Ranking and Scoring

How Ranking Works

A ranking expression determines which documents are scored and how they’re ordered:

Expression Evaluation Process

No ranking (rank=None): Documents are returned in index order (typically insertion order)
With ranking expression:
- Must contain at least one Knn expression
- Documents must appear in at least one Knn’s top-k results to be considered
- Documents must also appear in ALL Knn results where default=None
- Documents missing from a Knn with a default value get that default score
- Each Knn considers its top limit candidates (default: 16)
- Documents are sorted by score (ascending - lower scores first)
- Final results based on Search.limit()

Document Selection and Scoring

# Example 1: Single Knn - scores top 16 documents
rank = Knn(query="machine learning research")
# Only the 16 nearest documents get scored (default limit)

# Example 2: Multiple Knn with default=None
rank = Knn(query="research papers", limit=100) + Knn(query="academic publications", limit=100, key="sparse_embedding")
# Both Knn have default=None (the default)
# Documents must appear in BOTH top-100 lists to be scored
# Documents in only one list are excluded

# Example 3: Mixed default values
rank = Knn(query="AI research", limit=100) * 0.5 + Knn(query="scientific papers", limit=50, default=1000.0, key="sparse_embedding") * 0.5
# First Knn has default=None, second has default=1000.0
# Documents in first top-100 but not in second top-50:
#   - Get first distance * 0.5 + 1000.0 * 0.5 (second's default)
# Documents in second top-50 but not in first top-100:
#   - Excluded (must appear in all Knn where default=None)
# Documents in both lists:
#   - Get first distance * 0.5 + second distance * 0.5

When combining multiple Knn expressions, documents must appear in at least one Knn’s results AND must appear in every Knn where default=None. To avoid excluding documents, set default values on your Knn expressions.

The Knn Class

The Knn class performs K-nearest neighbor search to find similar vectors. It’s the primary way to add vector similarity scoring to your searches.

Sparse embeddings: To search custom sparse embedding fields, you must first configure a sparse vector index in your collection schema. See Sparse Vector Search Setup for configuration instructions.

from chromadb import Knn

# Basic search on default embedding field
Knn(query="What is machine learning?")

# Search with custom parameters
Knn(
    query="What is machine learning?",
    key="#embedding",      # Field to search (default: "#embedding")
    limit=100,            # Max candidates to consider (default: 16)
    return_rank=False     # Return rank position vs distance (default: False)
)

# Search custom sparse embedding field in metadata
Knn(query="machine learning", key="sparse_embedding")

Knn Parameters

Parameter	Type	Default	Description
`query`	str, List[float], SparseVector, or np.ndarray	Required	The query text or vector to search with
`key`	str	`"#embedding"`	Field to search - `"#embedding"` for dense embeddings, or a metadata field name for sparse embeddings
`limit`	int	`16`	Maximum number of candidates to consider
`default`	float or None	`None`	Score for documents not in KNN results
`return_rank`	bool	`False`	If `True`, return rank position (0, 1, 2…) instead of distance

"#embedding" (or K.EMBEDDING) refers to the default embedding field where Chroma stores dense embeddings. Sparse embeddings must be stored in metadata under a consistent key.

Query Formats

Text Queries

# Text query (most common - auto-embedded using collection schema)
Knn(query="machine learning applications")

# Text is automatically converted to embeddings using the collection's
# configured embedding function
Knn(query="What are the latest advances in quantum computing?")

Dense Vectors

# Python list
Knn(query=[0.1, 0.2, 0.3, 0.4])

# NumPy array
import numpy as np
embedding = np.array([0.1, 0.2, 0.3, 0.4])
Knn(query=embedding)

Sparse Vectors

# Sparse vector format: dictionary with indices and values
sparse_vector = {
    "indices": [1, 5, 10, 50],  # Non-zero indices
    "values": [0.5, 0.3, 0.8, 0.2]  # Corresponding values
}

# Search using sparse vector (must specify the metadata field)
Knn(query=sparse_vector, key="sparse_embedding")

Embedding Fields

Chroma currently supports:

