  We present the first continuum extrapolation of the hyperon octet axial
couplings ($g_{\Sigma \Sigma}$ and $g_{\Xi \Xi}$) from $N_f=2+1+1$ lattice QCD.
These couplings are important parameters in the low-energy effective field
theory description of the octet baryons and fundamental to the nonleptonic
decays of hyperons and to hyperon-hyperon and hyperon-nucleon scattering with
application to neutron stars. We use clover lattice fermion action for the
valence quarks with sea quarks coming from configurations of $N_f=2+1+1$ highly
improved staggered quarks (HISQ) generated by MILC Collaboration. Our work
includes the first calculation of $g_{\Sigma \Sigma}$ and $g_{\Xi \Xi}$
directly at the physical pion mass on the lattice, and a full account of
systematic uncertainty, including excited-state contamination, finite-volume
effects and continuum extrapolation, all addressed for the first time. We find
the continuum-limit hyperon coupling constants to be $g_{\Sigma
\Sigma}=0.4455(55)_\text{stat}(65)_\text{sys}$ and $g_{\Xi \Xi}
=-0.2703(47)_\text{stat}(13)_\text{sys}$, which correspond to low-energy
constants of $D = 0.708(10)_\text{stat}(6)_\text{sys}$ and $F =
0.438(7)_\text{stat}(6)_\text{sys}$. The corresponding SU(3) symmetry breaking
is 9\% which is about a factor of 2 smaller than the earlier lattice estimate.
