# AI & Embeddings

Vector Similarity Search is built into Turso and libSQL Server as a native feature.

Turso and libSQL enables vector search capability without an extension.

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Full support for vector search in the Turso platform starts from version `v0.24.24`

(use the `turso group show <group-name>`

command to check the group version).

## How it works

- Create a table with one or more vector columns (e.g.
`FLOAT32`

) - Provide vector values in binary format or convert text representation to binary using the appropriate conversion function (e.g.
`vector32(...)`

) - Calculate vector similarity between vectors in the table or from the query itself using dedicated vector functions (e.g.
`vector_distance_cos`

) - Create a special vector index to speed up nearest neighbors queries (use the
`libsql_vector_idx(column)`

expression in the`CREATE INDEX`

statement to create vector index) - Query the index with the special
`vector_top_k(idx_name, q_vector, k)`

table-valued function

# Vectors

### Types

LibSQL uses the native SQLite BLOB storage class for vector columns. To align with SQLite affinity rules, all type names have two alternatives: one that is easy to type and another with a `_BLOB`

suffix that is consistent with affinity rules.

We suggest library authors use type names with the `_BLOB`

suffix to make results more generic and universal. For regular applications, developers can choose either alternative, as the type name only serves as a **hint** for SQLite and external extensions.

As LibSQL does not introduce a new storage class, all metadata about vectors is also encoded in the `BLOB`

itself. This comes at the cost of a few bytes per row but greatly simplifies the design of the feature.

The table below lists six vector types currently supported by LibSQL. Types are listed from more precise and storage-heavy to more compact but less precise alternatives (the number of dimensions in vector $D$ is used to estimate storage requirements for a single vector).

Type name | Storage (bytes) | Description |
---|---|---|

`FLOAT64` | `F64_BLOB` | $8D + 1$ | Implementation of IEEE 754 double precision format for 64-bit floating point numbers |

`FLOAT32` | `F32_BLOB` | $4D$ | Implementation of IEEE 754 single precision format for 32-bit floating point numbers |

`FLOAT16` | `F16_BLOB` | $2D + 1$ | Implementation of IEEE 754-2008 half precision format for 16-bit floating point numbers |

`FLOATB16` | `FB16_BLOB` | $2D + 1$ | Implementation of bfloat16 format for 16-bit floating point numbers |

`FLOAT8` | `F8_BLOB` | $D + 14$ | LibSQL specific implementation which compresses each vector component to single `u8` byte `b` and reconstruct value from it using simple transformation: $\texttt{shift} + \texttt{alpha} \cdot b$ |

`FLOAT1BIT` | `F1BIT_BLOB` | $\lceil \frac{D}{8} \rceil + 3$ | LibSQL-specific implementation which compresses each vector component down to 1-bit and packs multiple components into a single machine word, achieving a very compact representation |

For most applications, the `FLOAT32`

type should be a good starting point, but you may want to explore more compact options if your table has a large number of rows with vectors.

While `FLOAT16`

and `FLOATB16`

use the same amount of storage, they provide different trade-offs between speed and accuracy. Generally, operations over `bfloat16`

are faster but come at the expense of lower precision.

### Functions

To work with vectors, LibSQL provides several functions that operate in the vector domain. Each function understands vectors in binary format aligned with the six types described above or in text format as a single JSON array of numbers.

Currently, LibSQL supports the following functions:

Function name | Description |
---|---|

`vector64` | `vector32` | `vector16` | `vectorb16` | `vector8` | `vector1bit` | Conversion function shiwh accepts valid vector and convert it to the corresponding target type |

`vector` | Alias for `vector32` conversion function |

`vector_extract` | Extraction function which accepts valid vector and return its text representation |

`vector_distance_cos` | Cosine distance (1 - cosine similarity) function which operates over vector of same type with same dimensionality |

`vector_distance_l2` | Euclidian distance function which operates over vector of same type with same dimensionality |

### Vectors usage

Create a table

Begin by declaring a column used for storing vectors with the `F32_BLOB`

datatype:

The number in parentheses `(4)`

specifies the dimensionality of the vector. This means each vector in this column will have exactly 4 components.

Generate and insert embeddings

Once you generate embeddings for your data (via an LLM), you can insert them into your table:

Popular tools like LangChain, Hugging Face or OpenAI can be used to generate embeddings.

Peform a vector similarity search

You can now write queries combining vectors and standard SQLite data:

The `vector_distance_cos`

function calculates the cosine **distance**, which
equals to 1 - cosine
similarity. Therefore, a
smaller distance indicates that the vectors are closer to each other.

