would be to initialize the state in a transition circuit via a separate, feed-forward, combinational circuit that approximates the equilibrium distribution of the Markov chain. Machine perception software that uses machine learning to construct fast, compact initializers is already in use[@shottonreal]. Analyzing the number of transitions needed to close the gap between a good initialization and the target distribution may be harder[@diaconismarkov]. However, some feedforward Monte Carlo inference strategies for Bayesian networks provably yield precise estimates of probabilities in polynomial time if the underlying probability model is sufficiently stochastic[@dagum1997optimal]; it remains to be seen if similar conditions apply to stateful stochastic transition circuits.

It may also be fruitful to search for novel electronic devices — or previously unusable dynamical regimes of existing devices — that are as well matched to the needs of intentionally stochastic circuits as transistors are to logical inverters, potentially even via a spiking implementation. Physical phenomena that proved too unreliable for implementing Boolean logic gates may be viable building blocks for machines that perform Bayesian inference.

Computer engineering has thus far focused on deterministic mechanisms of remarkable scale and complexity: billlions of parts that are expected to make trillions of state transitions with perfect repeatability[@intelInstructionErrors]. But 