The current standard method for amino acid signal identification in protein NMR spectra is sequential assignment using triple-resonance experiments. Good software and elaborate heuristics exist, but the process remains laboriously manual. Machine learning does help, but its training databases need millions of samples that cover all relevant physics and every kind of instrumental artifact. In this communication, we offer a solution to this problem. We propose polyadic decompositions to store millions of simulated three-dimensional NMR spectra, on-the-fly generation of artifacts during training, a probabilistic way to incorporate prior and posterior information, and integration with the industry standard CcpNmr software framework. The resulting neural nets take [1H,13C] slices of mixed pyruvate-labeled HNCA spectra (different CA signal shapes for different residue types) and return an amino acid probability table. In combination with primary sequence information, backbones of common proteins (GB1, MBP, and INMT) are rapidly assigned from just the HNCA spectrum.