|
| 1 | +# IVF (Inverted File) Index |
| 2 | + |
| 3 | +## Overview |
| 4 | + |
| 5 | +IVF indexing partitions vectors into clusters using k-means, then searches only the nearest clusters at query time instead of scanning every vector. This trades a small recall loss for a large speedup. |
| 6 | + |
| 7 | +## API |
| 8 | + |
| 9 | +### Build |
| 10 | + |
| 11 | +```sql |
| 12 | +-- 2-arg form (defaults: nlist=64, nprobe=sqrt(nlist), max_memory=100MB) |
| 13 | +SELECT vector_ivf_build('table', 'column'); |
| 14 | + |
| 15 | +-- 3-arg form with options |
| 16 | +SELECT vector_ivf_build('table', 'column', 'nlist=100,nprobe=20,max_memory=100MB'); |
| 17 | +``` |
| 18 | + |
| 19 | +| Option | Type | Default | Description | |
| 20 | +|--------------|---------|------------------|--------------------------------------------------| |
| 21 | +| `nlist` | int | 64 | Number of clusters (partitions) | |
| 22 | +| `nprobe` | int | sqrt(nlist) | Number of clusters to search at query time | |
| 23 | +| `max_memory` | size | 100MB | Memory budget for preloading cluster data | |
| 24 | + |
| 25 | +`max_memory` accepts human-readable suffixes: `KB`, `MB`, `GB`, or plain bytes. It is persisted in the `_sqliteai_vector` metadata table and automatically respected by `vector_ivf_preload`. |
| 26 | + |
| 27 | +Returns the number of vectors indexed. |
| 28 | + |
| 29 | +### Preload |
| 30 | + |
| 31 | +```sql |
| 32 | +SELECT vector_ivf_preload('table', 'column'); |
| 33 | +``` |
| 34 | + |
| 35 | +Loads centroids, per-cluster counts, and as much cluster data as fits within the `max_memory` budget into memory. Centroids and counts are always loaded (negligible size). Cluster data is loaded greedily in storage order until the budget is exhausted; remaining clusters fall back to disk reads at query time. |
| 36 | + |
| 37 | +### Search |
| 38 | + |
| 39 | +```sql |
| 40 | +-- Top-k (non-streaming) |
| 41 | +SELECT rowid, distance |
| 42 | +FROM vector_ivf_scan('table', 'column', vector('[0.1, 0.2, ...]'), 10); |
| 43 | + |
| 44 | +-- Streaming |
| 45 | +SELECT rowid, distance |
| 46 | +FROM vector_ivf_scan('table', 'column', vector('[0.1, 0.2, ...]')); |
| 47 | +``` |
| 48 | + |
| 49 | +Both modes support hybrid execution: preloaded clusters are scanned from memory, non-preloaded clusters are fetched from disk via `SELECT ... WHERE centroid_id IN (...)`. |
| 50 | + |
| 51 | +### Cleanup |
| 52 | + |
| 53 | +```sql |
| 54 | +SELECT vector_ivf_cleanup('table', 'column'); |
| 55 | +``` |
| 56 | + |
| 57 | +Frees all in-memory IVF data and drops the IVF table. |
| 58 | + |
| 59 | +## How It Works |
| 60 | + |
| 61 | +1. **Build** runs k-means (Lloyd's algorithm, 10 iterations) on the full dataset to produce `nlist` centroids. Each vector is assigned to its nearest centroid. A shadow table `ivf0_<table>_<column>` stores per-cluster: centroid blob, vector count, and a packed data blob (rows of `[int64_t rowid | vector_bytes]`). |
| 62 | + |
| 63 | +2. **Preload** reads the shadow table in a single pass. Centroids and counts are always loaded into `table_context`. For each cluster's data blob, if adding it would exceed `max_memory`, it is skipped (left as `NULL` in the `ivf_data` array). |
| 64 | + |
| 65 | +3. **Search** converts the query to F32, finds the `nprobe` nearest centroids via brute-force scan over centroids, then for each probe cluster: |
| 66 | + - If `ivf_data[cid] != NULL`: scan directly from memory. |
| 67 | + - Otherwise: include `cid` in a disk query (`WHERE centroid_id IN (...)`). |
| 68 | + |
| 69 | + Top-k mode feeds results into a max-heap. Streaming mode merges all probe cluster data into a single buffer. |
| 70 | + |
| 71 | +## Architecture |
| 72 | + |
| 73 | +``` |
| 74 | +vector_ivf_build() |
| 75 | + -> k-means clustering |
| 76 | + -> write shadow table ivf0_<table>_<column> |
| 77 | + -> serialize nlist, nprobe, max_memory to _sqliteai_vector |
| 78 | +
|
| 79 | +vector_ivf_preload() |
| 80 | + -> read shadow table |
| 81 | + -> always: centroids, counts into table_context |
| 82 | + -> within budget: cluster data into ivf_data[] |
| 83 | + -> over budget: ivf_data[cid] = NULL (disk fallback) |
| 84 | +
|
| 85 | +vector_ivf_scan (top-k or streaming) |
| 86 | + -> find nprobe nearest centroids |
| 87 | + -> scan preloaded clusters from memory |
| 88 | + -> query non-preloaded clusters from disk |
| 89 | + -> merge results |
| 90 | +``` |
| 91 | + |
| 92 | +### Key data structures in `table_context` |
| 93 | + |
| 94 | +| Field | Type | Description | |
| 95 | +|-------------------|------------|--------------------------------------------| |
| 96 | +| `ivf_nlist` | `int` | Number of clusters | |
| 97 | +| `ivf_nprobe` | `int` | Number of clusters to probe | |
| 98 | +| `ivf_max_memory` | `int64_t` | Memory budget in bytes | |
