We introduce Planning-guided Retrieval Augmented Generation (Plan$\times$RAG), a novel framework that augments the \emph{retrieve-then-reason} paradigm of existing RAG frameworks to \emph{plan-then-retrieve}. Plan$\times$RAG formulates a reasoning plan as a directed acyclic graph (DAG), decomposing queries into interrelated atomic sub-queries. Answer generation follows the DAG structure, allowing significant gains in efficiency through parallelized retrieval and generation. While state-of-the-art RAG solutions require extensive data generation and fine-tuning of language models (LMs), Plan$\times$RAG incorporates frozen LMs as plug-and-play experts to generate high-quality answers. Compared to existing RAG solutions, Plan$\times$RAG demonstrates significant improvements in reducing hallucinations and bolstering attribution due to its structured sub-query decomposition. Overall, Plan$\times$RAG offers a new perspective on integrating external knowledge in LMs while ensuring attribution by design, contributing towards more reliable LM-based systems.

Recent advances have shown that GP priors, or their finite realisations, can be encoded using deep generative models such as variational autoencoders (VAEs). These learned generators can serve as drop-in replacements for the original priors during MCMC inference. While this approach enables efficient inference, it loses information about the hyperparameters of the original models, and consequently makes inference over hyperparameters impossible and the learned priors indistinct. To overcome this limitation, we condition the VAE on stochastic process hyperparameters. This allows the joint encoding of hyperparameters with GP realizations and their subsequent estimation during inference. Further, we demonstrate that our proposed method, PriorCVAE, is agnostic to the nature of the models which it approximates, and can be used, for instance, to encode solutions of ODEs. It provides a practical tool for approximate inference and shows potential in real-life spatial and spatiotemporal applications.

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with latent processes endowed with a non-linear diffusion process prior are intractable problems. We build upon work within variational inference, approximating the posterior process as a linear diffusion process, and point out pathologies in the approach. We propose an alternative parameterization of the Gaussian variational process using a site-based exponential family description. This allows us to trade a slow inference algorithm with fixed-point iterations for a fast algorithm for convex optimization akin to natural gradient descent, which also provides a better objective for learning model parameters.

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.

Simulation-based techniques such as variants of stochastic Runge-Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and non-parametric models, and neural SDEs. Stochastic Runge-Kutta relies on the use of sampling schemes that can be inefficient in high dimensions. We address this issue by revisiting the classical SDE literature and derive direct approximations to the (typically intractable) Fokker-Planck-Kolmogorov equation by matching moments. We show how this workflow is fast, scales to high-dimensional latent spaces, and is applicable to scarce-data applications, where a non-parametric SDE with a driving Gaussian process velocity field specifies the model.