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As progress is made on training machine learning models on incrementally expanding classification tasks (i.e., incremental learning), a next step is to translate this progress to industry expectations. One technique missing from incremental learning is automatic architecture design via Neural Architecture Search (NAS). In this paper, we show that leveraging NAS for incremental learning results in strong performance gains for classification tasks. Specifically, we contribute the following: first, we create a strong baseline approach for incremental learning based on Differentiable Architecture Search (DARTS) and state-of-the-art incremental learning strategies, outperforming many existing strategies trained with similar-sized popular architectures; second, we extend the idea of architecture search to regularize architecture forgetting, boosting performance past our proposed baseline. We evaluate our method on both RF signal and image classification tasks, and demonstrate we can achieve up to a 10% performance increase over state-of-the-art methods. Most importantly, our contribution enables learning from continuous distributions on real-world application data for which the complexity of the data distribution is unknown, or the modality less explored (such as RF signal classification).