  This paper introduces alternators, a novel family of non-Markovian dynamical
models for sequences. An alternator features two neural networks: the
observation trajectory network (OTN) and the feature trajectory network (FTN).
The OTN and the FTN work in conjunction, alternating between outputting samples
in the observation space and some feature space, respectively, over a cycle.
The parameters of the OTN and the FTN are not time-dependent and are learned
via a minimum cross-entropy criterion over the trajectories. Alternators are
versatile. They can be used as dynamical latent-variable generative models or
as sequence-to-sequence predictors. When alternators are used as generative
models, the FTN produces interpretable low-dimensional latent variables that
capture the dynamics governing the observations. When alternators are used as
sequence-to-sequence predictors, the FTN learns to predict the observed
features. In both cases, the OTN learns to produce sequences that match the
data. Alternators can uncover the latent dynamics underlying complex sequential
data, accurately forecast and impute missing data, and sample new trajectories.
We showcase the capabilities of alternators in three applications. We first
used alternators to model the Lorenz equations, often used to describe chaotic
behavior. We then applied alternators to Neuroscience, to map brain activity to
physical activity. Finally, we applied alternators to Climate Science, focusing
on sea-surface temperature forecasting. In all our experiments, we found
alternators are stable to train, fast to sample from, yield high-quality
generated samples and latent variables, and outperform strong baselines such as
neural ODEs and diffusion models in the domains we studied.
