In-context learning (ICL) lets tabular foundation models make predictions without dataset-specific training or fine-tuning. These models achieve strong predictive accuracy, but interpreting how individual features contribute to the prediction remains difficult. In biology, for example, feature contributions can help identify biomarkers or risk genes. Post-hoc interpretability methods assign feature importance scores, but these scores do not indicate what the model actually uses and can lead to explanation errors. We introduce TICL$^3$ (Tabular In-Context Local Linear Learning), an interpretable-by-design predictor that uses a tabular foundation model to guide a simple linear prediction rule. TICL$^3$ first learns a shared linear model to capture dataset-level feature effects. Then, for each query, it retrieves similar training samples using representations from the foundation model and fits a second linear model to the residuals in that neighborhood. The shared model captures broad effects, while the local model corrects errors among similar samples. Their combined coefficients determine each feature contribution to the final query-specific linear score, so the same model makes and explains the prediction. Across 386 classification benchmark-dataset evaluations, TICL$^3$ trails TabICLv2 by 1.1 percentage points and outperforms CatBoost in 266 evaluations. It improves average support F1 over MAPLE by 4.7 points and achieves the best performance on both real-data selected-feature utility metrics.

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