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Zongyuan Li

Publications and source records attributed to Zongyuan Li.

At least 19 recordsLinked to original sources
arXiv2026

Millikelvin digital-to-analog converter for superconducting quantum processors

Scaling superconducting quantum processors is increasingly constrained by the wiring, heat load, and calibration overhead associated with delivering high-resolution analog signals from room temperature to qubits at millikelvin temperature. Here we demonstrate a superconducting digital-to-analog converter (DAC) integrated with high-coherence fluxonium qubits in a multi-chip module architecture. The DACs generate persistent analog flux signals for tuning qubit parameters and are programmed deterministically using single-flux-quantum (SFQ) pulses, providing a digital interface compatible with established SFQ routing and demultiplexing technologies. Operating at millikelvin temperature, the DACs enable in-situ tuning of fluxonium qubits without measurable degradation of qubit coherence. The presented device provides a static control primitive for flux-tunable qubits, enabling parameter homogenization and eliminating the need for individual room-temperature DC bias lines. These results establish SFQ-programmable millikelvin DACs as a building block for digitally controlled superconducting quantum processors.

quant-ph↗
arXiv2026

Reflection of Episodes: Learning to Play Game from Expert and Self Experiences

StarCraft II is a complex and dynamic real-time strategy (RTS) game environment, which is very suitable for artificial intelligence and reinforcement learning research. To address the problem of Large Language Model(LLM) learning in complex environments through self-reflection, we propose a Reflection of Episodes(ROE) framework based on expert experience and self-experience. This framework first obtains key information in the game through a keyframe selection method, then makes decisions based on expert experience and self-experience. After a game is completed, it reflects on the previous experience to obtain new self-experience. Finally, in the experiment, our method beat the robot under the Very Hard difficulty in TextStarCraft II. We analyze the data of the LLM in the process of the game in detail, verified its effectiveness.

cs.AI↗
arXiv2025

LLM-Cave: A benchmark and light environment for large language models reasoning and decision-making system

Large language models (LLMs) such as ChatGPT o1, ChatGPT o3, and DeepSeek R1 have shown great potential in solving difficult problems. However, current LLM evaluation benchmarks are limited to one-step interactions. Some of the existing sequence decision-making environments, such as TextStarCraftII and LLM-PySC2, are too complicated and require hours of interaction to complete a game. In this paper, we introduce LLM-Cave, a benchmark and light environment for LLM reasoning and decision-making systems. This environment is a classic instance in the era of Symbolism. Artificial intelligence enables the agent to explore the environment and avoid potential losses by reasoning about nearby dangers using partial observable state information. In the experiment, we evaluated the sequential reasoning ability, decision-making performance and computational efficiency of mainstream large language models (LLMs) such as GPT-4o-mini, o1-mini, and DeepSeek-R1. Experiments show that while Deepseek-R1 achieved the highest success rate on complex reasoning tasks, smaller models like 4o-mini significantly narrowed the performance gap on challenges by employing Chain of Speculation and Planner-Critic strategies, at the expense of reduced computational efficiency. This indicates that structured, multi-step reasoning combined with an LLM-based feedback mechanism can substantially enhance an LLM's decision-making capabilities, providing a promising direction for improving reasoning in weaker models and suggesting a new reasoning-centered benchmark for LLM assessment. Our code is open-sourced in https://github.com/puleya1277/CaveEnv.

cs.LG↗
arXiv2025

Memory-Augmented State Machine Prompting: A Novel LLM Agent Framework for Real-Time Strategy Games

This paper proposes Memory-Augmented State Machine Prompting (MASMP), a novel framework for LLM agents in real-time strategy games. Addressing key challenges like hallucinations and fragmented decision-making in existing approaches, MASMP integrates state machine prompting with memory mechanisms to unify structured actions with long-term tactical coherence. The framework features: (1) a natural language-driven state machine architecture that guides LLMs to emulate finite state machines and behavior trees through prompts, and (2) a lightweight memory module preserving strategic variables (e.g., tactics, priority units) across decision cycles. Experiments in StarCraft II demonstrate MASMP's 60% win rate against the hardest built-in AI (Lv7), vastly outperforming baselines (0%). Case studies reveal the method retains LLMs' semantic comprehension while resolving the "Knowing-Doing Gap" through strict state-action mapping, achieving both interpretability and FSM-like reliability. This work establishes a new paradigm for combining neural and symbolic AI in complex decision-making.

