Abstract <p>This paper presents several contributions to the field of informed machine learning. First, a Deep Gaussian Mixture Informed method for pseudo-labeling in semi-supervised time-series tasks is introduced. This approach captures inter-class differences more accurately, boosting the Transformers and enhancing the multi-layer perceptrons to competitive performance levels without additional observations. Second, a novel image classification architecture informed by factor analyzers with additive and impulse noise is developed, and its analytical properties are proven. Finally, the work provides initial results on using statistical distribution approximations for self-tuning loss functions.</p>