Fusion Strategies

When a feature search stage queries multiple embedding indexes (e.g., text + image), it produces separate ranked lists that need to be merged. Fusion strategies determine how those lists become one.

Strategy Reference

Strategy	Formula	Configuration	Best For
`rrf`	`1 / (k + rank)`	None (k=60 default)	General purpose, no tuning needed
`dbsf`	Distribution-based normalization	None	Different score distributions across features
`weighted`	`w₁·score₁ + w₂·score₂`	`weight` per search	Known feature importance
`max`	`max(score₁, score₂)`	None	Any single match is sufficient
`learned`	Thompson Sampling	Interaction data	Personalized, adaptive weights

Reciprocal Rank Fusion (RRF)

The default strategy. RRF ignores raw similarity scores and uses only rank position. This makes it robust when different features produce scores on different scales. Formula:

score(doc) = Σ  1 / (k + rank_i(doc))

Where k = 60 (constant that prevents top-ranked items from dominating) and rank_i is the document’s position in the i-th feature’s result list. Why it works: A document ranked #1 by text search and #3 by image search gets a higher fused score than a document ranked #2 by both. The rank-based approach means you don’t need to calibrate score ranges across features.

RRF scores are small on purpose — read order, not magnitude. Because the score is 1 / (k + rank) with k = 60, the best possible result scores about 1 / (60 + 1) ≈ 0.0164 per search (a little higher when several searches rank the same document). A top score of ~0.017 is expected and healthy — it is a fused rank position, not a similarity or a quality percentage, so a 0.0167 top hit does not mean the search matched poorly. Rank documents by their relative order. If you need an absolute similarity value (e.g. 0.0–1.0), use a single search without fusion, or a weighted/max strategy that preserves raw scores.

{
  "stage_name": "feature_search",
  "stage_type": "filter",
  "config": {
    "stage_id": "feature_search",
    "parameters": {
      "searches": [
        {
          "feature_uri": "mixpeek://text_extractor@v1/multilingual_e5_large_instruct_v1",
          "query": "{{INPUT.query}}",
          "top_k": 100
        },
        {
          "feature_uri": "mixpeek://multimodal_extractor@v1/vertex_multimodal_embedding",
          "query": "{{INPUT.query}}",
          "top_k": 100
        }
      ],
      "fusion": "rrf",
      "final_top_k": 25
    }
  }
}

RRF is the best default. Use it unless you have a specific reason to choose another strategy.

Distribution-Based Score Fusion (DBSF)

DBSF normalizes scores from each feature into a common distribution before combining them. This handles cases where one feature produces scores in [0.8, 0.99] and another in [0.1, 0.6]. How it works:

For each feature, compute the mean (μ) and standard deviation (σ) of scores
Normalize each score: normalized = (score - μ) / σ
Sum normalized scores across features

DBSF is useful when features have different score distributions, but the raw scores themselves carry meaningful information (unlike RRF which ignores scores entirely).

{
  "stage_name": "feature_search",
  "stage_type": "filter",
  "config": {
    "stage_id": "feature_search",
    "parameters": {
      "searches": [
        {
          "feature_uri": "mixpeek://text_extractor@v1/multilingual_e5_large_instruct_v1",
          "query": "{{INPUT.query}}",
          "top_k": 100
        },
        {
          "feature_uri": "mixpeek://multimodal_extractor@v1/vertex_multimodal_embedding",
          "query": "{{INPUT.query}}",
          "top_k": 100
        }
      ],
      "fusion": "dbsf",
      "final_top_k": 25
    }
  }
}

Weighted Fusion

You manually assign a weight to each search feature. Scores are multiplied by their weight and summed. Use this when you know from domain expertise that one feature is more important than another. Formula:

score(doc) = w₁ · score₁(doc) + w₂ · score₂(doc) + ...

Weights don’t need to sum to 1 — they’re relative importance indicators.

{
  "stage_name": "feature_search",
  "stage_type": "filter",
  "config": {
    "stage_id": "feature_search",
    "parameters": {
      "searches": [
        {
          "feature_uri": "mixpeek://text_extractor@v1/multilingual_e5_large_instruct_v1",
          "query": "{{INPUT.query}}",
          "top_k": 100,
          "weight": 0.7
        },
        {
          "feature_uri": "mixpeek://multimodal_extractor@v1/vertex_multimodal_embedding",
          "query": "{{INPUT.image_url}}",
          "top_k": 100,
          "weight": 0.3
        }
      ],
      "fusion": "weighted",
      "final_top_k": 25
    }
  }
}

Weighted fusion is sensitive to score scale differences. If text scores are in [0.8, 1.0] and image scores are in [0.1, 0.5], a 50/50 weight split will still favor text. Consider DBSF or RRF if score ranges differ significantly.

