From 055ff33d562b883573131fe199635baf0ad5ecc6 Mon Sep 17 00:00:00 2001 From: David Myriel Date: Wed, 17 Sep 2025 18:24:59 +0200 Subject: [PATCH 1/6] add blog --- content/blog/feature-rabitq-quantization.md | 145 ++++++++++++++++++ content/blog/geneva-feature-engineering.md | 2 +- .../benchmarks.png | Bin 0 -> 599778 bytes .../dbpedia-bench.png | Bin 0 -> 67526 bytes .../figure1.png | Bin 0 -> 230113 bytes .../gist-bench.png | Bin 0 -> 66548 bytes .../preview-image.png | Bin 0 -> 2283825 bytes 7 files changed, 146 insertions(+), 1 deletion(-) create mode 100644 content/blog/feature-rabitq-quantization.md create mode 100644 static/assets/blog/feature-rabitq-quantization.md/benchmarks.png create mode 100644 static/assets/blog/feature-rabitq-quantization.md/dbpedia-bench.png create mode 100644 static/assets/blog/feature-rabitq-quantization.md/figure1.png create mode 100644 static/assets/blog/feature-rabitq-quantization.md/gist-bench.png create mode 100644 static/assets/blog/feature-rabitq-quantization.md/preview-image.png diff --git a/content/blog/feature-rabitq-quantization.md b/content/blog/feature-rabitq-quantization.md new file mode 100644 index 00000000..8802fdfa --- /dev/null +++ b/content/blog/feature-rabitq-quantization.md @@ -0,0 +1,145 @@ +--- +title: "LanceDB's RaBitQ Quantization for Blazing Fast Vector Search" +date: 2025-09-17 +draft: false +featured: true +categories: ["Engineering"] +image: "/assets/blog/feature-rabitq-quantization.md/preview-image.png" +meta_image: "/assets/blog/feature-rabitq-quantization.md/preview-image.png" +description: "Introducing RaBitQ quantization in LanceDB for higher compression, faster indexing, and better recall on high‑dimensional embeddings." +author: David Myriel +author_avatar: "/assets/authors/david-myriel.jpg" +author_bio: "Writer." +author_twitter: "davidmyriel" +author_github: "davidmyriel" +author_linkedin: "davidmyriel" +--- + +Most [embedding models](/docs/embedding/) give you float32 vectors. That is precise, but wasteful. You pay in storage and query time. Scalar quantization can shrink the size, but not enough. Binary quantization can shrink it further, but at the cost of quality. + +Until now LanceDB has relied on **IVF_PQ** (Inverted File with Product Quantization) as its default compression and search strategy. IVF_PQ works well in many cases, but comes with trade-offs: building PQ codebooks is expensive, re-training is required when data distribution shifts, and distance estimation can be slow. Learn more about index types in [Indexing](/docs/indexing/). + +Today we are adding **RaBitQ quantization** to LanceDB. You now have a choice. `IVF_PQ` remains the default, but RaBitQ is available when you need higher compression, faster indexing, and better recall in high dimensions. See how this fits into [vector search](/docs/search/vector-search/) and [hybrid search](/docs/overview/hybrid-search/). + +> A 1024-dimensional float32 vector needs 4 KB. With RaBitQ and corrective factors the same vector takes about 136 bytes. `IVF_PQ` typically reduces this by 8–16x. + +## Why this matters for you + +High-dimensional vectors behave in ways that seem strange if you are used to 2D or 3D. In high dimensions almost every coordinate of a unit vector is close to zero. This is the **concentration of measure** phenomenon often discussed in [retrieval systems](/docs/search/optimize-queries/). + +RaBitQ takes advantage of this. It stores only the binary “sign pattern” of each normalized vector and relies on the fact that the error introduced is bounded. The RaBitQ paper proves the estimation error is **O(1/D)**, which is asymptotically optimal. In practice, the more dimensions your embeddings have, the more RaBitQ gives you for free. + +{{< admonition >}} +RaBitQ is most effective with embeddings of 512, 768, or 1024 