  The combination of quantum many-body and machine learning techniques has
recently proved to be a fertile ground for new developments in quantum
computing. Several works have shown that it is possible to classically
efficiently predict the expectation values of local observables on all states
within a phase of matter using a machine learning algorithm after learning from
data obtained from other states in the same phase. However, existing results
are restricted to phases of matter such as ground states of gapped Hamiltonians
and Gibbs states that exhibit exponential decay of correlations. In this work,
we drop this requirement and show how it is possible to learn local expectation
values for all states in a phase, where we adopt the Lindbladian phase
definition by Coser \& P\'erez-Garc\'ia [Coser \& P\'erez-Garc\'ia, Quantum 3,
174 (2019)], which defines states to be in the same phase if we can drive one
to other rapidly with a local Lindbladian. This definition encompasses the
better-known Hamiltonian definition of phase of matter for gapped ground state
phases, and further applies to any family of states connected by short unitary
circuits, as well as non-equilibrium phases of matter, and those stable under
external dissipative interactions. Under this definition, we show that $N =
O(\log(n/\delta)2^{polylog(1/\epsilon)})$ samples suffice to learn local
expectation values within a phase for a system with $n$ qubits, to error
$\epsilon$ with failure probability $\delta$. This sample complexity is
comparable to previous results on learning gapped and thermal phases, and it
encompasses previous results of this nature in a unified way. Furthermore, we
also show that we can learn families of states which go beyond the Lindbladian
definition of phase, and we derive bounds on the sample complexity which are
dependent on the mixing time between states under a Lindbladian evolution.
