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Typically, the training of machine learning systems assumes that unexpected or unreasonable data, otherwise called outliers (e.g., samples that are distinct from and not represented in the training data distribution), will never be encountered. Since outliers are samples not drawn from the data distribution of interest, the diversity of outliers precludes the ability to train with fully representative outlier data. The ability for machine learning algorithms operating in realistic environment to detect outliers is key to ensuring predictable behavior of the algorithms in those environments. Competency awareness in machine learning is, in general, the ability of an algorithm to identify when performance may break down, due to a lack of prior knowledge. Here, lack of prior knowledge refers to the similarity of the original training data and to future data encountered during operation. To this end, many methods exist that detect out-of-distribution outliers. These methods often require modifications to the algorithm, e.g. by changing network architectures, or by changing the training procedure entirely, thereby changing hardware requirements of existing algorithms. Yet other methods require entirely separate models to perform the out-of-distribution outlier detection. These methods require training two distinct models, one for detecting the outliers and one for classification, which increases the overall complexity of these approaches. This dissertation investigates using the null space, in a novel way, to integrate out-of-distribution outlier detection directly into an existing neural network used for classification, thus requiring only a single model. The proposed method, called Null Space Analysis (NuSA), works by computing and controlling the magnitude of null space projections in relation to the magnitude of the data throughout a neural network. Using these projections, NuSA then calculate a score that differentiates between expected data and potential outliers, while maintaining network performance. The null space is not only useful for detecting outliers but also contains information useful to human interpretation of neural networks and other tasks. The remainder of this document focuses on exploring the null space of neural networks focusing primarily on competency awareness in predicting outliers in real-world scenarios.