HeteroIR: Heterogeneous Influence Recommendation

• HeteroIR is a heterogeneous influence-based recommendation framework that models both invitation and acceptance dynamics to capture direct and secondary spread.
• It employs a two-stage approach, using supervised CTR-like models for behavior estimation and a capacity-limited influence estimator (HeteroInf) for spread prediction.
• Empirical evaluations on Tencent and Twitter datasets demonstrate improved Spread@K, Recall@K, and NDCG@K metrics, validating its practical impact in invitation campaigns.

to=arxiv_search.search 大发快三如何_code: {"^^^^^^^^5query5 (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^^^^^", "^^^^^^^^5max_results5 5} to=arxiv_search.search 天天中彩票在哪_code: {"^^^^^^^^5query5 Influence Maximization in User Recommendation^^^^^^^^5\5 "^^^^^^^^5max_results5 ^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^} to=arxiv_search.search _日本一级特黄大片_code: {"^^^^^^^^5query5 maximization recommendation user recommendation arXiv ^^^^5max_results5query5max_results5\5^^^^ ^^^^5max_results5query5max_results55^^^^ secondary spread", "^^^^^^^^5max_results5 ^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^} HeteroIR, short for Heterogeneous Influence-based Recommendation, is a model-agnostic framework for invitation-based user recommendation that augments conventional user-to-user ranking with explicit modeling of information propagation. It was introduced together with HeteroIM in “Heterogeneous Influence Maximization in User Recommendation” (&&&^^^^5query5^^^^&&&) to address a setting in which an inviter recommends a limited set of friends, some invitees accept, and accepted invitees may later become inviters themselves, thereby creating secondary spread. The framework is designed to preserve interaction willingness while valuing dissemination potential, and it does so through a two-stage architecture that predicts inviting and accepting behavior, constructs a heterogeneous spread probability, estimates capacity-limited influence, and ranks candidate invitees by a profit score combining direct and secondary effects (&&&^^^^5query5^^^^&&&).

^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^. Problem setting and motivation

HeteroIR is defined for invitation campaigns in which a platform first selects inviters PRESERVED_PLACEHOLDER_^^^^5query5^^^^ and invitees PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^, then uses a recommendation algorithm to present each inviter PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^ with a limited list of candidate friends PRESERVED_PLACEHOLDER_^^^^5query5^^^^. During the event, PRESERVED_PLACEHOLDER_^^^^5\5^^^^ may send invitations to recommended $v$, and a recommendation is valid only if $u$ invites $v$ and $v$ accepts. The central complication is that invitees can later become inviters, so the value of recommending $v$ depends not only on whether PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^ and PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ interact, but also on whether PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5^^^^ can trigger further spread (&&&^^^^5query5^^^^&&&).

The framework is motivated by a gap between two established families of methods. Standard recommendation models, including CTR-style or link-prediction systems such as AutoInt, FinalNet, and EulerNet, optimize interaction willingness for a pair PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^, but do not account for the secondary propagation that an accepted invitee may create. Classical influence-maximization methods, including IMM, OPIM-C, and RR-OPIM+, instead seek seeds with high expected spread, but typically ignore personalized invitation and acceptance behavior between specific inviter-invitee pairs (&&&^^^^5query5^^^^&&&).

A key empirical observation in the Tencent game data is that local social connectivity is a poor proxy for actual spreading power. The average user has about PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5^^^^ friends, yet actual spread influence is PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation55^^^^ times smaller on average, and the Pearson correlation between friend count and spread influence is only PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^6. This observation, stated as Observation ^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ (Low spread influence), motivates a recommendation criterion that values realized propagation rather than raw neighborhood size (&&&^^^^5query5^^^^&&&). A plausible implication is that pairwise recommendation quality and diffusion capacity must be modeled jointly rather than treated as interchangeable proxies.

^^^^5max_results5^^^^. Formalization and the meaning of “heterogeneous”

HeteroIR operates on an attributed directed graph

PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^7

where PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^8 is the user set, PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^9 is the directed social graph, PRESERVED_PLACEHOLDER_^^^^5max_results5query5^^^^ is the invite probability matrix, and PRESERVED_PLACEHOLDER_^^^^5max_results5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ is the accept probability vector (&&&^^^^5query5^^^^&&&). For a pair PRESERVED_PLACEHOLDER_^^^^5max_results5max_results5^^^^,

PRESERVED_PLACEHOLDER_^^^^5max_results5query5^^^^

is the probability that user PRESERVED_PLACEHOLDER_^^^^5max_results5\5^^^^ invites PRESERVED_PLACEHOLDER_^^^^5max_results55^^^^, while

PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^6

is the probability that PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^7 accepts an invitation from any inviter (&&&^^^^5query5^^^^&&&).

