---
title: 'RVRec: Plug-and-Play Embedding Enhancement'
url: https://www.emergentmind.com/topics/rvrec
type: topic
---

# RVRec: Plug-and-Play Embedding Enhancement

RVRec is a plug-and-play, model-agnostic embedding enhancement approach for explainable recommendation that augments an existing recommender rather than replacing it. Introduced in "A Plug-and-play Model-agnostic Embedding Enhancement Approach for Explainable Recommendation" [2509.03130], it is designed to improve both personalization and explainability by addressing two deficiencies in embedding-based recommendation: suboptimal representation of user preference under sparse implicit feedback, and low-value interactions used for explanation. Its two principal components are Probability-based Embedding Optimization (PEO), which models user and item embeddings as distributions and optimizes them with a contrastive loss based on negative 2-Wasserstein distance, and Multivariate Shapley Values Reweighting (MSVR), which evaluates the value of interactions and interaction coalitions and uses the most valuable coalition as explanation.

## 1. Problem setting and research gap

RVRec is motivated by a recurrent limitation in multimedia and explainable recommender systems: although additional information such as interactions, contexts, popularity, and prototype embeddings can enrich semantics, the resulting embeddings may still be insufficiently representative of the underlying preference distribution, and the explanations derived from those embeddings may have low value or be unstable [2509.03130]. The paper identifies two specific issues.

First, user and item embeddings learned from sparse implicit feedback are uncertain. A single deterministic vector can be a poor summary of a user or item because observational data are noisy, stochastic, and sparse. Existing distributional methods attempt to address this by modeling embeddings as Gaussian distributions, but the paper states that this often creates fuzzy decision boundaries and is difficult to integrate into arbitrary recommenders.

Second, most recommenders fit the entire interaction set uniformly even though not all historical interactions contribute equally to future recommendation. Existing explainable recommenders often select a single supporting item or compute ordinary single-feature Shapley values, which misses the combined effect of item sets. RVRec is built around the claim that the coalition of interactions can be more informative than any single interaction.

In this formulation, explainability is not treated as a purely post-hoc layer. The value of interactions is incorporated into representation learning itself. This suggests a view of explainable recommendation in which explanation quality and ranking quality are coupled through the geometry and weighting of embeddings rather than optimized separately.

## 2. Framework design and integration

RVRec, expanded in the paper as “representation and value enhanced recommendation,” is presented as a wrapper-style enhancement placed before the embedding interaction and prediction step of a backbone recommender [2509.03130]. Its training objective is

$$
\mathcal{L} = \mathcal{L}_{REC} + \lambda_1 \mathcal{L}_{PEO} + \lambda_2 \mathcal{L}_{MS},
$$

where $\mathcal{L}_{REC}$ is the original loss of the backbone recommender, $\mathcal{L}_{PEO}$ is the probability-based embedding optimization loss, and $\mathcal{L}_{MS}$ is the multivariate Shapley-values reweighting loss.

The architecture contains two main modules.

- **PEO**: a probability-based embedding optimization method that uses a contrastive loss based on negative 2-Wasserstein distance to improve the representativeness of user and item embeddings.
- **MSVR**: a multivariate Shapley values reweighting method that evaluates the value of interactions and interaction coalitions, identifies the most valuable coalition, and reweights embeddings accordingly.

The paper emphasizes that RVRec is not limited to MF-based recommenders. It can be attached to any recommender that produces user and item embeddings for similarity scoring, and the reported integrations are MF, RBMF, ACF, ProtoMF, and TransGNN. In this sense, the “plug-and-play” designation refers to the fact that RVRec does not require redesigning the entire recommender and can operate as an enhancement module on top of heterogeneous embedding-producing backbones.

This design also clarifies what RVRec is not. It is not introduced as a new standalone ranking architecture, and its contribution does not lie in a new scoring function for a specific backbone. Rather, it modifies the statistical form of embeddings and the value attribution of interactions before those embeddings are consumed by the downstream recommender.

## 3. Probability-based Embedding Optimization

PEO assumes that a user or item embedding is not a single point but has uncertainty in latent space [2509.03130]. For each user $\mathbf{u}_i$ and item $\mathbf{v}_j$, RVRec learns a mean vector and a variance vector, treated as parameters of a Gaussian-like distribution:

$$
N(\mu_{u_i}, \sigma^2_{u_i}), \quad N(\mu_{v_j}, \sigma^2_{v_j}).
$$

Given an input embedding $\mathbf{u}_i$, RVRec first applies a linear layer and ReLU:

$$
\mathbf{u}_i^\ast = \mathrm{ReLU}(\mathbf{W}_{\theta_1}\mathbf{u}_i).
$$

It then computes the mean and variance as

$$
\mu_{u_i} = \mathbf{u}_i + \mathbf{W}_{\theta_2}\mathbf{u}_i^\ast,
$$

$$
\sigma^2_{u_i} = \mathbf{W}_{\theta_3}\mathbf{u}_i^\ast.
$$

The residual form in the mean branch preserves the original embedding as an inductive bias while allowing refinement. The same process is applied to items.

