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In this study, we propose a tensor-based learning model to efficiently detect abnormalities on digital mammograms. Due to the fact that the availability of medical data is limited and often restricted by GDPR (general data protection regulation) compliance, the need for more sophisticated and less data-hungry approaches is urgent. Accordingly, our proposed artificial intelligence framework utilizes the canonical polyadic decomposition to decrease the trainable parameters of the wrapped Rank-R FNN model, leading to efficient learning using small amounts of data. Our model was evaluated on the open source digital mammographic database INBreast and compared with state-of-the-art models in this domain. The experimental results show that the proposed solution performs well in comparison with the other deep learning models, such as AlexNet and SqueezeNet, achieving 90% ± 4% accuracy and an F1 score of 84% ± 5%. Additionally, our framework tends to attain more robust performance with small numbers of data and is computationally lighter for inference purposes, due to the small number of trainable parameters.