Personalised Popularity Scores (PPS)

• Personalised Popularity Scores (PPS) are user-conditioned signals that measure item popularity relative to an individual’s history, neighborhood, or temporal context.
• They are implemented in various systems—such as sequential music and news recommendations—using methods like time-aware decay, similar-user analysis, and sub-ID modeling.
• Integration of PPS improves ranking accuracy and personalization while also addressing popularity bias, though balancing novelty remains a key challenge.

Personalised Popularity Scores (PPS) are user-conditioned popularity signals that replace a single global notion of “what is popular” with popularity measured relative to an individual user’s own history, neighborhood, or temporal context. In the supplied literature, PPS appears most explicitly in sequential music recommendation as a user-item-specific score derived from repeated consumption, but closely related formulations include personal popularity among similar users, time-aware personalized popularity, and evolving personal popularity. Across these variants, the central premise is stable: global popularity is the same for all users, whereas personalised popularity attempts to model user-specific demand, replay propensity, or conformity to popular items in a way that can improve ranking accuracy, debias recommendation, and alter the balance between exploitation and exploration (Abbattista et al., 2024).

1. Conceptual scope and historical development

An early anti-popularity line in recommendation explicitly argued for “punishing the recommended object that is the crowd's popular selection” through an Anti-popularity index (AP), claiming enhanced personality, accuracy and diversity with low computational complexity (Zhu et al., 2014). That position framed popularity not as a neutral baseline, but as a source of homogenization requiring user-specific correction.

Later work moved from anti-popularity to personalised popularity. In top-$N$ recommendation, TimePop introduced a time-aware personalized popularity by considering items popularity among neighbors and how it changes over time, using “Precursors” and temporal weighting rather than a single global count (Anelli et al., 2018). In news recommendation, PP-Rec combined a personalized matching score with a time-aware news popularity score and used a user-specific gate to determine how much popularity should influence ranking, especially for cold-start users (Qi et al., 2021). In general recommendation debiasing, PPAC formalized “personal popularity” as popularity among similar users rather than among all users, explicitly contrasting it with global popularity (Ning et al., 2024). In sequential music recommendation, PPS was then defined as a direct model of repeated listening behavior and integrated into Transformer-based recommenders by adding personalised popularity information to model scores (Abbattista et al., 2024). More recent work extended this trajectory with Evolving Personal Popularity, which quantifies each user’s recent preference for popular items and updates that signal over time (Tan et al., 20 May 2025), and with sub-ID-level PPS, which moves from item-level repetition to repetition over latent sub-identifiers in RecJPQ (Mallamaci et al., 7 Aug 2025).

This suggests that PPS is best understood not as a single fixed formula but as a family of user-aware popularity constructions. The common contrast is always against global popularity, but the conditioning variable differs: one user’s own repeat history, a similar-user neighborhood, recency and CTR, or a moving temporal window.

2. Formal definitions and score construction

Several representative formulations illustrate the range of PPS-style constructions in current work.

Formulation	Core score	Distinguishing signal
Sequential music PPS	$p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$	Repeated listening counts
Personal popularity (PP)	$p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$	Similar-user neighborhood
PP-Rec ranking gate	$s=(1-\eta)\cdot s_m+\eta\cdot s_p$	User-specific popularity weight
Evolving Personal Popularity	$$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$	Recent preference for popular items
Sub-ID-level PPS	$$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$	Repetition over sub-identifiers

In the sequential music setting, PPS starts from a user’s sequence $S=[s_1,\ldots,s_L]$ and a count vector $C=[c_1,\ldots,c_N]$, where $c_i$ is the number of times the user consumed item $i$. The personalized popularity probability for item $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$0 is $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$1. An additive smoothing parameter $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$2 is introduced, set to $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$3 in experiments; lower $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$4 gives higher contribution of personalized popularity, $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$5 reduces to raw popularity, and $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$6 makes popularity differences diminish toward uniformity (Abbattista et al., 2024).

