Completeness conjecture for deep NN-QM representations

A reflection-positive process is a stochastic process satisfying reflection positivity, and a symmetric Markov process is a Markov process invariant under time reflection. A deep NN-QM representation is a representation of a stochastic process as the output of a deep neural-network quantum-mechanics construction whose inputs are processes $y_t^{(i)}$.

Completeness conjecture. Every reflection-positive process admits a representation as a deep NN-QM whose inputs $y_t^{(i)}$ are symmetric Markov processes.

The results of the work establish the converse implication: every deep NN-QM with symmetric Markov inputs is reflection positive. The conjecture asserts completeness of this construction, namely that every reflection-positive process can be obtained in this way; the source presents proving or disproving it as a direction for future work.