dimensions. IVF_PQ often struggles more as dimensionality grows, making RaBitQ a strong complement. +{{< /admonition >}} + +## What happens under the hood + +When you index embeddings in LanceDB with RaBitQ your vectors are shifted around a centroid and normalized. They are snapped to the nearest vertex of a randomly rotated hypercube on the unit sphere. Each quantized vector is stored as **1 bit per dimension**. Index creation is managed the same way as other [vector indexes](/docs/indexing/vector-index/). + +Two small corrective factors are also stored: + +* the distance from the vector to the centroid +* the dot product between the vector and its quantized form + +At query time your input—whether text, image, audio, or video—is transformed in the same way. Comparisons become fast binary dot products, and the corrective factors restore fidelity. + +**Figure 1:** Geometry of query and data vectors in RaBitQ +![figure1](/assets/blog/feature-rabitq-quantization.md/figure1.png) + +This figure shows the geometric relationship between a data vector o, its quantized form o̅, and a query vector q. The auxiliary vector e₁ lies in the same plane. RaBitQ exploits the fact that in high-dimensional spaces, the projection of o̅ onto e₁ is highly concentrated around zero (red region on the right). This allows us to treat it as negligible, enabling accurate distance estimation with minimal computation. + +**Difference with IVF_PQ**: PQ requires training a codebook and splitting vectors into subvectors. RaBitQ avoids that entirely. Indexing is faster, maintenance is simpler, and results are more stable when you update your dataset. + +## Search in practice + +With IVF_PQ you first partition vectors into inverted lists, then run PQ-based comparisons inside each list. With RaBitQ the comparison step is even cheaper: a binary dot product plus small corrections. Both approaches benefit from [reranking](/docs/reranking/) with full-precision vectors. + +**Figure 2:** Candidate retrieval and re-ranking pipeline. Stage 1: approximate search. Stage 2: re-rank with full vectors. TODO + +Both approaches use a candidate set and re-ranking to ensure quality. But because RaBitQ’s approximations are tight, you often need fewer candidates to hit the same recall. + +For you this means recall above 95 percent with lower latency, even on large [multimodal datasets](/blog/multimodal-lakehouse/) on our test hardware. + +{{< admonition >}} +Always re-rank candidates with full precision vectors. IVF_PQ and RaBitQ both rely on approximation for candidate generation. +{{< /admonition >}} + +## Research context: RaBitQ-S + +The RaBitQ paper also introduces **RaBitQ-S**, a generalization to multi-bit quantization. Instead of limiting each coordinate to 1 bit, RaBitQ-S allows for 2–4 bits per dimension. This reduces error further and can outperform product quantization under the same compression budget. For background on token-based search that pairs well with these methods, see [Full‑Text Search](/docs/search/full-text-search/). + +⚠️ **RaBitQ-S is not yet available in LanceDB.** We mention it here only as research context. It shows the trajectory of this work, and the same principles that make RaBitQ efficient at 1 bit can be extended to higher precision when needed. + +*(Figure 8: Illustration of binary vs multi-bit quantization bins)* + +## Benchmarks +![benchmarks](/assets/blog/feature-rabitq-quantization.md/benchmarks.png) + +We tested IVF_PQ and RaBitQ side by side on two public datasets: + +* [**DBpedia 1M**](https://huggingface.co/datasets/KShivendu/dbpedia-entities-openai-1M) (OpenAI embeddings) +* [**GIST1M**](http://corpus-texmex.irisa.fr/) (dense 960-dimensional vectors) + +The tests were run on a consumer-grade PC: + +* CPU: Intel 12400F (6 cores, 12 threads) +* Disk: 1TB SSD +* No GPU + +### DBpedia (text embeddings, 768d) + +| Metric | IVF_PQ | RaBitQ | +| - | - | - | +| recall@10 | ~92% | **96%+** | +| throughput | ~350 QPS | **495 QPS** | +| index build time | ~85s | **~75s** | + +**Figure 3:** DBpedia benchmark results (recall@10, throughput, build time) +![DBpedia Benchmark](/assets/blog/feature-rabitq-quantization.md/dbpedia-bench.png) + +### GIST1M (image embeddings, 960d) + +| Metric | IVF_PQ | RaBitQ | +| - | - | - | +| recall@10 | ~90% | **94%** | +| throughput | ~420 QPS | **540–765 QPS** | +| index build time | ~130s | **~21s** | + +**Figure 4:** GIST1M benchmark results (recall@10, throughput, build time) +![GIST1M Benchmark](/assets/blog/feature-rabitq-quantization.md/gist-bench.png) + +{{< admonition >}} +On CPUs, RaBitQ already outperforms IVF_PQ on our test hardware. On GPUs the gap should widen further because RaBitQ operations are easier to parallelize. +{{< /admonition >}} + +## IVF_PQ vs RaBitQ + +When you use LanceDB today, the default quantization method is IVF_PQ. It works well for many workloads and gives you solid compression and recall. With RaBitQ now available, you have another option. The two approaches make very different trade-offs, especially when your vectors are high-dimensional or multimodal. + +| Feature | IVF_PQ (default) | RaBitQ (new) | +| ----- | ----- | ----- | +| **Compression ratio** | 8–16x typical | 32x and higher | +| **Index build time** | Slower, requires codebook training | Faster, no training needed | +| **Recall in high dimensions** | Good but drops with >512d | Stays high, error shrinks with more dimensions | +| **Query speed** | Good, but PQ distance estimation is slower | Faster, binary dot products dominate | +| **Update handling** | Requires re-training if distribution shifts | No retraining needed, robust to updates | +| **Best for** | General workloads, balanced compression | Large multimodal datasets, high-dim embeddings | + +What this means in practice is that you don’t have to pick one forever. IVF_PQ remains a great default for balanced workloads. But if you are working with very large datasets, embeddings above 512 dimensions, or multimodal collections where precision matters, RaBitQ can give you higher recall, faster queries, and far smaller storage footprints. Because RaBitQ does not depend on heavy codebook training, you can also update your data more easily without re-training the index. + +## What you can do today in LanceDB + +With IVF_PQ you already had scalable compression and fast ANN search. Now with RaBitQ you get an additional tool: + +* Use **IVF_PQ** for general-purpose workloads where codebooks make sense +* Use **RaBitQ** when you want maximum compression, faster indexing, or higher recall in high dimensions +* Mix RaBitQ-S with other modalities for adaptive precision control +* Keep more embeddings online for [RAG](/docs/overview/), multimodal search, and analytics + +## Proven and ready + +RaBitQ is not theoretical. Elastic integrated it into their BBQ quantization feature. Tensorchord built a cost-efficient vector search service with it. Both show strong improvements in recall and speed compared to classical product quantization. + +Now RaBitQ is available in LanceDB alongside IVF_PQ. You can choose the method that best fits your workload, and even switch as your dataset grows. If you’re exploring LanceDB for the first time, check out our [quickstart](/docs/), the [WikiSearch demo](/blog/feature-full-text-search/), and how this ties into the [Multimodal Lakehouse](/blog/multimodal-lakehouse/). + diff --git a/content/blog/geneva-feature-engineering.md b/content/blog/geneva-feature-engineering.md index d02cc894..93b69432 100644 --- a/content/blog/geneva-feature-engineering.md +++ b/content/blog/geneva-feature-engineering.md @@ -2,7 +2,7 @@ title: "LanceDB's Geneva: Scalable