Binary Quantized Neural Network Training Is W[1]-Hard Parameterized by Input and Output Dimensions

Ganian et al. (ICLR 2026) proved that quantized neural network training is fixed-parameter tractable when parameterized jointly by architecture treewidth, input dimension $α$, and output dimension $ω$, and left open whether $α+ω$ alone yields fixed-parameter tractability. We prove that 2-QNNT is W[1