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Deep learning has introduced significant improvements in many software analysis tasks. Although the Large Language Models (LLMs) based neural code models demonstrate commendable performance when trained and tested within the intra-project independent and identically distributed (IID) setting, they often struggle to generalize effectively to real-world inter-project out-of-distribution (OOD) data. In this work, we show that this phenomenon is caused by the heavy reliance on project-specific shortcuts for prediction instead of ground-truth evidence. We propose a Cond-Idf measurement to interpret this behavior, which quantifies the relatedness of a token with a label and its project-specificness. The strong correlation between model behavior and the proposed measurement indicates that without proper regularization, models tend to leverage spurious statistical cues for prediction. Equipped with these observations, we propose a novel bias mitigation mechanism that regularizes the model's learning behavior by leveraging latent logic relations among samples. Experimental results on two representative program analysis tasks indicate that our mitigation framework can improve both inter-project OOD generalization and adversarial robustness, while not sacrificing accuracy on intra-project IID data.