Symmetry-Aware Transformers for Asymmetric Causal Discovery in Financial Time Series

Financial markets exhibit fundamental asymmetries in temporal causality, where policy interventions create asymmetric transmission patterns that traditional symmetric modeling approaches fail to capture. This work introduces a mathematical framework that exploits the inherent symmetries of transformer architectures while preserving essential asymmetric temporal relationships in financial causal inference. We develop CausalFormer, a symmetry-aware neural architecture that maintains the permutation equivariance properties of self-attention mechanisms while enforcing strict temporal asymmetry constraints for causal discovery. The framework incorporates three mathematically principled components: (1) a symmetric attention matrix construction with asymmetric temporal masking that preserves the mathematical elegance of transformer operations while ensuring causal consistency, (2) a multi-scale convolution module with symmetric kernel initialization but asymmetric temporal receptive fields that captures policy transmission effects across heterogeneous time horizons, and (3) enhanced Nelson–Siegel decomposition that maintains the symmetric factor structure while modeling the evolution dynamics of asymmetric factors. Our mathematical formulation establishes the formal symmetry properties of the attention mechanism under temporal transformations while proving asymmetric convergence behaviors in policy transmission scenarios. The integration of symmetric optimization landscapes with asymmetric causal constraints enables simultaneous achievement of mathematical elegance and economic interpretability. Comprehensive experiments on monetary policy datasets demonstrate that the symmetry-aware design achieves a 15.3% improvement in the accuracy of causal effect estimations and a 12.7% enhancement in the predictive performance compared to those for existing methods while maintaining 91.2% causal consistency scores. The framework successfully identifies asymmetric policy transmission mechanisms, revealing that monetary tightening exhibits 40% faster propagation than easing policies, establishing new mathematical insights into the temporal asymmetries in financial systems. This work demonstrates how principled exploitation of architectural symmetries combined with domain-specific asymmetric constraints opens up new directions for mathematically rigorous yet economically interpretable deep learning in financial econometrics, with broad applications spanning computational finance, economic forecasting, and policy analysis.