Synergy Weighted Graph Convolutional Network (SWGCN)

• SWGCN is a graph convolutional network designed for multi-behavior recommendation by dynamically weighting user-item interactions.
• It integrates a Target Preference Weigher with a Synergy Alignment Task to refine auxiliary signals into accurate target predictions.
• Empirical results on Taobao, IJCAI, and Beibei datasets show significant improvements in HR and NDCG metrics with robust generalization.

The Synergy Weighted Graph Convolutional Network (SWGCN) is a purpose-built architecture for multi-behavior recommendation scenarios, designed to integrate and leverage diverse user activity traces—such as viewing, adding to cart, and purchasing—in order to improve the prediction of primary user conversions. SWGCN introduces dynamically adaptive edge weighting and explicit cross-behavioral alignment, combining a differentiable Target Preference Weigher (TPW) with a novel Synergy Alignment Task (SAT). When evaluated on three major e-commerce datasets (Taobao, IJCAI, Beibei), SWGCN demonstrates substantial improvements in canonical recommendation metrics, highlighting its generalizability and robustness in multi-behavior environments (Chen et al., 31 Jan 2026).

1. Problem Formulation and Model Architecture

SWGCN addresses the challenge that not all user–item interactions, even within the same behavioral class, are equally informative for recommendation. Classical multi-behavior methods often treat interactions with a one-hot scheme or fail to weight cross-behavioral signals according to their true impact on target behaviors. SWGCN overcomes these limitations via:

• Target Preference Weigher (TPW): Assigns adaptive, learned importance to each user–item interaction within each behavioral adjacency matrix, reflecting heterogeneous interaction intensities.
• Synergy Alignment Task (SAT): Guides the optimization toward maximizing the synergy between auxiliary signals (e.g., browsing) and target behaviors (e.g., purchases), using an Auxiliary Preference Valuator.

The SWGCN input comprises $R$ bipartite adjacency matrices ($\{\mathcal{A}_1, ..., \mathcal{A}_R\}$), partitioned by behavior type, with the $R$th denoting the target. User and item embeddings for each behavior are initialized independently, then updated through behavior-specific weighted GCN propagation. The per-behavior representations are fused via self-attention to yield unified embeddings, from which purchase-scores are computed.

2. Target Preference Weigher (TPW)

TPW replaces static interaction encoding and enables the model to differentiate strong from weak behavioral signals:

For each user $u$, item $i$, and behavior $r$: $$w_{u,i;r} = \frac{\exp\left(\mathrm{ELU}\left(\lvert \mathbf{e}_{u,r}^{(0)} - \mathbf{e}_{i,r}^{(0)} \rvert \,\beta_r^\top \right)\right)}{\sum_{j \in \mathcal{N}_r(u)} \exp\left(\mathrm{ELU}\left(\lvert \mathbf{e}_{u,r}^{(0)} - \mathbf{e}_{j,r}^{(0)} \rvert\, \beta_r^\top \right)\right)}$$ where $$\mathbf{e}_{u,r}^{(0)}, \mathbf{e}_{i,r}^{(0)} \in \mathbb{R}^d$$ are the initial user and item embeddings for behavior $r$, $\beta_r \in \mathbb{R}^d$ is trainable, and $\mathrm{ELU}$ denotes Exponential Linear Unit. This constructs a normalized, sample-specific edge-weighting, allowing strong auxiliary behaviors to more heavily inform the propagation.

In integration, the adjacency for each behavioral graph is: $$\widetilde{\mathcal{A}_r} = \begin{pmatrix} \lambda_s I_{N_u} & \mathcal{W}_r \odot \mathcal{A}_r \ (\mathcal{W}_r \odot \mathcal{A}_r)^\top & \lambda_s I_{N_i} \end{pmatrix}$$ with a self-loop weighting $\lambda_s$.

The layer update is: $$\mathcal{E}_r^{(l)} = \widetilde{D}_r^{-1/2}\,\widetilde{\mathcal{A}_r}\,\widetilde{D}_r^{-1/2}\,\mathcal{E}_r^{(l-1)}$$ where normalization is degree-based as in traditional GCNs.