The framework defines a heterogeneous spread probability

PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^8

This multiplicative form reflects a two-stage interaction process: an invitation must first be sent and then be accepted. In the paper’s terminology, the “heterogeneous” aspect is behavioral rather than structural: inviter and invitee roles are distinct, and edges are weighted by personalized, direction-sensitive spread probabilities instead of a single homogeneous propagation parameter (&&&^^^^5query5^^^^&&&).

The overall task is formalized as Recommendation with Influence Maximization (RIM): given PRESERVED_PLACEHOLDER_^^^^5max_results5^^^^9, produce capacity-limited recommendation lists that maintain interaction willingness and maximize spread coverage. For each inviter PRESERVED_PLACEHOLDER_^^^^5query5query5^^^^ and recommendation length PRESERVED_PLACEHOLDER_^^^^5query5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^, HeteroIR returns a ranked subset

PRESERVED_PLACEHOLDER_^^^^5query5max_results5^^^^

ordered by a profit score that integrates first-order interaction and second-order spread (&&&^^^^5query5^^^^&&&).

The paper also defines spread influence as the expected number of users influenced by a user PRESERVED_PLACEHOLDER_^^^^5query5query5^^^^. In HeteroIR, however, this quantity is not computed through full global diffusion simulation under arbitrary IC or LT cascades. Instead, it is approximated by a capacity-limited estimator, HeteroInf, that intentionally restricts effective propagation to a small number of high-probability neighbors (&&&^^^^5query5^^^^&&&).

^^^^5query5^^^^. Two-stage architecture and recommendation profit

HeteroIR is explicitly a two-stage framework. In the first stage, the system models behavior by estimating

PRESERVED_PLACEHOLDER_^^^^5query5\5^^^^

using standard supervised CTR-like models; in the reported implementation, EulerNet is used (&&&^^^^5query5^^^^&&&). In the second stage, these behavior estimates are transformed into spread-aware recommendation scores.

The central scoring function is the recommendation profit

PRESERVED_PLACEHOLDER_^^^^5query55^^^^

where PRESERVED_PLACEHOLDER_^^^^5query5^^^^6 is the HeteroInf estimate of user PRESERVED_PLACEHOLDER_^^^^5query5^^^^7’s heterogeneous influence (&&&^^^^5query5^^^^&&&). The two additive components are named ^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^st-IF and ^^^^5max_results5^^^^nd-IF. The first term, PRESERVED_PLACEHOLDER_^^^^5query5^^^^8, is the direct profit that the invitation from PRESERVED_PLACEHOLDER_^^^^5query5^^^^9 to PRESERVED_PLACEHOLDER_^^^^5\5query5^^^^ is realized. The second term, PRESERVED_PLACEHOLDER_^^^^5\5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^, scales the downstream influence of PRESERVED_PLACEHOLDER_^^^^5\5max_results5^^^^ by the probability that the initial interaction occurs and by PRESERVED_PLACEHOLDER_^^^^5\5query5^^^^, which encodes the inviter’s own acceptance propensity when acting as an invitee in other contexts (&&&^^^^5query5^^^^&&&).

This additive decomposition is the framework’s core synthesis. It preserves the local pairwise semantics of recommendation while introducing an explicit estimate of secondary spread. The paper characterizes HeteroIR as model-agnostic because the learned behavior components can be supplied by standard recommenders, while the final ranking rule is deterministic once PRESERVED_PLACEHOLDER_^^^^5\5\5^^^^, PRESERVED_PLACEHOLDER_^^^^5\55^^^^, and PRESERVED_PLACEHOLDER_^^^^5\5^^^^6 are available (&&&^^^^5query5^^^^&&&). It further states that HeteroIR itself has no additional trainable parameters beyond those used in the behavior models.

An important contrast is with HeteroIM. HeteroIR does not use reverse reachable sets or greedy seed selection. Instead, it assigns a pointwise score to each inviter-invitee pair and ranks candidates directly. This design keeps the framework simple and scalable while still injecting an influence-aware objective into recommendation (&&&^^^^5query5^^^^&&&).

