Jiyao Liu
Publications
A First-Principles Derivation of LLM Policy Optimization: From Expected Reward to GRPO and Its Structural Extensions
Policy gradient algorithms for language models optimize the same objective $J(θ) = \mathbb{E}*{τ\sim p*θ(τ)}[R(τ)]$, which has exactly two factors: the trajectory probability $p_θ(τ)$ and the reward $R(τ)$. Every method from REINFORCE to PPO to GRPO and their descendants modifies one or both factors to address a specific failure in the preceding formulation. Existing surveys organize these methods by domain or chronology, which obscures the rationale behind each design choice and the precise location of its intervention within the gradient estimator. This survey revisits the landscape of LLM policy optimization from $J(θ)$ on first principles and uses the trajectory side, induced by $p_θ(τ)$, and the reward side, induced by $R(τ)$, as the two axes along which methods are located. It covers the path from REINFORCE and PPO to GRPO, as well as post-GRPO variants, Agentic RL, and GRPO-OPD. The resulting framework is unified, diagnostic, and extensible: it analyzes methods from a shared objective, identifies which side each method modifies and why, and applies the same trajectory and reward axes across these settings. Across these settings, the framework also exposes compound failures that no single-side fix resolves and that therefore require joint design of the trajectory side and the reward side. The boundary cases and coupled failures identified by this map mark where existing solutions run out and provide a principled starting point for designing the next generation of LLM policy optimization algorithms.
Project Imaging-X: A Survey of 1000+ Open-Access Medical Imaging Datasets for Foundation Model Development
Foundation models have demonstrated remarkable success across diverse domains and tasks, primarily due to the thrive of large-scale, diverse, and high-quality datasets. However, in the field of medical imaging, the curation and assembling of such medical datasets are highly challenging due to the reliance on clinical expertise and strict ethical and privacy constraints, resulting in a scarcity of large-scale unified medical datasets and hindering the development of powerful medical foundation models. In this work, we present the largest survey to date of medical image datasets, covering over 1,000 open-access datasets with a systematic catalog of their modalities, tasks, anatomies, annotations, limitations, and potential for integration. Our analysis exposes a landscape that is modest in scale, fragmented across narrowly scoped tasks, and unevenly distributed across organs and modalities, which in turn limits the utility of existing medical image datasets for developing versatile and robust medical foundation models. To turn fragmentation into scale, we propose a metadata-driven fusion paradigm (MDFP) that integrates public datasets with shared modalities or tasks, thereby transforming multiple small data silos into larger, more coherent resources. Building on MDFP, we release an interactive discovery portal that enables end-to-end, automated medical image dataset integration, and compile all surveyed datasets into a unified, structured table that clearly summarizes their key characteristics and provides reference links, offering the community an accessible and comprehensive repository. By charting the current terrain and offering a principled path to dataset consolidation, our survey provides a practical roadmap for scaling medical imaging corpora, supporting faster data discovery, more principled dataset creation, and more capable medical foundation models.