Dense embeddings - Stored in the default embedding field ("#embedding" or K.EMBEDDING)
Sparse embeddings - Can be stored in metadata under a consistent key

# Text or dense embeddings - use the default embedding field
Knn(query="machine learning")              # Implicitly uses key="#embedding"
Knn(query="machine learning", key="#embedding")  # Explicit
Knn(query="machine learning", key=K.EMBEDDING)   # Using constant (same as "#embedding")

# Sparse embeddings - store in metadata under a consistent key
# The sparse vector should be stored under the same metadata key across all documents
Knn(query="machine learning", key="sparse_embedding")  # Search sparse embeddings in metadata

# NOT SUPPORTED: Dense embeddings in metadata
# Knn(query=[0.1, 0.2], key="some_metadata_field")  # Not supported

Currently, dense embeddings can only be stored in the default embedding field (#embedding). Only sparse vector embeddings can be stored in metadata, and they must be stored consistently under the same key across all documents. Additionally, only one sparse vector index is allowed per collection in metadata.

Support for multiple dense embedding fields and multiple sparse vector indices is coming in a future release. This will allow you to store and query multiple embeddings per document, with optimized indexing for each field.

Arithmetic Operations

Supported operators:

+ - Addition
- - Subtraction
* - Multiplication
/ - Division
- (unary) - Negation

Combine ranking expressions using arithmetic operators. Operator precedence follows Python’s standard rules.

# Weighted combination of two searches
text_score = Knn(query="machine learning research")
sparse_q = {"indices": [1, 5, 10], "values": [0.5, 0.3, 0.8]}
sparse_score = Knn(query=sparse_q, key="sparse_embedding")
combined = text_score * 0.7 + sparse_score * 0.3

# Scaling scores
normalized = Knn(query="quantum computing") / 100.0

# Adding baseline score
with_baseline = Knn(query="artificial intelligence") + 0.5

# Complex expressions (use parentheses for clarity)
final_score = (Knn(query="deep learning") * 0.5 + Knn(query="neural networks") * 0.3) / 1.8

Numbers in expressions are automatically converted to Val constants. For example, Knn(query=v) * 0.5 is equivalent to Knn(query=v) * Val(0.5).

Mathematical Functions

Supported functions:

exp() - Exponential (e^x)
log() - Natural logarithm
abs() - Absolute value
min() - Minimum of two values
max() - Maximum of two values

# Exponential - amplifies differences between scores
score = Knn(query="machine learning").exp()

# Logarithm - compresses score range
# Add constant to avoid log(0)
compressed = (Knn(query="deep learning") + 1).log()

# Absolute value - useful for difference calculations
diff = abs(Knn(query="neural networks") - Knn(query="machine learning"))

# Clamping scores to a range
score = Knn(query="artificial intelligence")
clamped = score.min(0.0).max(1.0)  # Clamp to [0, 1]

# Ensuring non-negative scores
positive_only = Knn(query="quantum computing").min(0.0)

Val for Constant Values

The Val class represents constant values in ranking expressions. Numbers are automatically converted to Val, but you can use it explicitly for clarity.

from chromadb import Val

# Automatic conversion (these are equivalent)
score1 = Knn(query="machine learning") * 0.5
score2 = Knn(query="machine learning") * Val(0.5)

# Explicit Val for named constants
baseline = Val(0.1)
boost_factor = Val(2.0)
final_score = (Knn(query="artificial intelligence") + baseline) * boost_factor

# Using Val in complex expressions
threshold = Val(0.8)
penalty = Val(0.5)
adjusted = Knn(query="deep learning").max(threshold) - penalty

Combining Ranking Expressions

You can combine multiple Knn searches using arithmetic operations for custom scoring strategies.

