Reconstruction of masked sequences <i>via</i> inverse mapping of incomplete information natural vectors

Alignment-free embedding methods, which map biological sequences into a fixed-dimensional space using mathematical techniques, hold significant value in biology. A key challenge in this field is constructing an inverse mapping to recover sequences from embedded vectors. The natural vector approach uniquely provides a theoretical one-to-one correspondence between sequences and high-order natural vectors, but reconstructing sequences from lower-order vectors remains unsolved. Moreover, when sequences contain masked regions, extracting features and constructing the inverse mapping to restore the original sequence, including the masked parts, becomes even more challenging. In this article, we define incomplete information natural vectors for masked sequences and develop a long short-term memory model that achieves over 99.9% accuracy in reconstructing unmasked positions in original sequences on SARS-CoV-2 and HIV-1 datasets, while also providing predictions for masked sites that significantly outperform random prediction. Our model can robustly handle sequences with varying masked nucleotides. Overall, our approach expands the scope of alignment-free embedding methods by enabling bidirectional conversion and addressing challenges posed by incomplete information.