PPAC defines global popularity as

$p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$7

where $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$8 is the set of users who have interacted with item $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$9, and defines user similarity by Jaccard overlap,

$p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$0

For each user $p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$1, the top $p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$2 most similar users form $p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$3, and personal popularity becomes

$p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$4

This construction makes popularity user-item-specific even when the item is not globally popular (Ning et al., 2024).

In PP-Rec, popularity is not a simple count but a predicted time-aware score. News content gives $p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$5, recency gives $p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$6, and a gated content-specific aggregator computes

$p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$7

after which recent CTR is incorporated through

$p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$8

The final ranking score is then

$p_{u,i}=\frac{|\mathcal{S}_u^i|}{|\mathcal{S}_u|}$9

with $s=(1-\eta)\cdot s_m+\eta\cdot s_p$0 produced from the user embedding (Qi et al., 2021).

Evolving Personal Popularity further changes the object being scored. Rather than asking whether a specific item is popular for a user, it measures whether the user recently prefers popular items at all. Local item popularity is

$s=(1-\eta)\cdot s_m+\eta\cdot s_p$1

and the user’s evolving personal popularity is

$s=(1-\eta)\cdot s_m+\eta\cdot s_p$2

This turns personalised popularity into a dynamic property of the user rather than solely of the user-item pair (Tan et al., 20 May 2025).

3. Integration into ranking models

The most direct PPS integration strategy is logit adjustment. In the music setting, PPS is combined with the sequential model’s output scores before applying the activation function. For softmax models such as BERT4Rec, the PPS is converted to logits through

$s=(1-\eta)\cdot s_m+\eta\cdot s_p$3

and the model uses $s=(1-\eta)\cdot s_m+\eta\cdot s_p$4, where $s=(1-\eta)\cdot s_m+\eta\cdot s_p$5. For sigmoid models such as SASRec and gSASRec, the relation

$s=(1-\eta)\cdot s_m+\eta\cdot s_p$6

is used. At each sequence position, the popularity vector is computed only from observed history after removing the current position, so popularity counts are based only on historical interactions up to the current timestamp and thus avoid data leakage (Abbattista et al., 2024).

PP-Rec uses a different integration architecture. The personalized matching score $s=(1-\eta)\cdot s_m+\eta\cdot s_p$7 and the time-aware popularity score $s=(1-\eta)\cdot s_m+\eta\cdot s_p$8 are not simply summed with a fixed coefficient; instead, a user-specific gate $s=(1-\eta)\cdot s_m+\eta\cdot s_p$9 determines how much the ranker relies on popularity. The same model also introduces a popularity-aware user encoder designed to eliminate popularity bias in user behaviors. With contextual news representations $$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$0 and popularity embeddings $$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$1, the attention weight for each clicked news is

$$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$2

and the final user embedding is

$$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$3

The role of popularity here is therefore dual: it informs candidate ranking and also reweights the history used for interest modeling (Qi et al., 2021).

TimePop integrates personalised popularity through local neighborhoods and time decay. A candidate precursor is a user who previously interacted with at least one item that the target user also interacted with, and did so before the target user; a threshold $$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$4 derived from the average number of such earlier interactions determines which candidate precursors become actual Precursors. Recommendation scores are then sums over precursor histories with temporal decay, and if a user has no precursors the method falls back to global popularity (Anelli et al., 2018).

CausalEPP embeds evolving personal popularity into a causal conformity effect. The prediction formula is

$$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$5

where the conformity term is

$$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$6

The exponential term penalizes mismatch between the user’s recent preference for popularity and the item’s current popularity. During inference, moving averages and gradient-based forecasting are used to compute forecasted values $$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$7 and $$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$8, and the conformity effect is recalculated using those evolved values (Tan et al., 20 May 2025).