Feature Engineering" date: 2025-08-21 draft: false -featured: true +featured: false categories: ["Engineering"] image: /assets/blog/geneva-feature-engineering/preview-image.png meta_image: /assets/blog/geneva-feature-engineering/preview-image.png diff --git a/static/assets/blog/feature-rabitq-quantization.md/benchmarks.png b/static/assets/blog/feature-rabitq-quantization.md/benchmarks.png new file mode 100644 index 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z9Qs+(dj(3^ouUZ`IT4t;Uf&SH2#9DR7j^Rq7z1{n#K`lsp7-{BN8DpSM<~8fMO4H* ze$%@S)02{SkjNmGaSKtM4k1^RzY_wZb5cr&^X};xRRToCf~_^CYZ8qB9W+2r8S8e( z9yi3eL%X$3rxQ-6<>(N{=wx<(R z5!o1Be;PV)>%@u3c5+VVLbaV4E=pLuuwUVx2G;6Ku9CTv1^o4X-Dsmrj+R4 zDMi;P)Bovw;BUqHa_wDZ+Qow>V7!z#jP-Y2C`||0v&x+DL49tM zz0+FGX!AT{TKMdd0Mnv&VDJNK1#Y)HigdP=O6;iACL)vuCxl|F3Dz1+^C&4VUaswc z*3i!-iUC$VxEV>MsFk9bSTGDDV$3|J6q4g{-x$#>(d+(TVJ;z`{KxwYYLH?eS5M7Y@6iZog-~i7UtN}W<3hQ zbXTAw-VmIlaGBsZAee8?bU_V65EloZb1x#s;Ds Date: Wed, 17 Sep 2025 18:35:48 +0200 Subject: [PATCH 2/6] add outro --- content/blog/feature-rabitq-quantization.md | 1 + .../feature-rabitq-quantization.md/outro.jpeg | Bin 0 -> 190985 bytes 2 files changed, 1 insertion(+) create mode 100644 static/assets/blog/feature-rabitq-quantization.md/outro.jpeg diff --git a/content/blog/feature-rabitq-quantization.md b/content/blog/feature-rabitq-quantization.md index 8802fdfa..d84ab2de 100644 --- a/content/blog/feature-rabitq-quantization.md +++ 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z94vjEEydTh`-|Bc=H>SvexHE<064EWy11I?ow*8sGyeeAt+tQtOwTFdF@g22V^_P9 zEz!aP@zj1*`vy^ijAW_PN98%bDe`mFdKve3kXQ^KnomL6xZ9h#Ze-sl;5!ecPd-jq z)hOc+*i;;MJwGa^AqoO0!unR` zm8HROk;^~K9FP|r4Zfql@~gyhrOh>zv0Dob~bUx zh~ixOpI`8+8xa)-ILQEZ5A8tFY_Zyew`#^4iu%v4zX+D?QC!G6q!w-ADWf zf%*6RFe|5qC@qui60kdao`dK=t!2W?6b5oLv;&TUv1PlK?sAfJ7#Qu+zCu*xT2Ha` zib{-4Tis6L^^8{Jq|t;U M*4Z9zBN)&B*&Si#g8%>k literal 0 HcmV?d00001 From 9c5a4504b3bbfd2b66c77bd70649c4134e8f7014 Mon Sep 17 00:00:00 2001 From: David Myriel Date: Thu, 18 Sep 2025 19:35:52 +0200 Subject: [PATCH 3/6] add fixes --- content/blog/feature-rabitq-quantization.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/content/blog/feature-rabitq-quantization.md b/content/blog/feature-rabitq-quantization.md index d84ab2de..a913bc25 100644 --- a/content/blog/feature-rabitq-quantization.md +++ b/content/blog/feature-rabitq-quantization.md @@ -27,7 +27,7 @@ Today we are adding **RaBitQ quantization** to LanceDB. You now have a choice. ` High-dimensional vectors behave in ways that seem strange if you are used to 2D or 3D. In high dimensions almost every coordinate of a unit vector is close to zero. This is the **concentration of measure** phenomenon often discussed in [retrieval systems](/docs/search/optimize-queries/). -RaBitQ takes advantage of this. It stores only the binary “sign pattern” of each normalized vector and relies on the fact that the error introduced is bounded. The RaBitQ paper proves the estimation error is **O(1/D)**, which is asymptotically optimal. In practice, the more dimensions your embeddings have, the more RaBitQ gives you for free. +RaBitQ takes advantage of this. It stores only the binary "sign pattern" of each normalized vector and relies on the fact that the error introduced is bounded. The RaBitQ paper proves the estimation error is **O(1/√D)**, which is asymptotically optimal. In practice, the more dimensions your embeddings have, the more RaBitQ gives you for free. {{< admonition >}} RaBitQ is most effective with embeddings of 512, 768, or 1024 dimensions. IVF_PQ often struggles more as dimensionality grows, making RaBitQ a strong complement. @@ -65,11 +65,11 @@ For you this means recall above 95 percent with lower latency, even on large [mu Always re-rank candidates with full precision vectors. IVF_PQ and RaBitQ both rely on approximation for candidate