Diverse EdTech Recommendations: Maximal Marginal Relevance (2D)

Recommendation Policy

Diversity ↔ Relevance λ 0.70

List size K 6

MMR Recommended List

No resources picked yet — press "Recommend next".

Avg. relevance (MMR)

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Avg. diversity (MMR)

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Picked

0 / 6

Topics covered

0 / 6

MMR vs. Naive Top-K

Naive avg. similarity

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MMR avg. similarity

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How it works

Every practice resource in the catalog and the student's current learning need are embedded as 2D vectors (this is exactly the position plotted on the canvas — a flattened topic-embedding space). Cosine similarity measures how aligned two vectors are:

sim(a, b) = (a · b) / (‖a‖ ‖b‖)

A naive "top-K by relevance" recommender (orange, dashed) just returns the K resources most similar to the query — which tends to return near-duplicates clustered around one topic. Maximal Marginal Relevance (MMR, blue) picks resources one at a time, each time maximizing:

MMR = argmax_d∈R\S [ λ·sim(d, query) − (1−λ)·max_s∈S sim(d, s) ]

R\S is every not-yet-picked resource, S is the list picked so far. The first term rewards relevance to the student's need; the second penalizes similarity to items already on the list, so each new pick must add something the list doesn't already cover. The chart above tracks each strategy's average pairwise similarity among its picked items as the list grows — lower means more diverse.

λ near 1 — behaves like plain top-K relevance ranking: a tight, possibly repetitive list around the query's own topic.
λ near 0 — chases maximum spread across topic clusters, even at the cost of relevance to what the student actually asked for.
λ ≈ 0.6–0.8 — the usual sweet spot: relevant to the student's need, but covering more than one topic cluster so the list is not ten near-identical practice problems.

This is the same re-ranking mechanic production EdTech recommenders use after an initial relevance/collaborative-filtering pass, so a personalized list doesn't collapse onto one over-represented topic.

Student query Picked (MMR) Picked (naive top-K) Unpicked resource