Max Fusion

Takes the maximum score across all features for each document. A document only needs to be a strong match on one feature to rank highly. Formula:

score(doc) = max(score₁(doc), score₂(doc), ...)

Use this when any single strong match is sufficient — for example, a product that matches either the text description or the visual similarity should rank high.

{
  "stage_name": "feature_search",
  "stage_type": "filter",
  "config": {
    "stage_id": "feature_search",
    "parameters": {
      "searches": [
        {
          "feature_uri": "mixpeek://text_extractor@v1/multilingual_e5_large_instruct_v1",
          "query": "{{INPUT.query}}",
          "top_k": 100
        },
        {
          "feature_uri": "mixpeek://image_extractor@v1/google_siglip_base_v1",
          "query": "{{INPUT.image_url}}",
          "top_k": 100
        }
      ],
      "fusion": "max",
      "final_top_k": 25
    }
  }
}

Learned Fusion

Learned fusion replaces static weights with weights that adapt automatically from user interaction data. Under the hood, it uses Thompson Sampling with Beta distributions to balance exploration (trying different weight combinations) with exploitation (using what’s known to work). See Learned Fusion for the full deep dive.

{
  "stage_name": "feature_search",
  "stage_type": "filter",
  "config": {
    "stage_id": "feature_search",
    "parameters": {
      "searches": [
        {
          "feature_uri": "mixpeek://text_extractor@v1/multilingual_e5_large_instruct_v1",
          "query": "{{INPUT.query}}",
          "top_k": 100
        },
        {
          "feature_uri": "mixpeek://multimodal_extractor@v1/vertex_multimodal_embedding",
          "query": "{{INPUT.image_url}}",
          "top_k": 100
        }
      ],
      "fusion": "learned",
      "final_top_k": 25
    }
  }
}

Choosing a Strategy

Do you have multiple search features?
├── No  → No fusion needed (single feature search)
└── Yes
    ├── Do you have interaction data (100+ signals)?
    │   ├── Yes → Use "learned" (adapts automatically)
    │   └── No
    │       ├── Do you know which features matter more?
    │       │   ├── Yes → Use "weighted"
    │       │   └── No
    │       │       ├── Do features have different score scales?
    │       │       │   ├── Yes → Use "dbsf"
    │       │       │   └── No → Use "rrf" (default)
    │       └── Is any single match sufficient?
    │           └── Yes → Use "max"

Performance Comparison

Strategy	Latency Overhead	Configuration Effort	Adapts Over Time	Best Quality Ceiling
RRF	< 5ms	None	No	Good
DBSF	< 5ms	None	No	Good
Weighted	< 5ms	Manual tuning	No	Good (if well-tuned)
Max	< 5ms	None	No	Moderate
Learned	< 10ms	Interaction tracking	Yes	Best

All strategies add minimal latency. The real difference is in quality: learned fusion converges toward optimal weights for your specific users and content, while static strategies require manual tuning or accept a one-size-fits-all approach.

Feature Search stage — where fusion is configured
Learned Fusion deep dive — Thompson Sampling explained
Interaction Signals — capturing the data that powers learned fusion
Evaluations — measuring the impact of different fusion strategies

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Resources

Fusion Strategies

Strategy Reference

Reciprocal Rank Fusion (RRF)

Distribution-Based Score Fusion (DBSF)

Weighted Fusion

Max Fusion

Learned Fusion

Choosing a Strategy

Performance Comparison

​Strategy Reference

​Reciprocal Rank Fusion (RRF)

​Distribution-Based Score Fusion (DBSF)

​Weighted Fusion

​Max Fusion

​Learned Fusion

​Choosing a Strategy

​Performance Comparison

​Related

Strategy Reference

Reciprocal Rank Fusion (RRF)

Distribution-Based Score Fusion (DBSF)

Weighted Fusion

Max Fusion

Learned Fusion

Choosing a Strategy

Performance Comparison

Related