Why Invariant Risk Minimization Fails on Tabular Data: A Gradient Variance Solution

Abstract Machine learning models trained on observational data from one environment frequently fail when deployed in another, because standard learning algorithms exploit spurious correlations alongside causal ones. Invariant learning methods address this problem by seeking representations that support stable prediction across training environments, but their behavior on tabular data remains poorly characterized. We present C aus T ab , a gradient variance regularization framework for causal invariant representation learning on mixed tabular data. C aus T ab penalizes the variance of parameter gradients across training environments, providing a richer invariance signal than the scalar penalty used by Invariant Risk Minimization (IRM). We provide formal results showing that the gradient variance penalty is zero at causally invariant solutions and positive at solutions that rely on spurious features. Through experiments on synthetic data across three spurious-correlation regimes, four cycles of the National Health and Nutrition Examination Survey (NHANES), and four hospital systems in the UCI Heart Disease dataset, we demonstrate that: (1) IRM consistently degrades relative to standard empirical risk minimization (ERM) on tabular data, losing up to 13.8 AUC points in spurious-dominant settings, a failure we trace mechanistically to penalty collapse during training; (2) C aus T ab matches or exceeds ERM in every experimental condition; (3) C aus T ab achieves consistently better probability calibration than both ERM and IRM; and (4) invariant learning methods fail when environments differ in outcome prevalence rather than in spurious feature correlations, a boundary condition we characterize both empirically and theoretically. We introduce the Spurious Dominance Index (SDI), a practical scalar diagnostic for determining whether a dataset requires invariant learning, and validate it across all experimental settings.