Stable Alpha: Adversarial Invariant Representation Learning for Nonlinear Asset Pricing under Temporal Distribution Shifts

Deep learning has emerged as a powerful paradigm for constructing nonlinear asset pricing factor models. However, temporal distribution shifts such as bull-bear transitions and industry rotations undermine the generalization of models trained under the i.i.d. assumption. As a result, existing models tend to exploit environment-specific correlations that are highly predictive in-sample but unstable across market regimes. To address this challenge, we propose $\textit{\textbf{CASH}}$, a causality-inspired asset pricing factor framework designed to learn invariant and minimally sufficient representations under temporal distribution shifts. CASH formulates an information-theoretic adversarial learning objective that systematically discards transient market noise by optimizing against an adversary designed to exploit spurious correlations, thereby distilling invariant factor-return relationships. The resulting invariant representation is then integrated into a conditional factor pricing model via a dynamic factor exposure network. Experiments on real-world stock datasets across multiple markets demonstrate that CASH consistently outperforms state-of-the-art baselines in out-of-sample return prediction and exhibits superior robustness under pronounced temporal regime shifts.