Dual Relation Fusion Network (DRFN)

• The paper introduces DRFN, a neural framework that fuses long-term static relations with short-term market dynamics to improve stock prediction.
• It employs cross-attention and recurrent fusion modules to integrate multimodal inputs and capture both persistent and transient market trends.
• Empirical evaluations show DRFN achieves lower RMSE and MAE with higher Pearson correlations in forecasting next-day returns on US and Chinese markets.

A Dual Relation Fusion Network (DRFN) is a neural framework designed to jointly model heterogeneous relational structures by recursively integrating static (long-term) and dynamic (short-term) relations. In financial prediction, DRFN leverages temporal multimodal inputs—such as quantitative indicators and qualitative news—alongside prior knowledge of business connections to forecast stock returns with enhanced sensitivity to co-movement and abrupt market shifts (Chen et al., 12 Oct 2025).

1. Foundational Motivation and Conceptual Design

The DRFN architecture is motivated by the observed complementarity between static relational structures—capturing persistent inter-stock connections—and dynamic relations that reflect rapid changes in market conditions. Existing methods typically operate with either fixed structural priors or exclusively learn short-term interactions, thus neglecting the interaction between stable and volatile network dynamics. DRFN is specifically constructed to address this, enabling robust operation under both long-term market regularities and sudden informational shocks.

The static relation matrix ($S_{\text{pre}}$) encodes predefined business interdependencies, often sourced from structured knowledge graphs such as Wikidata. Its limitation is the absence of ultra-short-term market information, notably overnight effects. DRFN resolves this via a relative static relation module, fusing $S_{\text{pre}}$ with the dynamic relation matrix from the previous trading session ($D_{\text{dynamic}}^{\theta-1}$) using learnable weights and balancing coefficients.

2. Static Relation Component

The relative static relation module updates the conventional static relation matrix to incorporate time-varying patterns and overnight influences. The module realizes this integration by applying the following computation:

$$S_{\text{relative}}^{(\theta)} = \alpha \cdot D_{\text{dynamic}}^{(\theta-1)} + (1 - \alpha) \cdot (W_s \odot S_{\text{pre}})$$

where $W_s$ is a learnable parameter tensor modulating static importance, $\odot$ denotes Hadamard (element-wise) multiplication, and $\alpha$ is a learnable scalar balancing the contributions of static and dynamic sources. This recurrent update mechanism enables the static topology to reflect not only enterprise embeddedness but also temporally conditioned relational strengths.

A plausible implication is that networks using only $S_{\text{pre}}$ will underestimate short-term volatility, while DRFN’s fusion exploits the directional flow of information from recent market events into the otherwise stationary relational graph.

3. Dynamic Relation Mechanism

The dynamic relation module of DRFN captures evolving short-term interdependencies through a distance-aware cross-attention mechanism. Temporal multimodal features—news ($h_{n}$) and market indicators ($h_{m}$)—are first fused:

$$x_i^{(\theta)} = \tanh( W_i [h_{i,m}^{(\theta)} \Vert h_{i,n}^{(\theta)}] + h_{i,m}^{(\theta)} T_i^{[1:K]} h_{i,n}^{(\theta)} + b_i )$$

Resulting hidden states $V^{(\theta)}$ are processed to obtain positive (synergistic) and negative (adversarial) relation matrices:

$$A^{(\theta, a)} = \frac{V^{(\theta)} (a V^{(\theta)})^T}{\sqrt{F}}$$

where $a \in \{+1, -1\}$ and $F$ denotes the hidden dimension. The L₁ distance between stock representations,

$$D_{ij}^{(\theta, a)} = \| v_{i}^{(\theta)} - a v_{j}^{(\theta)} \|_1$$

directly modulates the initial attention score via exponential weighting:

$$\tilde{A}^{(\theta,a)} = A^{(\theta,a)} \odot \exp(-D^{(\theta,a)})$$

A cross-attention strategy is employed to synthesize positive and negative relations:

$$F^{(\theta, a)} = \text{softmax}\left( \frac{ \tilde{A}^{(\theta,a)} \cdot (\tilde{A}^{(\theta,-a)})^T }{ \sqrt{Z} } \right) \cdot \tilde{A}^{(\theta,-a)}$$

The final dynamic relation matrix is projected via a GELU activation:

$$D_{\text{dynamic}}^{(\theta)} = \text{GELU}( [ F^{(\theta,+1)} \Vert F^{(\theta,-1)} ] W_d )$$

This process enables DRFN to respond to and encode rapid market transitions in the latent inter-stock relationship graph.