^^^^5\5^^^^. HeteroInf and algorithmic procedure

The spread term PRESERVED_PLACEHOLDER_^^^^5\5^^^^7 is computed by HeteroInf, a capacity-limited influence estimator introduced to reflect the empirical finding that real spreading capacity is much smaller than nominal friend count (&&&^^^^5query5^^^^&&&). For each user PRESERVED_PLACEHOLDER_^^^^5\5^^^^8, let PRESERVED_PLACEHOLDER_^^^^5\5^^^^9 denote the out-neighbors and let $v$^^^^5query5^^^^ be the subset of size $v$^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ with the largest spread probabilities $v$^^^^5max_results5^^^^. HeteroInf then defines

$v$^^^^5query5^^^^

This is a single-step influence measure rather than a multi-hop cascade simulation, and the global interaction capacity $v$^^^^5\5^^^^ is chosen by grid search; in deployment, the paper reports $v$5, matching the platform’s observed average spread capacity (&&&^^^^5query5^^^^&&&).

Operationally, HeteroIR proceeds in five steps. First, historical logs are used to train an invitation model for $v$6 and an acceptance model for $v$7. Second, the system computes the heterogeneous spread probability $v$8 for candidate edges. Third, for each user $v$9, it selects the top-$u$^^^^5query5^^^^ outgoing neighbors by $u$^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ and aggregates them to obtain $u$^^^^5max_results5^^^^. Fourth, it evaluates

$u$^^^^5query5^^^^

for each inviter $u$^^^^5\5^^^^ and candidate invitee $u$5. Fifth, it sorts candidates by $u$6 and returns the top $u$7 per inviter (&&&^^^^5query5^^^^&&&).

The paper gives the complexity of top-$u$8 selection as $u$9 per node when the average out-degree is $v$^^^^5query5^^^^, for a total of $v$^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ to compute HeteroInf over the graph (&&&^^^^5query5^^^^&&&). After model inference, the main additional costs are top-$v$^^^^5max_results5^^^^ aggregation and per-user sorting, which is one reason the framework is described as easy to integrate into an existing ranking stack.

The framework’s notion of spread profit can be written equivalently as

$v$^^^^5query5^^^^

The first term represents direct realized interaction; the second is a linear approximation to secondary spread. The paper explicitly notes that HeteroIR does not use RR sets or Monte Carlo simulation; those belong to HeteroIM rather than HeteroIR (&&&^^^^5query5^^^^&&&).

5. Training, evaluation, and empirical results

The reported implementation trains its behavior models on two Tencent datasets derived from game logs: an Exposure-Invitation dataset for $v$^^^^5\5^^^^, in which $v$5 if $v$6 invited $v$7 at time $v$8, and an Acceptance dataset for $v$9, in which $v$^^^^5query5^^^^ if $v$^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ accepted an invitation from any inviter. TXG-A is split into train, validation, and test by an $v$^^^^5max_results5^^^^ ratio, while TXG-B and TXG-C are holdout evaluation sets (&&&^^^^5query5^^^^&&&). For Twitter, mention events are treated as spread events, and DeepWalk embeddings together with other features are fed into EulerNet to predict spread probability directly (&&&^^^^5query5^^^^&&&).

The experimental datasets are large. TXG-A contains $v$^^^^5query5^^^^M nodes, $v$^^^^5\5^^^^M edges, and $v$5M spread events; TXG-B has $v$6M nodes, $v$7M edges, and $v$8M spreads; TXG-C has $v$9M nodes, $v$^^^^5query5^^^^M edges, and $v$^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^M spreads. The Twitter dataset has $v$^^^^5max_results5^^^^M nodes, $v$^^^^5query5^^^^M edges, and $v$^^^^5\5^^^^M spread events (&&&^^^^5query5^^^^&&&).

Evaluation uses both recommendation and spread metrics. The spread metrics are Spread@K, defined as total deduplicated spread coverage from direct spreads and secondary spreads, and NSpread@K,

$v$5

where $v$6 is the maximal achievable spread under brute-force selection of $v$7 neighbors per user (&&&^^^^5query5^^^^&&&). Recommendation quality is assessed by Recall@K and NDCG@K. In Tencent data, a correct recommendation requires both invitation and acceptance; on Twitter, a mention from $v$8 to $v$9 is treated as a valid interaction (&&&^^^^5query5^^^^&&&).

Against recommender baselines such as PPR, AutoInt, FinalNet, and EulerNet, and against influence-related baselines such as degree centrality, coreness, Windex, Monte-Carlo influence, LR influence, DeepInf, and TOPSIS, HeteroIR consistently improves both spread-aware and recommendation metrics (&&&^^^^5query5^^^^&&&). On TXG-B at PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5query5^^^^, the best recommender baseline, EulerNet, attains NSpread@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^, Recall@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5max_results5^^^^, and NDCG@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5query5^^^^, whereas HeteroIR reaches NSpread@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5\5^^^^, Recall@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query55^^^^, and NDCG@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^6 (&&&^^^^5query5^^^^&&&). On Twitter at PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^7, EulerNet yields NSpread@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^8, Recall@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^9, and NDCG@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^, while HeteroIR yields PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^, PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5^^^^, and PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^, respectively (&&&^^^^5query5^^^^&&&). The paper reports that the marked improvements for HeteroIR and HeteroIM have PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5^^^^-value PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation55^^^^.

