Re-Ranking for Diversity & Freshness

MMR, DPP, business-rule mixing, why the ranker alone over-concentrates

The ranker scores each item *independently* — it answers "how good is this item for this user?" one item at a time. That's exactly why the top-10 by score can be terrible as a *set*: if the user likes basketball, the 10 highest-scoring items are 10 near-identical basketball clips. The ranker has no notion that showing #2 right after #1 adds almost nothing because they're redundant.

MMR trades relevance against redundancy, greedily. Maximal Marginal Relevance picks items one at a time to maximize `λ·relevance(i) − (1−λ)·max similarity(i, already-picked)`. With λ=0.7 you mostly follow the ranker but penalize an item that's too similar to something already chosen. Concretely: item A scores 0.9, item B scores 0.88 but is 0.95 similar to A — MMR's marginal value for B collapses (0.7·0.88 − 0.3·0.95 ≈ 0.33) so a less-similar 0.80 item can leapfrog it.

DPP models diversity as volume, not pairwise patching. A Determinantal Point Process assigns a set a probability proportional to the *determinant* of a kernel matrix built from item quality and similarity — geometrically, the squared volume the item vectors span. Redundant items are near-parallel vectors spanning near-zero volume, so DPP naturally down-weights whole redundant *sets*, not just adjacent pairs. It's the principled cousin of MMR. Concretely, using the same A/B/C items from the MMR example above: for the redundant set {A, B}, the 2×2 kernel L = [[0.9², 0.9·0.88·0.95], [0.9·0.88·0.95, 0.88²]] = [[0.81, 0.752], [0.752, 0.774]] has det(L) = 0.81·0.774 − 0.752² ≈ 0.061 — tiny, because A and B are near-parallel (0.95 similar). For the diverse set {A, C}, L = [[0.81, 0.9·0.80·0.2], [0.9·0.80·0.2, 0.64]] = [[0.81, 0.144], [0.144, 0.64]] has det(L) = 0.81·0.64 − 0.144² ≈ 0.498 — about 8× larger, because A and C actually span volume (only 0.2 similar). DPP assigns {A, C} far higher probability than {A, B}, the same call MMR made by picking C over B — but reached by comparing whole-set volumes instead of one pairwise penalty.

Freshness and business rules ride the same re-rank stage. New items have thin engagement history, so the ranker systematically under-scores them (a cold-start feedback trap); a freshness boost or an explicit exploration slot in re-ranking counteracts it. Hard business rules — "no more than 2 items per creator in the top 10", "at least 1 item from a followed account" — are also applied here, *after* scoring, because they constrain the *set*, which the per-item ranker structurally cannot.

Key points

• The ranker scores items independently, so the top-k by score is often a redundant set. "Best 10 items" ≠ "best set of 10": 10 near-duplicate basketball clips each score high but collectively bore the user. Diversity is a *set* property the per-item ranker cannot express — it must be imposed after scoring.
• MMR = greedy relevance-minus-redundancy with a λ knob. Pick to maximize λ·rel − (1−λ)·max-sim-to-chosen. λ high → follow the ranker; λ low → aggressively diversify. Cheap, tunable, the default production diversifier.
• DPP = diversity as spanned volume, penalizing whole redundant sets. Set probability ∝ determinant of a quality×similarity kernel = squared volume of the item vectors; near-parallel (redundant) vectors span ~0 volume and are suppressed. More principled than MMR's pairwise patch, at higher compute.
• Freshness boosts and hard business rules live in re-ranking because they constrain the set. Cold items are under-scored by an engagement-trained ranker; freshness/exploration slots counteract it. "≤2 per creator", quotas, and mixing rules apply post-scoring — the per-item ranker can't enforce set-level constraints.

Recap

• The ranker scores each item independently, so the top-k by score is often a redundant set: it answers "how good is this item for this user?" one at a time, with no notion that #2 adds nothing after #1 if they're near-duplicates. "Best 10 items" ≠ "best set of 10" — diversity is a *set* property the per-item ranker structurally cannot express, so it must be imposed after scoring.
• MMR trades relevance against redundancy greedily: pick items one at a time to maximize λ·relevance(i) − (1−λ)·max-similarity(i, already-chosen). λ high → mostly follow the ranker; λ low → aggressively diversify. Concretely, a 0.88-relevance item that's 0.95-similar to an already-picked item collapses in marginal value, letting a less-similar 0.80 item leapfrog it. Cheap, tunable — the default production diversifier.
• DPP models diversity as spanned volume, not pairwise patching: a Determinantal Point Process gives a set probability ∝ the determinant of a quality×similarity kernel = the squared volume the item vectors span. Redundant items are near-parallel vectors spanning ~0 volume, so DPP down-weights whole redundant *sets*, not just adjacent pairs — the principled cousin of MMR, at higher compute. Concretely, using the earlier A/B/C example: {A, C}'s kernel determinant (≈0.498) is about 8× {A, B}'s (≈0.061) — DPP prefers the diverse set for the same reason MMR does, just measured as spanned volume instead of a pairwise penalty.
• Freshness/exploration slots counter the ranker's under-scoring of new items: thin engagement history makes an engagement-trained ranker systematically under-score fresh items (a cold-start feedback trap), so a freshness boost or explicit exploration slot in re-ranking counteracts it.
• Hard business rules are set-level, so they ride the same re-rank stage after scoring: "no more than 2 items per creator in the top 10," quotas, "at least 1 from a followed account" — these constrain the *set*, which the per-item ranker cannot enforce, so they're applied post-scoring, not in the ranker.

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