4. Recurrent Fusion of Static and Dynamic Relations

The key innovation in DRFN lies in recurrent bidirectional cross-attention fusion of static and dynamic relational views. After parallel formation of $S_{\text{relative}}^{(\theta)}$ and $D_{\text{dynamic}}^{(\theta)}$, these are integrated:

$$R^{(\theta)} = \text{GELU}( [ \text{Attention}(S_{\text{relative}}^{(\theta)}, D_{\text{dynamic}}^{(\theta)}, D_{\text{dynamic}}^{(\theta)}) \Vert \text{Attention}(D_{\text{dynamic}}^{(\theta)}, S_{\text{relative}}^{(\theta)}, S_{\text{relative}}^{(\theta)}) ] W_{\text{DRS}} )$$

with the standard scaled dot-product attention:

$$\text{Attention}(Q,K,V) = \text{softmax} \left( \frac{QK^T}{\sqrt{d_k}} \right) V$$

This bidirectional integration allows the long-term relational graph to dynamically evolve by recurrently incorporating new short-term evidence, while retaining the stabilizing anchors of business structure.

This suggests the DRFN recurrent architecture is uniquely equipped to maintain sensitivity to evolving interdependencies, preserving temporal continuity without omitting abrupt changes.

5. Performance Benchmarking and Sensitivity

Empirical evaluation of DRFN on datasets spanning US and Chinese stock markets demonstrates superior performance relative to LSTM, GRU, GCN, GAT, MASTER, SAMBA, and LSR-IGRU (Chen et al., 12 Oct 2025). Notably, DRFN achieves lower RMSE and MAE in next-day return forecasting, validating the utility of dual relation fusion.

Ablation studies confirm that either static-only or dynamic-only modules yield inferior accuracy. The comprehensive fusion, including multimodal feature alignment and adaptive residual connections, produces higher Pearson correlation coefficients between predicted relational strength changes and actual price movements. In case comparisons (e.g., AAPL, AMZN), DRFN more accurately tracks both direction and magnitude of price changes, evidencing improved responsiveness.

6. Mathematical Formulations and Predictive Output

A summary of principal mathematical components applied in DRFN is tabulated below:

Module	Formulation Example	Role
Static Relation Update	$$S_{\text{relative}}^{(\theta)} = \alpha \cdot D_{\text{dynamic}}^{(\theta-1)} + (1-\alpha) \cdot (W_s \odot S_{\text{pre}})$$	Fusing prior dynamic/static relations
Dynamic Relation Scoring	$$A^{(\theta, a)} = \frac{V^{(\theta)} (a V^{(\theta)})^T}{\sqrt{F}}$$	Measure synergistic/adversarial links
Distance Weighting	$$\tilde{A}^{(\theta,a)} = A^{(\theta,a)} \odot \exp(-D^{(\theta,a)})$$	Enhances attention by proximity
Fusion Attention	$$R^{(\theta)} = \text{GELU}([\,\cdots\,] W_{\text{DRS}})$$	Combines static/dynamic views
Output Prediction	$\hat{y}_{i}^{(t+1)} = \tanh(\cdots)$	Forecast next-day stock price

Final predictions are produced via an adaptive residual fusion layer, accounting for stock-specific weights and the contributions of both news and market features.

7. Practical Implications and Interpretability

DRFN’s dual relation approach facilitates robust forecasting across different market regimes, benefiting applications requiring both rapid responsiveness to market news and structural stability provided by long-established relations. Its multimodal integration of qualitative and quantitative signals enhances versatility and transferability. The modular architecture, with explicit attention pathways and recurrent updates, delivers interpretability regarding which relations and modalities primarily drive predictive accuracy.

A plausible implication is that DRFN’s explicit separation and recurrent fusion of static and dynamic relations lays the groundwork for extending similar architectures to domains where evolving multi-modal and multi-relational data are prevalent (e.g., multi-agent systems, industrial supply chains, macroeconomic indicators). The attention-based modules facilitate post-hoc analysis of relational influence—enabling targeted interventions in algorithmic trading or risk assessment workflows.