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Rui Pan

Rui Pan contributes to research discovery and scholarly infrastructure.

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Published work

6 published item(s)

preprint2026arXiv

Recursive Multi-Agent Systems

Recursive or looped language models have recently emerged as a new scaling axis by iteratively refining the same model computation over latent states to deepen reasoning. We extend such scaling principle from a single model to multi-agent systems, and ask: Can agent collaboration itself be scaled through recursion? To this end, we introduce RecursiveMAS, a recursive multi-agent framework that casts the entire system as a unified latent-space recursive computation. RecursiveMAS connects heterogeneous agents as a collaboration loop through the lightweight RecursiveLink module, enabling in-distribution latent thoughts generation and cross-agent latent state transfer. To optimize our framework, we develop an inner-outer loop learning algorithm for iterative whole-system co-optimization through shared gradient-based credit assignment across recursion rounds. Theoretical analyses of runtime complexity and learning dynamics establish that RecursiveMAS is more efficient than standard text-based MAS and maintains stable gradients during recursive training. Empirically, we instantiate RecursiveMAS under 4 representative agent collaboration patterns and evaluate across 9 benchmarks spanning mathematics, science, medicine, search, and code generation. In comparison with advanced single/multi-agent and recursive computation baselines, RecursiveMAS consistently delivers an average accuracy improvement of 8.3%, together with 1.2$\times$-2.4$\times$ end-to-end inference speedup, and 34.6%-75.6% token usage reduction. Code and Data are provided in https://recursivemas.github.io.

preprint2024arXiv

AstroLLaMA-Chat: Scaling AstroLLaMA with Conversational and Diverse Datasets

We explore the potential of enhancing LLM performance in astronomy-focused question-answering through targeted, continual pre-training. By employing a compact 7B-parameter LLaMA-2 model and focusing exclusively on a curated set of astronomy corpora -- comprising abstracts, introductions, and conclusions -- we achieve notable improvements in specialized topic comprehension. While general LLMs like GPT-4 excel in broader question-answering scenarios due to superior reasoning capabilities, our findings suggest that continual pre-training with limited resources can still enhance model performance on specialized topics. Additionally, we present an extension of AstroLLaMA: the fine-tuning of the 7B LLaMA model on a domain-specific conversational dataset, culminating in the release of the chat-enabled AstroLLaMA for community use. Comprehensive quantitative benchmarking is currently in progress and will be detailed in an upcoming full paper. The model, AstroLLaMA-Chat, is now available at https://huggingface.co/universeTBD, providing the first open-source conversational AI tool tailored for the astronomy community.

preprint2024arXiv

Uniform Asymptotic Approximation Method with Pöschl-Teller Potential

In this paper, we study analytical approximate solutions of the second-order homogeneous differential equations with the existence of only two turning points (but without poles), by using the uniform asymptotic approximation (UAA) method. To be more concrete, we consider the Pöschl-Teller (PT) potential, for which analytical solutions are known. Depending on the values of the parameters involved in the PT potential, we find that the upper bounds of the errors of the approximate solutions in general are $\lesssim 0.15\% \sim 10\% $, to the first-order approximation of the UAA method. The approximations can be easily extended to high-order, with which the errors are expected to be much smaller. Such obtained analytical solutions can be used to study cosmological perturbations in the framework of quantum cosmology, as well as quasi-normal modes of black holes.

preprint2022arXiv

Eigencurve: Optimal Learning Rate Schedule for SGD on Quadratic Objectives with Skewed Hessian Spectrums

Learning rate schedulers have been widely adopted in training deep neural networks. Despite their practical importance, there is a discrepancy between its practice and its theoretical analysis. For instance, it is not known what schedules of SGD achieve best convergence, even for simple problems such as optimizing quadratic objectives. In this paper, we propose Eigencurve, the first family of learning rate schedules that can achieve minimax optimal convergence rates (up to a constant) for SGD on quadratic objectives when the eigenvalue distribution of the underlying Hessian matrix is skewed. The condition is quite common in practice. Experimental results show that Eigencurve can significantly outperform step decay in image classification tasks on CIFAR-10, especially when the number of epochs is small. Moreover, the theory inspires two simple learning rate schedulers for practical applications that can approximate eigencurve. For some problems, the optimal shape of the proposed schedulers resembles that of cosine decay, which sheds light to the success of cosine decay for such situations. For other situations, the proposed schedulers are superior to cosine decay.

preprint2019arXiv

Path integral approach to the calculation of the characteristic function of work

Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work statistics in quantum systems by employing Feynman's path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schrödinger's formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach to the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems.

preprint2019arXiv

Quantum corrections to the entropy and its application in the study of quantum Carnot engines

Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the statistical mechanical entropy is defined by Gibbs. The relation between these two definitions of entropy is still not fully explored. In this work, we study this problem by employing the phase-space formulation of quantum mechanics. For those quantum states having well-defined classical counterparts, we study the quantum-classical correspondence and quantum corrections of the entropy. We expand the von Neumann entropy in powers of ${\hbar}$ by using the phase-space formulation, and the zeroth order term reproduces the Gibbs entropy. We also obtain the explicit expression of the quantum corrections of the entropy. Moreover, we find that for the thermodynamic equilibrium state, all terms odd in ${\hbar}$ are exactly zero. As an application, we derive quantum corrections for the net work extraction during a quantum Carnot cycle. Our results bring important insights to the understanding of quantum entropy and may have potential applications in the study of quantum heat engines.