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• The innovative use of multi-headed neural networks in combination with tandem neural networks solves the non-uniqueness problem of Layered Photonic Structures. • A self-attentive mechanism is added to the front of the inverse network to improve the accuracy and problem-solving capability of the network-aided design. • The generalization capability of the forward network is improved using cross-validation, which results in a significant improvement in the overall network performance. Neural networks have proven to be an influential tool in assisting with the inverse design of nanophotonic structures. However, the issue of non-uniqueness poses a significant limitation to this approach, as disparate designs can produce nearly identical spectra. This problem can result in the neural network failing to converge or producing erroneous results. In this study, we propose a multi-headed tandem neural network (MTNN) approach to address this issue. This method enables the neural network to generate multiple sets of outputs and utilize tandem neural networks (TNNs), and self-attention mechanisms, among other techniques, to constrain the results, and let these multiple outputs be fitted separately to different results. This allows the neural network to converge without sacrificing the simplex solution in the face of multimodal solutions. We employ the MTNN approach to inverse engineer a multilayer photonic structure comprised of two sets of oxide films, and the multiple outputs provide numerous valuable solutions. Our approach presents an effective solution for the inverse design of photonic structures afflicted with non-uniqueness problems. [ABSTRACT FROM AUTHOR]