Estimating causal effects under interference is a common problem in social science and economics. However, it is challenging due to the complex dependency structure induced by network connections. In this paper, we propose GAUGER, a Generalized regression Adjustment framework via Graph-weighted Exposure-level Residualization for design-based causal inference under general interference. We first reveal a surprising mismatch between accuracy and efficiency in this setting: model adjustments that minimize prediction error (e.g., MSE) do not necessarily lead to the most variance reduction of the treatment effect estimator. To address this mismatch, we propose a two-step approach: (1) leveraging a strong prediction model to learn outcome patterns from the network and covariates, and (2) applying a novel calibration scheme called Graph-weighted Exposure-level Residualization (GER) that directly targets variance reduction. The resulting estimator is consistent for target causal parameters, enjoys provable variance reduction, and is asymptotically normal with a conservative variance estimator for valid statistical inference. As a practical implementation of the pipeline, we present a scheme that leverages Graph Neural Networks (GNNs) to construct the prediction model and use GER to steer the model adjustment for better variance reduction. Numerical studies show substantial efficiency gains over existing methods.

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