  Modern high-stakes systems, such as healthcare or robotics, often generate
vast streaming event sequences. Our goal is to design an efficient,
plug-and-play tool to elicit logic tree-based explanations from Large Language
Models (LLMs) to provide customized insights into each observed event sequence.
Built on the temporal point process model for events, our method employs the
likelihood function as a score to evaluate generated logic trees. We propose an
amortized Expectation-Maximization (EM) learning framework and treat the logic
tree as latent variables. In the E-step, we evaluate the posterior distribution
over the latent logic trees using an LLM prior and the likelihood of the
observed event sequences. LLM provides a high-quality prior for the latent
logic trees, however, since the posterior is built over a discrete
combinatorial space, we cannot get the closed-form solution. We propose to
generate logic tree samples from the posterior using a learnable GFlowNet,
which is a diversity-seeking generator for structured discrete variables. The
M-step employs the generated logic rules to approximate marginalization over
the posterior, facilitating the learning of model parameters and refining the
tunable LLM prior parameters. In the online setting, our locally built,
lightweight model will iteratively extract the most relevant rules from LLMs
for each sequence using only a few iterations. Empirical demonstrations
showcase the promising performance and adaptability of our framework.