# Linear combination - weighted average of different searches
dense_score = Knn(query="machine learning applications")
sparse_score = Knn(query="machine learning applications", key="sparse_embedding")
combined = dense_score * 0.8 + sparse_score * 0.2

# Multi-query search - combining different perspectives
general_score = Knn(query="artificial intelligence overview")
specific_score = Knn(query="neural network architectures")
multi_query = general_score * 0.4 + specific_score * 0.6

# Boosting with constant
base_score = Knn(query="quantum computing")
# Note: K("boost") would need to be part of select() to use in ranking
final_score = base_score * (1 + Val(0.1))  # Fixed 10% boost

For advanced hybrid search combining multiple ranking strategies, consider using RRF (Reciprocal Rank Fusion) which is specifically designed for this purpose.

Dictionary Syntax

You can also construct ranking expressions using dictionary syntax. This is useful when building ranking expressions programmatically. Supported dictionary operators:

$knn - K-nearest neighbor search
$val - Constant value
$sum - Addition of multiple ranks
$sub - Subtraction (left - right)
$mul - Multiplication of multiple ranks
$div - Division (left / right)
$abs - Absolute value
$exp - Exponential
$log - Natural logarithm
$max - Maximum of multiple ranks
$min - Minimum of multiple ranks

# Knn as dictionary
rank_dict = {
    "$knn": {
        "query": "machine learning research",
        "key": "#embedding",  # Optional, defaults to "#embedding"
        "limit": 100,         # Optional, defaults to 16
        "return_rank": False  # Optional, defaults to False
    }
}

# Val as dictionary
const_dict = {"$val": 0.5}

# Arithmetic operations
sum_dict = {
    "$sum": [
        {"$knn": {"query": "deep learning"}},
        {"$val": 0.5}
    ]
}  # Same as Knn(query="deep learning") + 0.5

mul_dict = {
    "$mul": [
        {"$knn": {"query": "neural networks"}},
        {"$val": 0.8}
    ]
}  # Same as Knn(query="neural networks") * 0.8

# Complex expression
weighted_combo = {
    "$sum": [
        {"$mul": [
            {"$knn": {"query": "machine learning"}},
            {"$val": 0.7}
        ]},
        {"$mul": [
            {"$knn": {"query": "machine learning", "key": "sparse_embedding"}},
            {"$val": 0.3}
        ]}
    ]
}  # Same as Knn(query="machine learning") * 0.7 + Knn(query="machine learning", key="sparse_embedding") * 0.3

# Use in Search
search = Search(rank=rank_dict)

Understanding Scores

Lower scores = better matches - Chroma uses distance-based scoring
Score range - Depends on your embedding model and distance metric
No ranking - When rank=None, results are returned in natural storage order
Distance vs similarity - Scores represent distance; for similarity, use 1 - score (for normalized embeddings)

Edge Cases and Important Behavior

Default Ranking

When no ranking is specified (rank=None), results are returned in index order (typically insertion order). This is useful when you only need filtering without scoring.

# No ranking - results in index order
search = Search().where(K("status") == "active").limit(10)
# Score for each document is simply its index position

Combining Knn Expressions with default=None

Documents must appear in at least one Knn’s results to be candidates, AND must appear in ALL Knn results where default=None.

# Problem: Restrictive filtering with default=None
rank = Knn(query="machine learning", limit=100) * 0.7 + Knn(query="deep learning", limit=100) * 0.3
# Both have default=None
# Only documents in BOTH top-100 lists get scored

# Solution: Set default values for more inclusive results
rank = (
    Knn(query="machine learning", limit=100, default=10.0) * 0.7 +
    Knn(query="deep learning", limit=100, default=10.0) * 0.3
)
# Now documents in either top-100 list can be scored
# Documents get default score (10.0) for Knn where they don't appear

Vector Dimension Mismatch

Query vectors must match the dimension of the indexed embeddings. Mismatched dimensions will result in an error.

# If your embeddings are 384-dimensional
Knn(query=[0.1, 0.2, 0.3])  # Error - only 3 dimensions
Knn(query=[0.1] * 384)      # Correct - 384 dimensions

The return_rank Parameter

Set return_rank=True when using Knn with RRF to get rank positions (0, 1, 2…) instead of distances.

