AI models of code have made significant progress over the past few years. However, many models are actually not learning task-relevant source code features. Instead, they often fit non-relevant but correlated data, leading to a lack of robustness and generalizability, and limiting the subsequent practical use of such models. In this work, we focus on improving the model quality through signal awareness, i.e., learning the relevant signals in the input for making predictions. We do so by leveraging the heterogeneity of code samples in terms of their signal-to-noise content. We perform an end-to-end exploration of model signal awareness, comprising: (i) uncovering the reliance of AI models of code on task-irrelevant signals, via prediction-preserving input minimization; (ii) improving models’ signal awareness by incorporating the notion of code complexity during model training, via curriculum learning; (iii) improving models’ signal awareness by generating simplified signal-preserving programs and augmenting them to the training dataset; and (iv) presenting a novel interpretation of the model learning behavior from the perspective of the dataset, using its code complexity distribution. We propose a new metric to measure model signal awareness, Signal-aware Recall, which captures how much of the model’s performance is attributable to task-relevant signal learning. Using a software vulnerability detection use-case, our model probing approach uncovers a significant lack of signal awareness in the models, across three different neural network architectures and three datasets. Signal-aware Recall is observed to be in the sub-50s for models with traditional Recall in the high 90s, suggesting that the models are presumably picking up a lot of noise or dataset nuances while learning their logic. With our code-complexity-aware model learning enhancement techniques, we are able to assist the models toward more task-relevant learning, recording up-to 4.8× improvement in model signal awareness. Finally, we employ our model learning introspection approach to uncover the aspects of source code where the model is facing difficulty, and we analyze how our learning enhancement techniques alleviate it.