To compare user and item distributions, RVRec uses the negative 2-Wasserstein distance:

$$
d(\mathbf{u}_i, \mathbf{v}_j) = -\left( \lVert \mu_{u_i} - \mu_{v_j} \rVert_2^2 + \mathrm{tr}\left( \Sigma_{u_i} + \Sigma_{v_j} - 2(\Sigma_{u_i}^{1/2}\Sigma_{v_j}\Sigma_{u_i}^{1/2})^{1/2} \right) \right).
$$

Because the covariance matrices are diagonal, the paper simplifies this to

$$
d(\mathbf{u}_i, \mathbf{v}_j) = -\left( \lVert \mu_{u_i} - \mu_{v_j} \rVert_2^2 + \lVert \sigma_{u_i} - \sigma_{v_j} \rVert_2^2 \right).
$$

The use of the negative distance ensures that larger similarity corresponds to a larger score. The paper states a preference for Wasserstein distance over KL divergence because it satisfies the triangle inequality and avoids vanishing gradients.

PEO is trained with a BPR-style contrastive objective:

$$
\mathcal{L}_{PEO} = \sum_{\substack{\mathcal{R}(i,j)=1\\ \mathcal{R}(i,k)=0}} \ln \left( \mathrm{Sigmoid}\big( d(\mathbf{u}_i,\mathbf{v}_j) - d(\mathbf{u}_i,\mathbf{v}_k) \big) \right).
$$

For a positive pair $(i,j)$ and a negative pair $(i,k)$, the model learns $d(\mathbf{u}_i,\mathbf{v}_j) > d(\mathbf{u}_i,\mathbf{v}_k)$. The intended effect is a latent space in which representative positives are brought closer, negatives are separated, and uncertainty remains explicit. The paper’s ablation further reports that adding the residual inductive bias in the mean branch improves all metrics for both MF and ProtoMF.

## 4. Multivariate Shapley Values Reweighting

MSVR is introduced because ordinary Shapley values evaluate interactions independently, whereas recommendation explanations often depend on the joint effect of item groups [2509.03130]. RVRec therefore defines both a single-interaction value and a coalition value.

For a single item $i$, the paper defines the Shapley value as

$$
\phi(i) = \nu(i) = \frac{(|R|-|i|-1)!\,|i|!}{|R|!} \left[ v(R) - v(R/i) \right],
$$

where $R$ denotes the interaction set and $v(\cdot)$ is the value function measuring recommendation effect. In the recommender setting, $v(\cdot)$ is based on how much the recommendation score changes when interactions are removed, using the inner product between the user embedding and item embedding relative to the ground-truth interaction indicator.

For a coalition $c_i$, the paper defines

$$
\phi(c_i) = \nu(c_i)\times \frac{|c_i|}{2} + \sum_{j \in c_i} \nu(j),
$$

with

$$
\nu(c_i) = \frac{(|R|-|c_i|-1)!\,|c_i|!}{|R|!} \left[ v(R) - v(R/c_i) \right].
$$

This decomposes coalition value into a coalition-level effect, measured by removing the whole group, and a member-wise effect, measured by the sum of individual Shapley values inside the coalition. The paper interprets the coalition term as capturing the joint influence of items that ordinary single-item Shapley misses.

Because exhaustive coalition enumeration is too expensive, RVRec constructs coalitions probabilistically. For adjacent historical items, it computes a coalition probability using cosine similarity:

$$
p_k = \cos(\mathbf{v}_k,\mathbf{v}_{k+1}).
$$

It then samples a Bernoulli variable

$$
g_k \sim \mathcal{B}(p_k), \quad g_k \in \{0,1\},
$$

and forms a partition

$$
\Omega_g = \{g_1 c_1, g_2 c_2, \dots, g_{|R|-1} c_{|R|-1}\}.
$$

The multivariate Shapley objective maximizes the expected total value of the coalitions in the partition:

$$
\mathcal{L}_{U\text{-}MS} = -\mathbb{E}_{g \sim \mathcal{B}(p)} \sum_{c_k^* \in \Omega_g} \phi(c_k^*).
$$

An item-side version $\mathcal{L}_{I\text{-}MS}$ is defined analogously, and the total loss is

$$
\mathcal{L}_{MS} = \mathcal{L}_{U\text{-}MS} + \mathcal{L}_{I\text{-}MS}.
$$

The explanation is obtained by selecting the coalition with maximum Shapley value,

$$
c_k^* = \arg\max_{c_k^* \in \Omega_g} \phi(c_k^*),
$$

and using the average of the embeddings in that coalition to enhance the target embedding:

$$
\mathbf{u}_i^{c} = \mathrm{AGG}_{\mathrm{average} \left( \mu_{u_i}, \{\mu_{v_j} \mid j \in c_k^*\} \right).
$$

The significance of this module lies in its treatment of explanation as a coalition-selection problem rather than a single-supporting-item problem. A plausible implication is that RVRec’s explanation mechanism is intended to align more closely with clustered preference patterns, where several past interactions jointly support the recommendation.