PPAC takes yet another route by combining learned and observed popularity signals. During training,

$$s_u^t=\frac{|\{(u,i):i\in\mathcal{D}_u^{t-w_1,t}\ \text{and}\ p_i^t>\hat{p}^t\}|}{|\mathcal{D}_u^{t-w_1,t}|}$$9

where $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$0, $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$1, and $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$2 predict the base score, personal popularity, and global popularity. At inference, the final score is

$$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$3

This formulation explicitly amplifies personal popularity while down-weighting global popularity through tunable coefficients $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$4 and $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$5 (Ning et al., 2024).

4. Empirical behavior and what PPS captures

The strongest quantitative evidence in the supplied material comes from sequential music recommendation. A Personalized Most Popular recommender based solely on user-specific popularity outperformed existing state-of-the-art models, and augmenting BERT4Rec, SASRec, and gSASRec with personalized popularity awareness produced statistically significant gains ranging from $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$6 to $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$7 in NDCG@5 and NDCG@10. On Yandex, for NDCG@100, Personalized Most Popular scored $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$8, BERT4Rec $$\mathrm{sPPS}_i=\sum_{j=1}^m \log(c_j^{(u)}[z_j^{(i)}]+\varepsilon)$$9, BERT4Rec + PPS $S=[s_1,\ldots,s_L]$0, SASRec $S=[s_1,\ldots,s_L]$1, SASRec + PPS $S=[s_1,\ldots,s_L]$2, gSASRec $S=[s_1,\ldots,s_L]$3, and gSASRec + PPS $S=[s_1,\ldots,s_L]$4. The improvements were tested with a paired $S=[s_1,\ldots,s_L]$5-test and Bonferroni correction (Abbattista et al., 2024).

PP-Rec reported that incorporating popularity can improve both accuracy and diversity in news recommendation. On MSN, PP-Rec achieved AUC $S=[s_1,\ldots,s_L]$6 versus the best listed baseline LSTUR at AUC $S=[s_1,\ldots,s_L]$7. The method also improved cold-start performance for users with $S=[s_1,\ldots,s_L]$8 clicked news and increased intra-list average distance and new topic ratio, indicating that popularity can act as a corrective signal when pure interest matching is too narrow (Qi et al., 2021).

PPAC provides evidence that personalized popularity and global popularity behave differently in practice. “MostPPop,” which recommends by personal popularity, consistently outperformed “MostPop,” which recommends by global popularity. Across MovieLens-1M, Gowalla, and Yelp2018, PPAC improved over the best prior debiasing baseline by up to $S=[s_1,\ldots,s_L]$9 in Recall@50 and $C=[c_1,\ldots,c_N]$0 in NDCG@50. The paper also reports that for approximately $C=[c_1,\ldots,c_N]$1 of users, more than $C=[c_1,\ldots,c_N]$2 out of their top-$C=[c_1,\ldots,c_N]$3 PP items were not among the globally top-$C=[c_1,\ldots,c_N]$4 popular items, directly illustrating that personalised popularity is not merely a rescaled version of global popularity (Ning et al., 2024).

Behavioral experiments on social ranking reinforce the same point from a different angle. When people chose between options characterized only by average review score and popularity, the best aggregate model was a relative logit,

$C=[c_1,\ldots,c_N]$5

which predicted $C=[c_1,\ldots,c_N]$6 of book choices and $C=[c_1,\ldots,c_N]$7 of movie choices. Training models on individual data improved predictive accuracy by over $C=[c_1,\ldots,c_N]$8 for books and $C=[c_1,\ldots,c_N]$9 for movies relative to aggregate models, showing substantial diversity in how users trade off quality and popularity (Analytis et al., 2017).

These results indicate that PPS often captures a strong regularity that more expressive models may otherwise miss: repeated consumption, local conformity, or user-specific preference for popular items. A plausible implication is that popularity should be treated as a structured user signal rather than as a nuisance variable to be globally penalized.

5. Bias, novelty, and debiasing

PPS does not automatically solve popularity bias. In music recommendation, item-level PPS explicitly models repetition, but that same mechanism can reinforce already-known content. When the item-level PPS weight increases, accuracy improves but novelty sharply decreases; on Last.fm, novelty drops from $c_i$0 at low $c_i$1 to $c_i$2 at $c_i$3. The paper characterizes this as a “you-get-what-you-know” regime (Mallamaci et al., 7 Aug 2025).

