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A basic element in most independent component analysis (ICA) algorithms is the choice of a model for the score functions of the unknown sources. In this letter, a novel ICA algorithm is proposed, which is truly blind to the particular underlying distribution of the mixed signals. Using a multilayer network density estimation technique, the algorithm reconstructs score functions of the source signals. We show with experiments involving linear mixtures of various source signals with different statistical characteristics that the new algorithm not only outperforms state-of-the-art ICA methods but also our approach only requires a fraction of the sample sizes in order to outperform methods with partially adaptive score functions.