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

// Example 1: Single Knn - scores top 16 documents
const rank1 = Knn({ query: "machine learning research" });
// Only the 16 nearest documents get scored (default limit)

// Example 2: Multiple Knn with default undefined
const rank2 = Knn({ query: "research papers", limit: 100 })
  .add(Knn({ query: "academic publications", limit: 100, key: "sparse_embedding" }));
// Both Knn have default undefined (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
const rank3 = Knn({ query: "AI research", limit: 100 }).multiply(0.5)
  .add(Knn({ query: "scientific papers", limit: 50, default: 1000.0, key: "sparse_embedding" }).multiply(0.5));
// First Knn has default undefined, 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 is undefined)
// Documents in both lists:
//   - Get first distance * 0.5 + second distance * 0.5

use chroma::types::{Key, QueryVector, RankExpr};

let rank1 = RankExpr::Knn {
    query: QueryVector::Dense(vec![0.1, 0.2, 0.3]),
    key: Key::Embedding,
    limit: 16,
    default: None,
    return_rank: false,
};

let rank2 = RankExpr::Knn {
    query: QueryVector::Dense(vec![0.1, 0.2, 0.3]),
    key: Key::Embedding,
    limit: 100,
    default: None,
    return_rank: false,
};

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.

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")

import { Knn } from 'chromadb';

// 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)
  returnRank: 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

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?")

// 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)

// Array
Knn({ query: [0.1, 0.2, 0.3, 0.4] });

// Float32Array or other typed arrays
const embedding = new Float32Array([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")

// Sparse vector format: object with indices and values
const sparseVector = {
  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: sparseVector, 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

// 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

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

// Weighted combination of two searches
const textScore = Knn({ query: "machine learning research" });
const sparseQ = { indices: [1, 5, 10], values: [0.5, 0.3, 0.8] };
const sparseScore = Knn({ query: sparseQ, key: "sparse_embedding" });
const combined = textScore.multiply(0.7).add(sparseScore.multiply(0.3));

// Scaling scores
const normalized = Knn({ query: "quantum computing" }).divide(100.0);

// Adding baseline score
const withBaseline = Knn({ query: "artificial intelligence" }).add(0.5);

// Complex expressions (use chaining for clarity)
const finalScore = Knn({ query: "deep learning" }).multiply(0.5)
  .add(Knn({ query: "neural networks" }).multiply(0.3))
  .divide(1.8);

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)

// Exponential - amplifies differences between scores
const score = Knn({ query: "machine learning" }).exp();

// Logarithm - compresses score range
// Add constant to avoid log(0)
const compressed = Knn({ query: "deep learning" }).add(1).log();

// Absolute value - useful for difference calculations
const diff = Knn({ query: "neural networks" }).subtract(Knn({ query: "machine learning" })).abs();

// Clamping scores to a range
const score2 = Knn({ query: "artificial intelligence" });
const clamped = score2.min(0.0).max(1.0);  // Clamp to [0, 1]

// Ensuring non-negative scores
const positiveOnly = 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

import { Val, Knn } from 'chromadb';

// Automatic conversion (these are equivalent)
const score1 = Knn({ query: "machine learning" }).multiply(0.5);
const score2 = Knn({ query: "machine learning" }).multiply(Val(0.5));

// Explicit Val for named constants
const baseline = Val(0.1);
const boostFactor = Val(2.0);
const finalScore = Knn({ query: "artificial intelligence" }).add(baseline).multiply(boostFactor);

// Using Val in complex expressions
const threshold = Val(0.8);
const penalty = Val(0.5);
const adjusted = Knn({ query: "deep learning" }).max(threshold).subtract(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

// Linear combination - weighted average of different searches
const denseScore = Knn({ query: "machine learning applications" });
const sparseScore = Knn({ query: "machine learning applications", key: "sparse_embedding" });
const combined = denseScore.multiply(0.8).add(sparseScore.multiply(0.2));

// Multi-query search - combining different perspectives
const generalScore = Knn({ query: "artificial intelligence overview" });
const specificScore = Knn({ query: "neural network architectures" });
const multiQuery = generalScore.multiply(0.4).add(specificScore.multiply(0.6));

// Boosting with constant
const baseScore = Knn({ query: "quantum computing" });
// Note: K("boost") would need to be part of select() to use in ranking
const finalScore = baseScore.multiply(Val(1).add(Val(0.1)));  // Fixed 10% boost

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

// No ranking - results in index order
const search = new Search().where(K("status").eq("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

// Problem: Restrictive filtering with default undefined
const rank1 = Knn({ query: "machine learning", limit: 100 }).multiply(0.7)
  .add(Knn({ query: "deep learning", limit: 100 }).multiply(0.3));
// Both have default undefined
// Only documents in BOTH top-100 lists get scored

// Solution: Set default values for more inclusive results
const rank2 = Knn({ query: "machine learning", limit: 100, default: 10.0 }).multiply(0.7)
  .add(Knn({ query: "deep learning", limit: 100, default: 10.0 }).multiply(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

// If your embeddings are 384-dimensional
Knn({ query: [0.1, 0.2, 0.3] });         // Error - only 3 dimensions
Knn({ query: Array(384).fill(0.1) });   // 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...

// 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", returnRank: 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

// Knn.limit - candidates to consider for scoring
const rank = Knn({ query: "artificial intelligence", limit: 1000 });  // Score top 1000 candidates

// Search.limit - results to return
const search = new 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()

import { Search, K, Knn, Val } from 'chromadb';

// Complex ranking with filtering and mathematical functions
const search = new Search()
  .where(
    K("status").eq("published")
      .and(K("category").isIn(["tech", "science"]))
  )
  .rank(
    // Combine two queries with weights
    Knn({ query: "latest AI research developments" }).multiply(0.7)
      .add(Knn({ query: "artificial intelligence breakthroughs" }).multiply(0.3))
      .exp()  // Amplify score differences
      .min(0.0)  // Ensure non-negative
  )
  .limit(20)
  .select(K.DOCUMENT, K.SCORE, "title", "category");

const results = await collection.search(search);

// Process results using rows() for cleaner access
const rows = results.rows()[0];  // Get first (and only) search results
for (const [i, row] of rows.entries()) {
  console.log(`${i+1}. ${row.metadata?.title}`);
  console.log(`   Score: ${row.score?.toFixed(3)}`);
  console.log(`   Category: ${row.metadata?.category}`);
  console.log(`   Preview: ${row.document?.substring(0, 100)}...`);
  console.log();
}

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

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

​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

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