  Large language models (LLMs) can be seen as atomic units of computation
mapping sequences to a distribution over sequences. Thus, they can be seen as
stochastic language layers in a language network, where the learnable
parameters are the natural language prompts at each layer. By stacking two such
layers and feeding the output of one layer to the next, we obtain a Deep
Language Network (DLN). We first show how to effectively perform prompt
optimization for a 1-Layer language network (DLN-1). Then, we present an
extension that applies to 2-layer DLNs (DLN-2), where two prompts must be
learned. The key idea is to consider the output of the first layer as a latent
variable, which requires inference, and prompts to be learned as the parameters
of the generative distribution. We first test the effectiveness of DLN-1 in
multiple reasoning and natural language understanding tasks. Then, we show that
DLN-2 can reach higher performance than a single layer, showing promise that we
might reach comparable performance to GPT-4, even when each LLM in the network
is smaller and less powerful.
