  The classical limit on the accretion luminosity of a neutron star is given by
the Eddington luminosity. The advanced models of accretion onto magnetized
neutron stars account for the appearance of magnetically confined accretion
columns and allow the accretion luminosity to be higher than the Eddington
value by a factor of tens. However, the recent discovery of pulsations from
ultraluminous X-ray source (ULX) in NGC 5907 demonstrates that the accretion
luminosity can exceed the Eddington value up to by a factor of 500. We propose
a model explaining observational properties of ULX-1 in NGC 5907 without any ad
hoc assumptions. We show that the accretion column at extreme luminosity
becomes advective. Enormous energy release within a small geometrical volume
and advection result in very high temperatures at the bottom of accretion
column, which demand to account for the energy losses due to neutrino emission
which can be even more effective than the radiation energy losses. We show that
the total luminosity at the mass accretion rates above $10^{21}\,{\rm
g\,s^{-1}}$ is dominated by the neutrino emission similarly to the case of
core-collapse supernovae. We argue that the accretion rate measurements based
on detected photon luminosity in case of bright ULXs powered by neutron stars
can be largely underestimated due to intense neutrino emission. The recently
discovered pulsating ULX-1 in galaxy NGC 5907 with photon luminosity of $\sim
10^{41}\,{\rm erg\,s^{-1}}$ is expected to be even brighter in neutrinos and is
thus the first known Neutrino Pulsar.
