Manifold Bandits: Bayesian Curriculum Learning over the Latent Geometry of Large Language Models

A new framework called Bayesian Manifold Curriculum (BMC) proposes a structure-aware method for sampling training problems in large language models, moving beyond the common practice of prioritizing prompts of intermediate difficulty, according to a preprint posted to arXiv [1]. The paper, submitted on 18 June 2026 by researcher Darrien McKenzie, frames problem sampling during reinforcement learning as a manifold-structured bandit problem with endogenous non-stationarity [1][2]. In this view, problems are related through the model's latent representation space, and sampling decisions can steer how learning signals evolve across that space [2]. The BMC framework organizes problems into a hierarchical task tree and applies Bayesian learning to guide sampling [1][2]. Empirically, the authors find that different sampling strategies induce tradeoffs between productivity, diversity, and utility in downstream performance [1][2]. The results indicate that prioritizing difficulty alone is insufficient for strong downstream performance, highlighting the importance of incorporating structure and type-awareness into problem sampling [2]. The preprint appears on arXiv, an open-access repository of electronic preprints that, as of November 2024, receives about 24,000 submissions per month and hosts over two million articles [6]. The work is categorized under machine learning and was posted in the cs.LG browse context [1]. The paper's abstract page also links to several community-developed tools through the arXivLabs framework, including Bibliographic Explorer and Connected Papers, which allow readers to navigate citation trees and explore related research [4][5]. arXivLabs, launched in 2020, provides a formalized framework for third-party collaborators to build experimental features on the platform while adhering to values of openness, community, and user data privacy [4].