LLM Flow Processes for Text-Conditioned Regression

Recent work has demonstrated surprisingly good performance of pre-trained LLMs on regression tasks (for example, time-series prediction), with the ability to incorporate expert prior knowledge and the information contained in textual metadata. However we observe major error cascades even in short sequences $\lesssim 100$ points; these models are also computationally intensive and difficult to parallelise. Marginal LLM predictions do not suffer this issue and are trivially parallelised, but can predict over-broad densities. To address this, we propose combining these densities with a lightweight (diffusion-based) neural process. We show that this combination leads to better-calibrated predictions overall, outputs locally consistent trajectories, and leads to text-conditioned function space selection in the meta-learner. As part of this work we propose a gradient-free (and non-Monte Carlo) method for sampling from a product-of-experts of a score model and an `expert' (here the LLM predictive densities). We believe this general method is of independent interest as it is applicable whenever an expert can be convolved with a Gaussian in closed form.