generation. {{< /admonition >}} -## Research context: RaBitQ-S +## Research context: extended-RaBitQ -The RaBitQ paper also introduces **RaBitQ-S**, a generalization to multi-bit quantization. Instead of limiting each coordinate to 1 bit, RaBitQ-S allows for 2–4 bits per dimension. This reduces error further and can outperform product quantization under the same compression budget. For background on token-based search that pairs well with these methods, see [Full‑Text Search](/docs/search/full-text-search/). +The [RaBitQ paper](https://arxiv.org/abs/2409.09913) also introduces **extended-RaBitQ**, a generalization to multi-bit quantization. Instead of limiting each coordinate to 1 bit, extended-RaBitQ allows for 2–4 bits per dimension. This reduces error further and can outperform product quantization under the same compression budget. For background on token-based search that pairs well with these methods, see [Full‑Text Search](/docs/search/full-text-search/). -⚠️ **RaBitQ-S is not yet available in LanceDB.** We mention it here only as research context. It shows the trajectory of this work, and the same principles that make RaBitQ efficient at 1 bit can be extended to higher precision when needed. +⚠️ **extended-RaBitQ is not yet available in LanceDB.** We mention it here only as research context. It shows the trajectory of this work, and the same principles that make RaBitQ efficient at 1 bit can be extended to higher precision when needed. *(Figure 8: Illustration of binary vs multi-bit quantization bins)* @@ -119,7 +119,7 @@ When you use LanceDB today, the default quantization method is IVF_PQ. It works | Feature | IVF_PQ (default) | RaBitQ (new) | | ----- | ----- | ----- | -| **Compression ratio** | 8–16x typical | 32x and higher | +| **Compression ratio** | 8–16x typical | Up to 32x | | **Index build time** | Slower, requires codebook training | Faster, no training needed | | **Recall in high dimensions** | Good but drops with >512d | Stays high, error shrinks with more dimensions | | **Query speed** | Good, but PQ distance estimation is slower | Faster, binary dot products dominate | From 7ff4081d64b369ec3e5b457efda519373a12a69b Mon Sep 17 00:00:00 2001 From: BubbleCal Date: Tue, 30 Sep 2025 16:41:35 +0800 Subject: [PATCH 4/6] add explaination about rabitq quantization Signed-off-by: BubbleCal --- content/blog/feature-rabitq-quantization.md | 57 ++++++++++++++------- 1 file changed, 38 insertions(+), 19 deletions(-) diff --git a/content/blog/feature-rabitq-quantization.md b/content/blog/feature-rabitq-quantization.md index a913bc25..76aebf83 100644 --- a/content/blog/feature-rabitq-quantization.md +++ b/content/blog/feature-rabitq-quantization.md @@ -44,6 +44,24 @@ Two small corrective factors are also stored: At query time your input—whether text, image, audio, or video—is transformed in the same way. Comparisons become fast binary dot products, and the corrective factors restore fidelity. +Formally, RaBitQ maps a vector \(v\) to a binary vector \(v_{qb}\) and a hypercube vertex \(v_h\) on the unit sphere: + +$$ +v_h[i]=\begin{cases}\dfrac{1}{\sqrt{D}}, & \text{if } v_{qb}[i] = 1, \\ +-\dfrac{1}{\sqrt{D}}, & \text{if } v_{qb}[i] = 0.\end{cases} +$$ + +To remove bias, RaBitQ samples a random orthogonal matrix \(P\) and sets the final quantized vector to + +$$ +v_q = P\, v_h. +$$ + +During indexing, for each data vector \(v\), we compute the residual around a centroid \(c\), normalize it, map it to bits via the inverse rotation \(P^{-1}\), and store two corrective scalars alongside the bits: the centroid distance \(d_c = \|v-c\|\) and the inner product with the quantized direction \(d_s = \langle v_q, v_n \rangle\). At search time, the query is processed with the same rotation to enable extremely fast binary dot products plus lightweight corrections for accurate distance estimates. + +Figure 1a: 2D illustration of mapping a vector to the nearest unit‑sphere hypercube vertex (RabitQ overview) +![RabitQ 2D mapping](/assets/blog/feature-rabitq-quantization.md/plot_rq.svg) + **Figure 1:** Geometry of query and data vectors in RaBitQ ![figure1](/assets/blog/feature-rabitq-quantization.md/figure1.png) @@ -71,9 +89,10 @@ The [RaBitQ paper](https://arxiv.org/abs/2409.09913) also introduces **extended- ⚠️ **extended-RaBitQ is not yet available in LanceDB.