3. Synergy Alignment Task (SAT)

SAT operationalizes inter-behavioral synergistic alignment:

• The Auxiliary Preference Valuator computes a preference signal between $(u, i)$ for each auxiliary behavior $r < R$:

$$\widetilde{w}_{u,i;r} = \|\mathbf{e}_{u,r}^{(0)} - \mathbf{e}_{i,r}^{(0)}\|_2^2$$

• The Synergy Alignment Loss enforces agreement between TPW weights and these auxiliary-derived signals:

$$L_{SAT} = \frac{1}{R} \sum_{r=1}^R \left[ \frac{1}{N_r} \sum_{(u,i) \in \mathcal{E}_r} (W_{u,i;r} - \widetilde{W}_{u,i;r})^2 \right] + \frac{\gamma_1}{R} \sum_{r=1}^R \|\widetilde{\mathcal{W}_r}\|_2^2$$

By penalizing discrepancies, SAT prioritizes auxiliary signals that more closely mirror the target behavior, effectively down-weighting spurious interactions.

A plausible implication is that items active in both auxiliary and target behaviors yield higher alignment and are favored for recommendation, naturally denoising secondary behaviors.

4. Layer-wise Propagation and Embedding Fusion

Each layer of the GCN operates in accordance with a LightGCN-style architecture—eschewing additional weight matrices or nonlinear activation except within TPW. For user $u$ in behavior $r$: $$\mathbf{e}_{u,r}^{(l)} = \frac{\lambda_s}{\sqrt{d_{u,r}}} \mathbf{e}_{u,r}^{(l-1)} + \sum_{j \in \mathcal{N}_r(u)} \frac{w_{u,j;r}}{\sqrt{d_{u,r}d_{j,r}}} \mathbf{e}_{j,r}^{(l-1)}$$ Self-attention is employed to fuse the behavior-specific embeddings $\{\mathcal{E}_r^{(L)}\}$, resulting in a unified representation $\mathcal{E}^*$ used for final purchase prediction.

5. Training, Optimization, and Implementation

The objective combines both the SAT loss and a BPR-style pairwise ranking loss: $$\mathrm{Loss} = \lambda_a L_{SAT} + (1-\lambda_a) L_{BPR}$$

$$L_{BPR} = \sum_{(u,i,j)\in O} -\ln\sigma(\tilde y_{u,i} - \tilde y_{u,j}) + \gamma_2 \|\Theta\|_2^2$$

with $\sigma$ the sigmoid function. Adam is used as the optimizer (learning rate $1\times 10^{-3}$); regularization coefficients are set to $10^{-5}$. Key implementation choices include embedding dimension $d=32$, three graph convolution layers, batch size 2048, and four negative samples per positive. Self-loop and SAT balancing weights ($\lambda_s$, $\lambda_a$) are dataset-tuned within $[0.2, 1.0]$.

Dropout is introduced only on the messages ($\mathcal{E}_r^{(l)}$) with a rate of 0.2, and implicit node dropout is induced via low TPW scores. Early stopping is based on HR@10 metric with a patience of 50 epochs.

6. Empirical Results and Comparative Analysis

SWGCN demonstrates pronounced improvements on benchmark datasets:

Dataset	Hit Ratio (HR)	NDCG	Relative Gain vs Baseline
Taobao	112.49%	156.36%	MBGCN/GHCF
IJCAI	+2.77%	+3.77%	Strongest baseline
Beibei	+3.02%	+0.75%	Strongest baseline

Ablation studies reveal key algorithmic dependencies:

• Removing SAT reduces HR and NDCG by 24.70% and 32.79% (Taobao), highlighting its role in cross-behavior alignment.
• Removing TPW results in greater drops (–38.53% HR, –48.23% NDCG on Taobao), demonstrating the necessity of dynamic edge-weighting.

This suggests TPW is the principal source of model expressiveness, whereas SAT is critical for leveraging auxiliary behavior in noisy settings.

7. Limitations and Prospects for Extension

SWGCN is constrained by several factors:

• Synergy modeling is pairwise; interactions involving three or more behaviors simultaneously are not fully captured.
• Validation is performed exclusively on e-commerce logs. Real-world multi-behavior datasets may include clickstreams, social interaction traces, or multi-modal signals, potentially limiting the model’s immediate applicability without extension.

Future enhancements proposed include:

• Extending SAT to model higher-order behavior combinations.
• Incorporating heterogeneous, multi-modal, or temporally structured behavioral streams.
• Investigating adaptive behavior selection or curriculum learning mechanisms to address sparsity and noise in extremely large-scale or unbalanced datasets (Chen et al., 31 Jan 2026).

SWGCN is available as open-source software at https://github.com/FangdChen/SWGCN, providing a reference implementation for replication and further research.