Data quality is a common problem in machine learning, especially in high-stakes settings such as healthcare. Missing data affects accuracy, calibration, and feature attribution in complex patterns. Developers often train models on carefully curated datasets to minimize missing data bias; however, this reduces the usability of such models in production environments, such as real-time healthcare records. Making machine learning models robust to missing data is therefore crucial for practical application. While some classifiers naturally handle missing data, others, such as deep neural networks, are not designed for unknown values. We propose a novel neural network modification to mitigate the impacts of missing data. The approach is inspired by neuromodulation that is performed by biological neural networks. Our proposal replaces the fixed weights of a fully-connected layer with a function of an additional input (reliability score) at each input, mimicking the ability of cortex to up- and down-weight inputs based on the presence of other data. The modulation function is jointly learned with the main task using a multi-layer perceptron. We tested our modulating fully connected layer on multiple classification, regression, and imputation problems, and it either improved performance or generated comparable performance to conventional neural network architectures concatenating reliability to the inputs. Models with modulating layers were more robust against degradation of data quality by introducing additional missingness at evaluation time. These results suggest that explicitly accounting for reduced information quality with a modulating fully connected layer can enable the deployment of artificial intelligence systems in real-time settings.