The sub-ID extension sPPS addresses that limitation by modeling repeated behavior at a finer granularity. In RecJPQ, each item is represented as a tuple of sub-identifiers,

$c_i$4

and the user-specific count for split $c_i$5 and sub-ID $c_i$6 is

$c_i$7

For candidate item $c_i$8, the sub-ID popularity score is

$c_i$9

followed by standardization. The final logits are

$i$0

At fixed NDCG@40 around $i$1, sPPS achieves novelty around $i$2, whereas PPS achieves around $i$3, a $i$4 improvement at the same accuracy. At novelty $i$5, sPPS improves NDCG@40 over PPS by $i$6 on Last.fm and $i$7 on Yandex (Mallamaci et al., 7 Aug 2025).

Other debiasing approaches are complementary rather than identical to PPS. PBiLoss adds a popularity-aware auxiliary loss,

$i$8

with Popular Positive and Popular Negative sampling, and evaluates fairness through PRU and PRI. On Epinions with LightGCN + PopNeg-FT, PRU decreased from $i$9 to $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$00 and PRI from $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$01 to $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$02, while F1@10, NDCG@10, and MAP@10 were maintained or slightly improved (Naeimi et al., 25 Jul 2025). PopSI, by contrast, uses multi-behavior tensor factorization and projects item factors onto the orthogonal complement of explicit popularity features,

$p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$03

achieving the highest or near-highest Recall@20 and NDCG@20 together with low PRI on the reported e-commerce datasets (Han et al., 2024).

The main misconception corrected by this literature is that personalised popularity and debiasing are the same intervention. PPS can improve personalization by embracing repeat preference, or reduce homogenization by replacing global popularity with local popularity, but some PPS variants also intensify memorization unless additional structure is imposed.

6. Evaluation, interpretation, and terminological issues

A useful evaluative lens is the personalization metric

$p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$04

which defines personalization as a weighting between performance on user-specific data and performance on a general global dataset. In this formulation, the global term acts as regularization against overfitting on small per-user datasets, and the break-even value

$p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$05

can be used to compare two approaches. Applied to PPS-style models, this makes clear that highly personalized popularity signals increase personal fit but can reduce global fit if they over-specialize (Brasher et al., 2018).

The literature therefore distinguishes several non-equivalent objects that are often conflated. Global popularity is the fraction of all users who interacted with an item. Personal popularity in PPAC is popularity among similar users. PPS in sequential music is the user’s own historical frequency of consuming an item. Time-aware popularity in PP-Rec is predicted from content, recency, and near real-time CTR. Evolving Personal Popularity is a dynamic user-level tendency to interact with popular items. TimePop uses popularity among temporal neighbors. These are related constructions, but they operationalize different causal stories and produce different failure modes.

The acronym itself is also overloaded. In multi-agent reinforcement learning, PPS can denote “Periodically Parameter Sharing,” with variants A-PPS, RS-PPS, and PP-PPS for QMIX; this use concerns partial neural network synchronization and reward-weighted aggregation, not popularity scoring (Zhang et al., 2024). Outside item recommendation, personalised popularity language can also refer to influence scores over social networks, such as the $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$06-score,

$p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$07

which measures the average fraction of posts of origin $p_P(j)=\frac{c_j}{\sum_{z=1}^{N} c_z}$08 on other users’ Walls and combines graph position with self-posting and re-posting activity (Giovanidis et al., 2021).

Taken together, the current literature presents Personalised Popularity Scores as a broad design principle for replacing homogeneous popularity heuristics with user-conditioned popularity signals. The decisive technical questions are not whether popularity should be used, but which popularity is being modeled, at what granularity, under what temporal constraints, and with what mechanism for balancing personalization, novelty, and debiasing.