  Multilayer switch networks are proposed as artificial generators of
high-dimensional discrete data (e.g., binary vectors, categorical data, natural
language, network log files, and discrete-valued time series). Unlike
deconvolution networks which generate continuous-valued data and which consist
of upsampling filters and reverse pooling layers, multilayer switch networks
are composed of adaptive switches which model conditional distributions of
discrete random variables. An interpretable, statistical framework is
introduced for training these nonlinear networks based on a maximum-likelihood
objective function. To learn network parameters, stochastic gradient descent is
applied to the objective. This direct optimization is stable until convergence,
and does not involve back-propagation over separate encoder and decoder
networks, or adversarial training of dueling networks. While training remains
tractable for moderately sized networks, Markov-chain Monte Carlo (MCMC)
approximations of gradients are derived for deep networks which contain latent
variables. The statistical framework is evaluated on synthetic data,
high-dimensional binary data of handwritten digits, and web-crawled natural
language data. Aspects of the model's framework such as interpretability,
computational complexity, and generalization ability are discussed.
