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SIXO is a new method for smoothing sequential Monte Carlo (SMC) that uses density ratio estimation to incorporate future information into the particle proposal.
Consider a Gaussian random walk where only the last state is observed. Filtering SMC fails to produce a useful posterior distribution over unseen latent states because the filtering distributions do not incorporate the observation until the last timestep. The smoothing distributions, however, make full use of the observation to produce ideal distributions over the unseen latents.
SIXO performs smoothing SMC by fitting "twisting functions" that estimate the likelihood of all future observations given the current latent state. When you apply SIXO to the Gaussian random walk, it obtains good samples from the posterior over trajectories while previous methods fail.