### Vector Limitations

- Euclidian distance is
**not supported**for 1-bit`FLOAT1BIT`

vectors - LibSQL can only operate on vectors with no more than 65536 dimensions

## Indexing

Nearest neighbors (NN) queries are popular for various AI-powered applications (RAG uses NN queries to extract relevant information, and recommendation engines can suggest items based on embedding similarity).

LibSQL implements DiskANN algorithm in order to speed up approximate neareast neighbors queries for tables with vector colums.

The DiskANN algorithm trades search accuracy for speed, so LibSQL queries may return slightly suboptimal neighbors for tables with a large number of rows.

### Vector Index

LibSQL introduces a custom index type that helps speed up nearest neighbors queries against a fixed distance function (cosine similarity by default).

From a syntax perspective, the vector index differs from ordinary application-defined B-Tree indices in that it must wrap the vector column into a `libsql_vector_idx`

marker function like this

Vector index works only for column with one of the vector types described above

The vector index is fully integrated into the LibSQL core, so it inherits all operations and most features from ordinary indices:

- An index created for a table with existing data will be automatically populated with this data
- All updates to the base table will be
**automatically**reflected in the index - You can rebuild index from scratch using
`REINDEX movies_idx`

command - You can drop index with
`DROP INDEX movies_idx`

command - You can create partial vector index with a custom filtering rule:

### Query

At the moment vector index must be queried **explicitly** with special `vector_top_k(idx_name, q_vector, k)`

table-valued function. The function accepts index name, query vector and amount of neighbors to return. This function search for `k`

approximate nearest neighbors and return `ROWID`

of these rows or `PRIMARY KEY`

if base index do not have ROWID.

In order for table-valued function to work query vector **must** have same vector type and same dimensionality.

### Settings

LibSQL vector index optionall can accept settings which must be specified as a variadic parameters of the `libsql_vector_idx`

function as a strings in the format `key=value`

:

At the momen LibSQL supports following settings:

Setting key | Value type | Description |
---|---|---|

`metric` | `cosine` | `l2` | Which distance function to use for building index. Default: `cosine` |

`max_neighbors` | positive integer | How many neighbors to store for every node in the DiskANN graph. The lower the setting — the less storage index will use in exchange to search precision. Default: $3 \sqrt{D}$ where $D$ — dimensionality of vector column |

`compress_neighbors` | `float1bit` |`float8` |`float16` |`floatb16` |`float32` | Which vector type must be used to store neighbors for every node in the DiskANN graph. The more compact vector type is used for neighbors — the less storage index will use in exchange to search precision. Default: no comperssion (neighbors has same type as base table) |

`alpha` | positive float $\geq 1$ | “Density” parameter of general sparse neighborhood graph build during DiskANN algorithm. The lower parameter — the more sparse is DiskANN graph which can speed up query speed in exchange to lower search precision. Default: `1.2` |

`search_l` | positive integer | Setting which limits amount of neighbors visited during vector search. The lower the setting — the faster will be search query in exchange to search precision. Default: `200` |

`insert_l` | positive integer | Setting which limits amount of neighbors visited during vector insert. The lower the setting — the faster will be insert query in exchange to DiskANN graph navigability properties. Default: `70` |

Vector index for column of type `T1`

with `max_neighbors=M`

and `compress_neighbors=T2`

will approximately use $\texttt{N} (Storage(\texttt{T1}) + \texttt{M} \cdot Storage(\texttt{T2}))$ storage bytes for `N`

rows.

### Index usage

Create a table

Begin by declaring a column used for storing vectors with the `F32_BLOB`

datatype:

The number in parentheses `(4)`

specifies the dimensionality of the vector. This means each vector in this column will have exactly 4 components.

Generate and insert embeddings

Once you generate embeddings for your data (via an LLM), you can insert them into your table:

Popular tools like LangChain, Hugging Face or OpenAI can be used to generate embeddings.

Create an Index

Create an index using the `libsql_vector_idx`

function:

This creates an index optimized for vector similarity searches on the `embedding`

column.

The `libsql_vector_idx`

marker function is **required** and used by libSQL to
distinguish `ANN`

-indices from ordinary B-Tree indices.

Query the indexed table

This query uses the `vector_top_k`

table-valued function to efficiently find the top 3 most similar vectors to `[0.064, 0.777, 0.661, 0.687]`

using the index.

### Index limitations

- Vector index works only for tables
**with**`ROWID`

or with singular`PRIMARY KEY`

. Composite`PRIMARY KEY`

without`ROWID`

is not supported

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