Abstract: The Bayesian approach for feedforward neural networks has been applied to the extraction of the nucleon axial form factor from the neutrino-deuteron-scattering data measured by the Argonne National Laboratory bubble-chamber experiment. This framework allows to perform a model-independent determination of the axial form factor from data. When the low 0.05 < Q(2) < 0.10-GeV2 data are included in the analysis, the resulting axial radius disagrees with available determinations. Furthermore, a large sensitivity to the corrections from the deuteron structure is obtained. In turn, when the low-Q(2) region is not taken into account with or without deuteron corrections, no significant deviations from previous determinations have been observed. A more accurate determination of the nucleon axial form factor requires new precise measurements of neutrino-induced quasielastic scattering on hydrogen and deuterium.