  Numerous models for supervised and reinforcement learning benefit from
combinations of discrete and continuous model components. End-to-end learnable
discrete-continuous models are compositional, tend to generalize better, and
are more interpretable. A popular approach to building discrete-continuous
computation graphs is that of integrating discrete probability distributions
into neural networks using stochastic softmax tricks. Prior work has mainly
focused on computation graphs with a single discrete component on each of the
graph's execution paths. We analyze the behavior of more complex stochastic
computations graphs with multiple sequential discrete components. We show that
it is challenging to optimize the parameters of these models, mainly due to
small gradients and local minima. We then propose two new strategies to
overcome these challenges. First, we show that increasing the scale parameter
of the Gumbel noise perturbations during training improves the learning
behavior. Second, we propose dropout residual connections specifically tailored
to stochastic, discrete-continuous computation graphs. With an extensive set of
experiments, we show that we can train complex discrete-continuous models which
one cannot train with standard stochastic softmax tricks. We also show that
complex discrete-stochastic models generalize better than their continuous
counterparts on several benchmark datasets.