** We mention it here only as research context. It shows the trajectory of this work, and the same principles that make RaBitQ efficient at 1 bit can be extended to higher precision when needed. -*(Figure 8: Illustration of binary vs multi-bit quantization bins)* +Figure 8: Illustration of binary vs multi-bit quantization bins ## Benchmarks + ![benchmarks](/assets/blog/feature-rabitq-quantization.md/benchmarks.png) We tested IVF_PQ and RaBitQ side by side on two public datasets: @@ -89,22 +108,22 @@ The tests were run on a consumer-grade PC: ### DBpedia (text embeddings, 768d) -| Metric | IVF_PQ | RaBitQ | -| - | - | - | -| recall@10 | ~92% | **96%+** | -| throughput | ~350 QPS | **495 QPS** | -| index build time | ~85s | **~75s** | +| Metric | IVF_PQ | RaBitQ | +| ---------------- | -------- | ----------- | +| recall@10 | ~92% | **96%+** | +| throughput | ~350 QPS | **495 QPS** | +| index build time | ~85s | **~75s** | **Figure 3:** DBpedia benchmark results (recall@10, throughput, build time) ![DBpedia Benchmark](/assets/blog/feature-rabitq-quantization.md/dbpedia-bench.png) ### GIST1M (image embeddings, 960d) -| Metric | IVF_PQ | RaBitQ | -| - | - | - | -| recall@10 | ~90% | **94%** | -| throughput | ~420 QPS | **540–765 QPS** | -| index build time | ~130s | **~21s** | +| Metric | IVF_PQ | RaBitQ | +| ---------------- | -------- | --------------- | +| recall@10 | ~90% | **94%** | +| throughput | ~420 QPS | **540–765 QPS** | +| index build time | ~130s | **~21s** | **Figure 4:** GIST1M benchmark results (recall@10, throughput, build time) ![GIST1M Benchmark](/assets/blog/feature-rabitq-quantization.md/gist-bench.png) @@ -117,14 +136,14 @@ On CPUs, RaBitQ already outperforms IVF_PQ on our test hardware. On GPUs the gap When you use LanceDB today, the default quantization method is IVF_PQ. It works well for many workloads and gives you solid compression and recall. With RaBitQ now available, you have another option. The two approaches make very different trade-offs, especially when your vectors are high-dimensional or multimodal. -| Feature | IVF_PQ (default) | RaBitQ (new) | -| ----- | ----- | ----- | -| **Compression ratio** | 8–16x typical | Up to 32x | -| **Index build time** | Slower, requires codebook training | Faster, no training needed | -| **Recall in high dimensions** | Good but drops with >512d | Stays high, error shrinks with more dimensions | -| **Query speed** | Good, but PQ distance estimation is slower | Faster, binary dot products dominate | -| **Update handling** | Requires re-training if distribution shifts | No retraining needed, robust to updates | -| **Best for** | General workloads, balanced compression | Large multimodal datasets, high-dim embeddings | +| Feature | IVF_PQ (default) | RaBitQ (new) | +| ----------------------------- | ------------------------------------------- | ---------------------------------------------- | +| **Compression ratio** | 8–16x typical | Up to 32x | +| **Index build time** | Slower, requires codebook training | Faster, no training needed | +| **Recall in high dimensions** | Good but drops with >512d | Stays high, error shrinks with more dimensions | +| **Query speed** | Good, but PQ distance estimation is slower | Faster, binary dot products dominate | +| **Update handling** | Requires re-training if distribution shifts | No retraining needed, robust to updates | +| **Best for** | General workloads, balanced compression | Large multimodal datasets, high-dim embeddings | What this means in practice is that you don’t have to pick one forever. IVF_PQ remains a great default for balanced workloads. But if you are working with very large datasets, embeddings above 512 dimensions, or multimodal collections where precision matters, RaBitQ can give you higher recall, faster queries, and far smaller storage footprints. Because RaBitQ does not depend on heavy codebook training, you can also update your data more easily without re-training the index. From 04e19d0f28a030f14e944e171f953e398792ac13 Mon Sep 17 00:00:00 2001 From: BubbleCal Date: Tue, 30 Sep 2025 16:49:49 +0800 Subject: [PATCH 5/6] add figure Signed-off-by: BubbleCal --- .../plot_rq.svg | 1630 +++++++++++++++++ 1 file changed, 1630 insertions(+) create mode 100644 static/assets/blog/feature-rabitq-quantization.md/plot_rq.svg diff --git a/static/assets/blog/feature-rabitq-quantization.md/plot_rq.svg b/static/assets/blog/feature-rabitq-quantization.md/plot_rq.svg new file mode 100644 index 00000000..35936074 --- /dev/null +++ b/static/assets/blog/feature-rabitq-quantization.md/plot_rq.svg @@ -0,0 +1,1630 @@ + + + + + + + + 2025-09-19T17:30:46.830999 + image/svg+xml + + + Matplotlib v3.10.6, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From 00d1046db9b4f4cd038942621be11b7841806893 Mon Sep 17 00:00:00 2001 From: BubbleCal Date: Thu, 9 Oct 2025 22:47:07 +0800 Subject: [PATCH 6/6] fix formulations Signed-off-by: BubbleCal --- content/blog/feature-rabitq-quantization.md | 36 ++++++++++++--------- 1 file changed, 21 insertions(+), 15 deletions(-) diff --git a/content/blog/feature-rabitq-quantization.md b/content/blog/feature-rabitq-quantization.md index 76aebf83..ae88b5e0 100644 --- a/content/blog/feature-rabitq-quantization.md +++ b/content/blog/feature-rabitq-quantization.md @@ -7,11 +7,11 @@ categories: ["Engineering"] image: "/assets/blog/feature-rabitq-quantization.md/preview-image.png" meta_image: "/assets/blog/feature-rabitq-quantization.md/preview-image.png" description: "Introducing RaBitQ quantization in LanceDB for higher compression, faster indexing, and better recall on high‑dimensional embeddings." -author: David Myriel +author: David Myriel, Yang Cen author_avatar: "/assets/authors/david-myriel.jpg" -author_bio: "Writer." +author_bio: "Writer, Software Engineer @ LanceDB" author_twitter: "davidmyriel" -author_github: "davidmyriel" +author_github: "davidmyriel, BubbleCal" author_linkedin: "davidmyriel" --- @@ -27,7 +27,7 @@ Today we are adding **RaBitQ quantization** to LanceDB. You now have a choice. ` High-dimensional vectors behave in ways that seem strange if you are used to 2D or 3D. In high dimensions almost every coordinate of a unit vector is close to zero. This is the **concentration of measure** phenomenon often discussed in [retrieval systems](/docs/search/optimize-queries/). -RaBitQ takes advantage of this. It stores only the binary "sign pattern" of each normalized vector and relies on the fact that the error introduced is bounded. The RaBitQ paper proves the estimation error is **O(1/√D)**, which is asymptotically optimal. In practice, the more dimensions your embeddings have, the more RaBitQ gives you for free. +RaBitQ takes advantage of this. It stores only the binary "sign pattern" of each normalized vector and relies on the fact that the error introduced is bounded. The RaBitQ paper proves the estimation error is **O(1/√D)** (decreases proportionally to the inverse square root of dimensions), which is asymptotically optimal. In practice, the more dimensions your embeddings have, the more RaBitQ gives you for free. {{< admonition >}} RaBitQ is most effective with embeddings of 512, 768, or 1024 