Matryoshka-256 binary funnel + rerank (OpenAI text-embedding-3)

Perf record: 065-matryoshka-256-openai-funnel.json. c8a.4xlarge (Zen5, 16 vCPU) spot, us-east-2. First run on a genuine Matryoshka embedding — closes the question left open by the prefix experiments (014/027): Cohere v3 isn't Matryoshka, so truncating it to 256 collapsed recall to ~0.72. Here we use an embedding trained to be truncatable.

Setup

• Dataset: OpenAI text-embedding-3-large, precomputed (Qdrant's dbpedia-entities 1M set — no embedding to run). text-embedding-3-large is MRL-trained (256 is a documented operating point). We slice the native 1536-d vectors to 256 and L2-renormalize (OpenAI's Matryoshka recipe). 990k base + 10k queries, exact GT.
• Engine: the shipped 1-bit binary funnel — sign-bit codes (256 bits = 32 B/vec), rotation ×2 + residual (both free recall), tile=8 — then exact f32 rerank of the top-C shortlist. Same code path as the Cohere runs; only the data differs.

Result — recall dials from 0.95 to 0.998 on the rerank width

Chosen operating point: C=2000 — recall 0.9878, 4227 QPS, p50 3.1 ms, p99 3.15 ms. (+4 recall points over C=500 for ~30% fewer QPS and <1 ms more latency.)

What it shows

• Matryoshka holds — no collapse. A non-Matryoshka 256-prefix capped low (0.72, the "bit-floor" dead end). Here recall climbs smoothly to 0.998: the 256-bit code + rotation/residual produces a high-quality Hamming shortlist, so the true neighbours are in the top-C and rerank recovers them. 256-bit + rerank is a real, tunable operating point on a Matryoshka embedding.
• 256 bits is compact and fast — 31.7 MB of codes for 990k vectors; even at 0.998 recall it holds ~2000 QPS at ~6.5 ms p50.

Caveats

• Box size differs from the hardware sweep. This ran on a 16-vCPU c8a.4xlarge; the Cohere sweep (062/064) used 8-vCPU .2xlarge. So the QPS here is not directly comparable to the ~2310 QPS Zen5 Cohere-1024 number. Recall is CPU-independent, so the recall figures are final; the throughput needs an equal-box re-run to compare.
• One dataset/embedding (OpenAI text-embedding-3-large). The model is closed; only the vectors are open. A fully-open reproduction would embed with Nomic v1.5 (MRL).
• Only the 256 dim measured here; the full 512/768/1024/1536 recall-vs-bits curve on the same box was not run.