| 99 | +| `ivf_centroids` | `float *` | `[nlist * dim]` F32 centroid vectors | |
| 100 | +| `ivf_counts` | `int *` | `[nlist]` vector count per cluster | |
| 101 | +| `ivf_data` | `void **` | `[nlist]` per-cluster packed data or NULL | |
| 102 | + |
| 103 | +### Metadata persistence |
| 104 | + |
| 105 | +Three keys are stored in `_sqliteai_vector` via `sqlite_serialize`: |
| 106 | + |
| 107 | +| Key | SQLite Type | Value | |
| 108 | +|--------------|------------------|--------------------------| |
| 109 | +| `nlist` | `SQLITE_INTEGER` | Number of clusters | |
| 110 | +| `nprobe` | `SQLITE_INTEGER` | Default probe count | |
| 111 | +| `max_memory` | `SQLITE_INTEGER` | Budget in bytes | |
| 112 | + |
| 113 | +These are restored on `sqlite_unserialize` so that `vector_ivf_preload` works correctly after reopening the database. |
| 114 | + |
| 115 | +## Pros and Cons |
| 116 | + |
| 117 | +### Pros |
| 118 | + |
| 119 | +- **Significant speedup**: Only `nprobe` out of `nlist` clusters are searched, reducing work proportionally. The benchmark shows 3.8x speedup with nprobe=20 out of nlist=100. |
| 120 | +- **Bounded memory**: The `max_memory` setting prevents preload from consuming unbounded RAM. A 1M x 768-dim F32 dataset (~3 GB of vector data) can be queried with only 100 MB of preloaded data. |
| 121 | +- **Hybrid execution**: Preloaded clusters are scanned at memory speed; non-preloaded clusters transparently fall back to disk. No user-facing API change is needed. |
| 122 | +- **Works with all vector types**: F32, F16, BF16, I8, U8 (not BIT, which is rejected at build time). |
| 123 | +- **Greedy preload**: The most commonly stored clusters (those encountered first in storage order) get preloaded, which is a reasonable heuristic when clusters are stored by ID. |
| 124 | + |
| 125 | +### Cons |
| 126 | + |
| 127 | +- **Recall loss**: IVF is an approximate method. Vectors near cluster boundaries may be missed if their cluster isn't probed. The benchmark shows recall@10 = 0.50 with nprobe=20/nlist=100 on random data. Real-world data with more structure typically yields higher recall. |
| 128 | +- **Build time**: k-means is expensive. Building on 1M x 768-dim vectors takes ~10 minutes. This is a one-time cost. |
| 129 | +- **Static index**: The IVF index is not updated when rows are inserted or deleted. A rebuild is required to incorporate new data. |
| 130 | +- **Greedy preload order**: Clusters are loaded in storage order (by centroid_id), not by frequency or size. A popularity-based or size-based ordering could be more optimal but adds complexity. |
| 131 | +- **No partial cluster loading**: A cluster is either fully loaded or not at all. Very large clusters that exceed the remaining budget are skipped entirely even if most of their data would fit. |
| 132 | +- **Random data pessimism**: The benchmark uses uniformly random vectors, which is the worst case for clustering (no natural structure to exploit). Real datasets with semantic clusters will show better recall and speedup. |
| 133 | + |
| 134 | +## Benchmark Results |
| 135 | + |
| 136 | +**Configuration**: 1M vectors, 768 dimensions, F32, K=10, nlist=100, nprobe=20, max_memory=100MB |
| 137 | + |
| 138 | +``` |
| 139 | +=== IVF Benchmark === |
| 140 | + Vectors: 1000000 Dim: 768 K: 10 nlist: 100 nprobe: 20 |
| 141 | +
|
| 142 | +Inserting 1000000 vectors ... |
| 143 | + Insert: 3479.5 ms |
| 144 | + Brute force: 429.8 ms (10 results) RSS: 4475.6 MB |
| 145 | +Building IVF index (nlist=100) ... |
| 146 | + IVF build: 651678.8 ms |
| 147 | + IVF preload: 452.4 ms RSS: 3883.2 MB |
| 148 | + IVF search: 113.8 ms (10 results) RSS: 3883.6 MB |
| 149 | +
|
| 150 | + Recall@10: 0.50 (5/10 ground-truth hits) |
| 151 | + Speedup: 3.8x (429.8 ms -> 113.8 ms) |
| 152 | +
|
| 153 | + Memory: |
| 154 | + Brute force search: -0.3 MB |
| 155 | + IVF preload: -592.4 MB (RSS after preload: 3883.2 MB) |
| 156 | + IVF search: 0.4 MB |
| 157 | +
|
| 158 | +Benchmark: 4 passed, 0 failed |
| 159 | +``` |
| 160 | + |
| 161 | +| Metric | Value | |
| 162 | +|---------------------|-------------| |
| 163 | +| Brute force latency | 429.8 ms | |
| 164 | +| IVF search latency | 113.8 ms | |
| 165 | +| Speedup | 3.8x | |
| 166 | +| Recall@10 | 0.50 | |
| 167 | +| IVF build time | ~10.9 min | |
| 168 | +| IVF preload time | 452.4 ms | |
| 169 | +| IVF search RSS delta| 0.4 MB | |
| 170 | + |
| 171 | +The IVF preload RSS delta of -592.4 MB confirms the memory cap is working: instead of loading all ~3 GB of cluster data, only clusters fitting within the 100 MB budget are preloaded. The remaining clusters are fetched from disk during search, which still achieves a 3.8x speedup over brute force. |
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