straight from a search result to the evidence in the original source.

Illustrative results

How much notice must my landlord give before entering my home? How many days do I have to return something I bought online? How much notice do I have to give before I resign? Can my landlord keep my deposit for normal wear and tear? What is the late fee if I pay my rent after the due date? How long is the warranty on my laptop? Can I end my lease early if I move for work? How long do I have to report a wrong charge on my credit card? How long does my non-compete last after I leave? Does my car insurance cover a hire car while mine is repaired? How many days of paid sick leave do I get a year? How much unused leave can I carry over?

CALDEX

Tenancy agreement.pdf Page 9 Terms of sale.pdf Page 9 Employment contract.pdf Page 11 Tenancy agreement.pdf Page 13 Tenancy agreement.pdf Page 10 Warranty terms.pdf Page 9 Tenancy agreement.pdf Page 15 Cardholder agreement.pdf Page 21 Employment contract.pdf Page 17 Motor insurance policy.pdf Page 19 Employee handbook.pdf Page 15 Employee handbook.pdf Page 12

The landlord must give at least 24 hours’ written notice before entering the property. You may cancel your order within 14 days of delivery without giving a reason. Either party may end this contract by giving one month’s written notice. No deduction may be made from the deposit for fair wear and tear. A late fee of 5% of the monthly rent applies from the sixth day after the due date. This product is covered against defects for 24 months from the date of purchase. The tenant may end this tenancy early by giving 60 days’ notice and one month’s rent. You must tell us about a billing error within 60 days of the statement date. For 12 months after your employment ends, you may not work for a direct competitor. We will pay for a hire car for up to 21 days while your car is repaired after a claim. Full-time employees receive ten days of paid sick leave each calendar year. Unused leave carries over for up to five days into the next year.

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Others

doc_20417 · 0.84 doc_73105 · 0.81 doc_11892 · 0.86 doc_20417 · 0.79 doc_20417 · 0.82 doc_56230 · 0.88 doc_20417 · 0.77 doc_90344 · 0.83 doc_11892 · 0.80 doc_38761 · 0.85 doc_48213 · 0.84 doc_48213 · 0.87

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