This paper introduces the front-propagation algorithm, a novel eXplainable AI (XAI) technique designed to elucidate the decision-making logic of deep neural networks. Unlike other popular explainability algorithms such as Integrated Gradients or Shapley Values, the proposed algorithm is able to extract an accurate and consistent linear function explanation of the network in a single forward pass of the trained model. This nuance sets apart the time complexity of the front-propagation as it could be running real-time and in parallel with deployed models. We packaged this algorithm in a software called $\texttt{front-prop}$ and we demonstrate its efficacy in providing accurate linear functions with three different neural network architectures trained on publicly available benchmark datasets.