## 5. Experimental protocol and reported performance

The empirical study uses three real-world implicit-feedback datasets, binarized for top-$N$ recommendation, with k-core filtering and randomized training data to remove sequential information [2509.03130].

| Dataset | Users / Items | Interactions / Sparsity |
|---|---:|---:|
| ML-1M | 6,034 / 3,125 | 574,376 / 96.95% |
| AMAZON | 6,950 / 14,494 | 132,209 / 99.87% |
| LFM2B-1M | 3,555 / 77,985 | 877,365 / 99.68% |

The reported k-core settings are $k=5$ for ML-1M and AMAZON, and $k=10$ for LFM2B-1M. RVRec is plugged into MF, RBMF, ACF, ProtoMF, and TransGNN. Recommendation quality is evaluated with HR@K and NDCG@K. Explainability is evaluated with PN, PS, and FNS, and later analysis adds ERS-HE and EQS-LE. For explanation comparison, the baselines are CCR and Shapley + backbone recommenders. For probability modeling ablation, the comparator is DDN.

Across all datasets and backbones, RVRec is reported to improve performance consistently. Representative gains include the following.

- **MF + RVRec**: ML-1M HR@5 +8.84%, NDCG@5 +13.55%; AMAZON HR@5 +13.58%, NDCG@5 +8.11%; LFM2B-1M HR@5 +4.32%, NDCG@5 +7.53%.
- **ProtoMF + RVRec**: ML-1M HR@5 +8.81%, NDCG@5 +8.62%; AMAZON HR@5 +10.15%, NDCG@5 +11.86%; LFM2B-1M HR@5 +3.79%, NDCG@5 +2.36%.
- **TransGNN + RVRec**: ML-1M HR@5 +15.41%, NDCG@5 +28.73%; AMAZON HR@5 +4.20%, NDCG@5 +7.17%; LFM2B-1M HR@5 +17.16%, NDCG@5 +22.84%.

The paper emphasizes that RVRec is especially effective on sparse datasets, attributing this to better uncertainty modeling and value-aware reweighting under sparse supervision.

The explainability results follow the same pattern. The paper reports that better recommendation accuracy tends to correlate with better explanation quality, that RVRec outperforms both CCR and Shapley-based baselines, and that multivariate coalition explanations are more persuasive than single-item explanations. In human and LLM evaluation, ProtoMF+RVRec reaches about 85% reasonable explanations on ERS-HE, compared with 80% for CCR and 76% for ProtoMF+Shapley. On EQS-LE, ProtoMF+RVRec attains around 4.16 with GPT-3.5 and 4.27 with DeepSeek, higher than the two baselines.

## 6. Ablations, interpretation, and limitations

The ablation studies are organized around the two RVRec modules and the wrapper objective [2509.03130]. For PEO, the paper compares the residual mean branch,

$$
\mu_{u_i} = \mathbf{u}_i + \mathbf{W}_{\theta_2}\mathbf{u}_i^\ast,
$$

with the version without bias,

$$
\mu_{u_i} = \mathbf{W}_{\theta_2}\mathbf{u}_i^\ast.
$$

Adding the bias improves all metrics for both MF and ProtoMF, which the paper interprets as evidence that preserving the original embedding while refining it is beneficial. PEO is also compared to DDN under a cold-start setting, where it performs strongly while remaining easier to integrate than full distribution-embedding recommenders.

For MSVR, the paper compares ProtoMF, ProtoMF + U-MSVR, ProtoMF + I-MSVR, ProtoMF + UI-MSVR, ProtoMF + PEO, and ProtoMF + RVRec. The reported result is that both user-side and item-side multivariate Shapley modules help, using both sides together is better than using either alone, and combining MSVR with PEO gives the best overall performance. The paper explicitly interprets this as evidence that explanation and value modeling improve the learned representations rather than functioning merely as post-hoc interpretability.

Hyperparameter sensitivity analyses vary $\lambda_1$ and $\lambda_2$ and report that increasing each from very small values improves performance, confirming the value of both PEO and MSVR. A t-SNE visualization on ML-1M with TransGNN shows that TransGNN+RVRec yields more balanced and uniformly distributed user/item embeddings than TransGNN alone. A movie recommendation case study for a specific user reports that ProtoMF+RVRec gives the most coherent recommendation and explanation, while ProtoMF+Shapley and CCR are weaker because they rely more heavily on single-item explanation.

The paper also implies several limitations. Coalition construction is simplified through adjacent-item pairing and Bernoulli sampling, so richer coalition discovery mechanisms might capture more complex relationships. The explanation mechanism still depends on embedding similarity and interaction history, so highly idiosyncratic user preferences may remain difficult to model. It also notes that the assumption that higher coalition value corresponds to better explanation may not hold perfectly for every user. Potential future work suggested in the paper includes more principled coalition discovery, richer interaction modeling beyond adjacent historical items, extension to other recommendation paradigms such as sequential or cross-domain recommendation, and more robust user-centric evaluation of explanation faithfulness.

Source: https://www.emergentmind.com/topics/rvrec