  The Bayesian approach for feed-forward 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 (ANL) bubble
chamber experiment. This framework allows to perform a model-independent
determination of the axial form factor from data.. When the low $0.05 < Q^2 <
0.10$ GeV$^2$ data is 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 the dipole ansatz 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.
