Kevin Course

Andrew F. Ilersich, Kevin Course, Prasanth B. Nair

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle with stochastic dynamics and fail to quantify prediction uncertainty, limiting their utility in robust decision-making contexts. To address these challenges, we introduce a data-driven framework for learning continuous-time stochastic ROMs that generalize across parameter spaces and forcing conditions. Our approach, based on amortized stochastic variational inference, leverages a reparametrization trick for Markov Gaussian processes to eliminate the need for computationally expensive forward solvers during training. This enables us to jointly learn a probabilistic autoencoder and stochastic differential equations governing the latent dynamics, at a computational cost that is independent of the dataset size and system stiffness. Additionally, our approach offers the flexibility of incorporating physics-informed priors if available. Numerical studies are presented for three challenging test problems, where we demonstrate excellent generalization to unseen parameter combinations and forcings, and significant efficiency gains compared to existing approaches.

Kevin Course, Prasanth B. Nair

We consider the problem of inferring latent stochastic differential equations (SDEs) with a time and memory cost that scales independently with the amount of data, the total length of the time series, and the stiffness of the approximate differential equations. This is in stark contrast to typical methods for inferring latent differential equations which, despite their constant memory cost, have a time complexity that is heavily dependent on the stiffness of the approximate differential equation. We achieve this computational advancement by removing the need to solve differential equations when approximating gradients using a novel amortization strategy coupled with a recently derived reparametrization of expectations under linear SDEs. We show that, in practice, this allows us to achieve similar performance to methods based on adjoint sensitivities with more than an order of magnitude fewer evaluations of the model in training.

Dai Li, Kevin Course, Wei Li et al.

While scaling laws promise significant performance gains for recommender systems, efficiently deploying hyperscale models remains a major unsolved challenge. In contrast to fields where FMs are already widely adopted such as natural language processing and computer vision, progress in recommender systems is hindered by unique challenges including the need to learn from online streaming data under shifting data distributions, the need to adapt to different recommendation surfaces with a wide diversity in their downstream tasks and their input distributions, and stringent latency and computational constraints. To bridge this gap, we propose to leverage the Foundation-Expert Paradigm: a framework designed for the development and deployment of hyperscale recommendation FMs. In our approach, a central FM is trained on lifelong, cross-surface, multi-modal user data to learn generalizable knowledge. This knowledge is then efficiently transferred to various lightweight, surface-specific "expert" models via target-aware embeddings, allowing them to adapt to local data distributions and optimization goals with minimal overhead. To meet our training, inference and development needs, we built HyperCast, a production-grade infrastructure system that re-engineers training, serving, logging and iteration to power this decoupled paradigm. Our approach is now deployed at Meta serving tens of billions of user requests daily, demonstrating online metric improvements over our previous one-stage production system while improving developer velocity and maintaining infrastructure efficiency. To the best of our knowledge, this work represents the first successful deployment of a Foundation-Expert paradigm at this scale, offering a proven, compute-efficient, and developer-friendly blueprint to realize the promise of scaling laws in recommender systems.