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Fe-B-Si system is a matrix for synthesis of new functional materials with exceptional magnetic and mechanical properties. Progress in this area is associated with the search for optimal doping conditions. This theoretical and experimental study is aimed to address the influence of Ta alloying on the structure of undercooled (Fe0.75B0.15Si0.1)100-xTax (x=0-2) melts, their undercoolability and the processes of structure formation during solidification. Small concentration of Ta complicates standard ab initio and machine learning investigations. We developed a technique for fast and stable training of machine learning interatomic potential (MLIP) in this case and uncovered the structure of the undercooled melts. Molecular dynamic simulations with MLIP showed that at Ta concentration of 1 at.% there is a sharp change in the chemical short-range ordering in the melt associated with a change in the interaction of Ta atoms. This effect leads to a restructuring of the cluster formation in the system. At the same time, our experimental investigation shows that melts with a Ta content of 1 at.% have the greatest tendency to undercoolability. Alloying with Ta promotes the formation of primary crystals of Fe2B, and at a concentration of more than 1.5 at.% Ta, also of FeTaB. Herewith, near 1 at.% Ta, the crystallization of the melt proceeds nontrivially: with the formation of two intermediate metastable phases Fe3B and Fe2Ta Laves phase. Also, the highest tendency to amorphization under conditions of quick quenching is exhibited by a melt with a Ta concentration of 1 at.%. The results not only provide understanding of optimal alloying of Fe-B-Si materials but also promote a machine learning method for numerical design of metallic alloys with a small dopant concentration.