The ablation results clarify the role of the two score components. On Twitter, removing ^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^st-IF reduces Recall@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ from PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^6 to PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^7, NDCG@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ from PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^8 to PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^9, and NSpread@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ from PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5query5^^^^ to PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^. Removing ^^^^5max_results5^^^^nd-IF reduces NSpread@^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ from PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5max_results5^^^^ to PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5query5^^^^ and NSpread@^^^^5max_results5^^^^ from PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5\5^^^^ to PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results55^^^^ (&&&^^^^5query5^^^^&&&). This suggests that direct interaction willingness is indispensable for recommendation quality, while secondary influence is the principal source of spread improvement.

The influence-estimation comparison further supports HeteroInf. The paper states that HeteroInf achieves the highest Hit@K at finding truly influential spreaders on TXG-B and TXG-C, especially for small PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5^^^^6, and that plugging HeteroInf into the HeteroIR score yields better NSpread@K and NDCG@K than using Monte-Carlo influence or linear-regression influence (&&&^^^^5query5^^^^&&&).

6. Deployment, limitations, and scope of the term

HeteroIR and HeteroIM were deployed in two large Tencent FPS-game propagation events, X^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ and X^^^^5max_results5^^^^, with treatment groups of PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5^^^^7M and PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5^^^^8M users, respectively (&&&^^^^5query5^^^^&&&). The deployment used EulerNet for the base probability estimates, set the interaction capacity to PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5max_results5^^^^9, and partitioned users into communities following Saveski et al. to randomize treatment while controlling network effects (&&&^^^^5query5^^^^&&&). Online evaluation used three metrics: Secondary Invite Rate (Sec-IR), the fraction of invitees who themselves send invitations; Secondary Invite Times (Sec-IT), the average number of secondary invitations per invitee; and Reach Retain Rate (RRR), the fraction of invitees who log in the next day (&&&^^^^5query5^^^^&&&).

In event X^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^, the baseline “Intimacy” achieved Sec-IR PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5query5^^^^, Sec-IT PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^, and RRR PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5max_results5^^^^, whereas HeteroIR achieved Sec-IR PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5query5^^^^, Sec-IT PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5\5^^^^, and RRR PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query55^^^^ (&&&^^^^5query5^^^^&&&). In event X^^^^5max_results5^^^^, the baseline achieved Sec-IR PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^6, Sec-IT PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^7, and RRR PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^8, while HeteroIR achieved Sec-IR PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5query5^^^^9, Sec-IT PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5query5^^^^, and RRR PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5^^^^ (&&&^^^^5query5^^^^&&&). The abstract summarizes these results as an online A/B-test improvement of about PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5max_results5^^^^ for HeteroIR and PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5query5^^^^ for HeteroIM (&&&^^^^5query5^^^^&&&).

The framework also has clear limitations. HeteroInf is single-step and capacity-limited, so it does not explicitly model multi-hop IC-style cascades. The propagation model assumes

PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5\5^^^^

and treats PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\55^^^^ as independent of inviter identity. The interaction capacity PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5^^^^6 is a single global parameter rather than a personalized PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5^^^^7. HeteroIR is model-agnostic but not end-to-end: invite and accept models are trained separately from the spread-aware ranking rule, and the optimization objective of the learned models is not NSpread@K itself (&&&^^^^5query5^^^^&&&). The paper identifies personalized interaction capacity and richer spread-aware learning objectives as directions for future work.

A common misconception is that “HeteroIR” is a universally standardized term. In fact, the label is polysemous across arXiv. In recommendation, it denotes Heterogeneous Influence-based Recommendation (&&&^^^^5query5^^^^&&&). In wireless communications, closely related terminology appears in the form of a heterogeneous intelligent reflecting surface (HE-IRS), also described as HeteroIR in context (&&&^^^^5query5^^^^9&&&). In oxide spintronics and condensed-matter literature, “HeteroIR” is also used as a shorthand for iridate-based heterostructures (&&&^^^^5\5query5^^^^&&&). Within the recommendation literature, however, HeteroIR specifically refers to the spread-aware invitation-recommendation framework built around the score

PRESERVED_PLACEHOLDER_^^^^5HeteroIR (Hou et al., 19 Aug 2025) Heterogeneous Influence-based Recommendation5\5^^^^8

its HeteroInf influence estimator, and its objective of reconciling interaction willingness with spread coverage (&&&^^^^5query5^^^^&&&).