Struct MmrConfig 

pub struct MmrConfig {
    pub lambda: f32,
    pub top_k: usize,
}

Maximal Marginal Relevance (MMR) configuration.

Background

MMR was introduced by Carbonell & Goldstein (1998) to address a fundamental tension in information retrieval: relevance vs. diversity.

Traditional ranking optimizes relevance only, leading to redundant results. If the top-5 results are all about the same aspect of a topic, the user gains little from results 2-5.

MMR balances:

• Relevance: How well does this document match the query?
• Diversity: How different is this document from already-selected ones?

Historical Context

Year	Development
1998	MMR introduced (Carbonell & Goldstein)
2008	xQuAD extends MMR with explicit subtopics
2012	PM-2 proportional model
2020s	MMR widely used in RAG to reduce redundancy

MMR remains the go-to algorithm for diversity because:

1. Simple to implement and explain
2. Single tunable parameter (λ)
3. Works with any similarity function
4. Greedy selection is fast

Mathematical Formulation

At each step, select the document that maximizes:

MMR(d) = λ · Sim(d, q) - (1-λ) · max_{s∈S} Sim(d, s)

Where:

• d is a candidate document
• q is the query
• S is the set of already-selected documents
• Sim(d, q) is relevance (query-document similarity)
• max_{s∈S} Sim(d, s) is redundancy (max similarity to any selected doc)
• λ in [0,1] balances relevance and diversity

The λ Parameter

λ Value	Effect
λ = 1.0	Pure relevance (standard ranking)
λ = 0.7	Mild diversity (typical for search)
λ = 0.5	Balanced relevance/diversity
λ = 0.3	Strong diversity preference
λ = 0.0	Pure diversity (maximally spread results)

Computational Complexity

• Naïve: O(k·n·|S|) where k=results wanted, n=candidates, |S|=selected set
• In practice: O(k·n²) worst case, often much better with pruning

Reference

Carbonell & Goldstein, “The Use of MMR, Diversity-Based Reranking for Reordering Documents and Producing Summaries”, SIGIR 1998.

Fields

lambda: f32

Balance parameter λ ∈ [0,1].

• λ = 1.0: pure relevance (no diversity)
• λ = 0.5: balanced
• λ = 0.0: pure diversity

top_k: usize

Maximum results to return.

Implementations

impl MmrConfig

pub fn new(lambda: f32) -> Self

Create MMR config with specified lambda.

Arguments

• lambda: Balance between relevance and diversity. Valid: [0.0, 1.0].

Panics

Panics if lambda is outside [0.0, 1.0].

pub const fn with_top_k(self, top_k: usize) -> Self

Set the number of results to return.

Trait Implementations

impl Clone for MmrConfig

fn clone(&self) -> MmrConfig

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for MmrConfig

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for MmrConfig

fn default() -> Self

Returns the “default value” for a type.

impl PartialEq for MmrConfig

fn eq(&self, other: &MmrConfig) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for MmrConfig

impl StructuralPartialEq for MmrConfig