# For regular scoring - use distances
Knn(query="machine learning")  # Returns: 0.23, 0.45, 0.67...

# For RRF - use rank positions
Knn(query="machine learning", return_rank=True)  # Returns: 0, 1, 2...

The limit Parameter

The limit parameter in Knn controls how many candidates are considered, not the final result count. Use Search.limit() to control the number of results returned.

# Knn.limit - candidates to consider for scoring
rank = Knn(query="artificial intelligence", limit=1000)  # Score top 1000 candidates

# Search.limit - results to return
search = Search().rank(rank).limit(10)  # Return top 10 results

Complete Example

Here’s a practical example combining different ranking features:

from chromadb import Search, K, Knn, Val

# Complex ranking with filtering and mathematical functions
search = (Search()
    .where(
        (K("status") == "published") &
        (K("category").is_in(["tech", "science"]))
    )
    .rank(
        # Combine two queries with weights
        (
            Knn(query="latest AI research developments") * 0.7 +
            Knn(query="artificial intelligence breakthroughs") * 0.3
        ).exp()  # Amplify score differences
        .min(0.0)  # Ensure non-negative
    )
    .limit(20)
    .select(K.DOCUMENT, K.SCORE, "title", "category")
)

results = collection.search(search)

# Process results using rows() for cleaner access
rows = results.rows()[0]  # Get first (and only) search results
for i, row in enumerate(rows):
    print(f"{i+1}. {row['metadata']['title']}")
    print(f"   Score: {row['score']:.3f}")
    print(f"   Category: {row['metadata']['category']}")
    print(f"   Preview: {row['document'][:100]}...")
    print()

Tips and Best Practices

Normalize your vectors - Ensure consistent scoring by normalizing query vectors
Use appropriate limit values - Higher limits in Knn mean more accurate but slower results
Set return_rank=True for RRF - Essential when using Reciprocal Rank Fusion
Test score ranges - Understand your model’s typical score ranges for better thresholding
Combine strategies wisely - Linear combinations work well for similar score ranges

Next Steps

Learn about Group By & Aggregation to diversify search results by category
Learn about hybrid search with RRF for advanced ranking strategies
See practical examples of ranking in real-world scenarios
Explore batch operations for multiple searches

Features

Schema

Search API

Sync

Package Search

How Ranking Works

Expression Evaluation Process

Document Selection and Scoring

The Knn Class

Knn Parameters

Query Formats

Text Queries

Dense Vectors

Sparse Vectors

Embedding Fields

Arithmetic Operations

Mathematical Functions

Val for Constant Values

Combining Ranking Expressions

Dictionary Syntax

Understanding Scores

Edge Cases and Important Behavior

Default Ranking

Combining Knn Expressions with default=None

Vector Dimension Mismatch

The return_rank Parameter

The limit Parameter

Complete Example

Tips and Best Practices

Next Steps

Features

Schema

Search API

Sync

Package Search

​How Ranking Works

​Expression Evaluation Process

​Document Selection and Scoring

​The Knn Class

​Knn Parameters

​Query Formats

​Text Queries

​Dense Vectors

​Sparse Vectors

​Embedding Fields

​Arithmetic Operations

​Mathematical Functions

​Val for Constant Values

​Combining Ranking Expressions

​Dictionary Syntax

​Understanding Scores

​Edge Cases and Important Behavior

​Default Ranking

​Combining Knn Expressions with default=None

​Vector Dimension Mismatch

​The return_rank Parameter

​The limit Parameter

​Complete Example

​Tips and Best Practices

​Next Steps

How Ranking Works

Expression Evaluation Process

Document Selection and Scoring

The Knn Class

Knn Parameters

Query Formats

Text Queries

Dense Vectors

Sparse Vectors

Embedding Fields

Arithmetic Operations

Mathematical Functions

Val for Constant Values

Combining Ranking Expressions

Dictionary Syntax

Understanding Scores

Edge Cases and Important Behavior

Default Ranking

Combining Knn Expressions with default=None

Vector Dimension Mismatch

The return_rank Parameter

The limit Parameter

Complete Example

Tips and Best Practices

Next Steps