dimensions. IVF_PQ often struggles more as dimensionality grows, making RaBitQ a strong complement. @@ -44,20 +44,26 @@ Two small corrective factors are also stored: At query time your input—whether text, image, audio, or video—is transformed in the same way. Comparisons become fast binary dot products, and the corrective factors restore fidelity. -Formally, RaBitQ maps a vector \(v\) to a binary vector \(v_{qb}\) and a hypercube vertex \(v_h\) on the unit sphere: +Formally, RaBitQ maps a vector **v** to a binary vector **v_qb** and a hypercube vertex **v_h** on the unit sphere: -$$ -v_h[i]=\begin{cases}\dfrac{1}{\sqrt{D}}, & \text{if } v_{qb}[i] = 1, \\ --\dfrac{1}{\sqrt{D}}, & \text{if } v_{qb}[i] = 0.\end{cases} -$$ +``` +v_h[i] = +1/√D if v_qb[i] = 1 +v_h[i] = -1/√D if v_qb[i] = 0 +``` -To remove bias, RaBitQ samples a random orthogonal matrix \(P\) and sets the final quantized vector to +where D is the number of dimensions. Each component is either a positive or negative value scaled by the square root of dimensions. -$$ -v_q = P\, v_h. -$$ +To remove bias, RaBitQ samples a random orthogonal matrix **P** and sets the final quantized vector to: -During indexing, for each data vector \(v\), we compute the residual around a centroid \(c\), normalize it, map it to bits via the inverse rotation \(P^{-1}\), and store two corrective scalars alongside the bits: the centroid distance \(d_c = \|v-c\|\) and the inner product with the quantized direction \(d_s = \langle v_q, v_n \rangle\). At search time, the query is processed with the same rotation to enable extremely fast binary dot products plus lightweight corrections for accurate distance estimates. +``` +v_q = P × v_h +``` + +During indexing, for each data vector **v**, we compute the residual around a centroid **c**, normalize it, map it to bits via the inverse rotation **P⁻¹**, and store two corrective scalars alongside the bits: +- **Centroid distance**: `d_c = ||v - c||` (Euclidean distance from vector to centroid) +- **Inner product**: `d_s = ⟨v_q, v_n⟩` (dot product between quantized and normalized vectors) + +At search time, the query is processed with the same rotation to enable extremely fast binary dot products plus lightweight corrections for accurate distance estimates. Figure 1a: 2D illustration of mapping a vector to the nearest unit‑sphere hypercube vertex (RabitQ overview) ![RabitQ 2D mapping](/assets/blog/feature-rabitq-quantization.md/plot_rq.svg) @@ -65,7 +71,7 @@ Figure 1a: 2D illustration of mapping a vector to the nearest unit‑sphere hype **Figure 1:** Geometry of query and data vectors in RaBitQ ![figure1](/assets/blog/feature-rabitq-quantization.md/figure1.png) -This figure shows the geometric relationship between a data vector o, its quantized form o̅, and a query vector q. The auxiliary vector e₁ lies in the same plane. RaBitQ exploits the fact that in high-dimensional spaces, the projection of o̅ onto e₁ is highly concentrated around zero (red region on the right). This allows us to treat it as negligible, enabling accurate distance estimation with minimal computation. +This figure shows the geometric relationship between a data vector **o**, its quantized form **o_bar**, and a query vector **q**. The auxiliary vector **e1** lies in the same plane. RaBitQ exploits the fact that in high-dimensional spaces, the projection of **o_bar** onto **e1** is highly concentrated around zero (red region on the right). This allows us to treat it as negligible, enabling accurate distance estimation with minimal computation. **Difference with IVF_PQ**: PQ requires training a codebook and splitting vectors into subvectors. RaBitQ avoids that entirely. Indexing is faster, maintenance is simpler, and results are more stable when you update your dataset.

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