cs.AI↗
arXiv2025

LLM-PySC2: Starcraft II learning environment for Large Language Models

The tremendous potential has been demonstrated by large language models (LLMs) in intelligent decision-making problems, with unprecedented capabilities shown across diverse applications ranging from gaming AI systems to complex strategic planning frameworks. However, the StarCraft II platform, which has been widely adopted for validating decision-making algorithms in the past decade, has not yet provided substantial support for this emerging domain. To address issues that LLMs cannot interface with the hundreds of actions of the pysc2 backend and the lack of native support for multi-agent (MA) collaboration, we propose the LLM-PySC2 environment. This is the first environment that offers LLMs the complete pysc2 action space with sufficient multi-modal information and game Wiki knowledge. With an asynchronous query architecture, the environment efficiently interacts with LLMs that maintain a constant latency regardless of the scale of the agents' population. In the experiments, we evaluated LLMs' decision-making performance in both the macro-decision and micro-operation scenarios, with traditional StarCraft II Multi-Agent Challenge (SMAC) tasks and a series of new proposed. Results indicate that LLMs possess the potential to achieve victories in complex scenarios but cannot constantly generate correct decisions, especially in the recovered pysc2 action space and MA settings. Without task-relevant instructions, the pre-trained models suffer from issues such as hallucinations and inefficient collaboration. Our findings suggest that StarCraft II still challenges in the era of large models, revealing that there is a lot to do to develop an advanced LLM decision-making system, and the proposed LLM-PySC2 environment will support future development of LLM-based decision-making solutions.

cs.AI↗
arXiv2025

Retrieval Augmented Learning: A Retrial-based Large Language Model Self-Supervised Learning and Autonomous Knowledge Generation

The lack of domain-specific data in the pre-training of Large Language Models (LLMs) severely limits LLM-based decision systems in specialized applications, while post-training a model in the scenarios requires significant computational resources. In this paper, we present Retrial-Augmented Learning (RAL), a reward-free self-supervised learning framework for LLMs that operates without model training. By developing Retrieval-Augmented Generation (RAG) into a module for organizing intermediate data, we realized a three-stage autonomous knowledge generation of proposing a hypothesis, validating the hypothesis, and generating the knowledge. The method is evaluated in the LLM-PySC2 environment, a representative decision-making platform that combines sufficient complexity with domain-specific knowledge requirements. Experiments demonstrate that the proposed method effectively reduces hallucination by generating and utilizing validated knowledge, and increases decision-making performance at an extremely low cost. Meanwhile, the approach exhibits potential in out-of-distribution(OOD) tasks, robustness, and transferability, making it a cost-friendly but effective solution for decision-making problems and autonomous knowledge generation.

cs.AI↗
arXiv2025

Hierarchical Expert Prompt for Large-Language-Model: An Approach Defeat Elite AI in TextStarCraft II for the First Time

Since the emergence of the Large Language Model (LLM), LLM has been widely used in fields such as writing, translating, and searching. However, there is still great potential for LLM-based methods in handling complex tasks such as decision-making in the StarCraft II environment. To address problems such as lack of relevant knowledge and poor control over subtasks of varying importance, we propose a Hierarchical Expert Prompt (HEP) for LLM. Our method improves the understanding of game situations through expert-level tactical knowledge, improving the processing quality of tasks of varying importance through a hierarchical framework. Our approach defeated the highest level (Elite) standard built-in agent in TextStarCraft II for the first time and consistently outperformed the baseline method in other difficulties. Our experiments suggest that the proposed method is a practical solution for tackling complex decision-making challenges. The replay video can be viewed on https://www.bilibili.com/video/BV1uz42187EF and https://youtu.be/dO3PshWLV5M, and our codes have been open-sourced on https://github.com/luchang1113/HEP-LLM-play-StarCraftII.

cs.AI↗
arXiv2025

Unique continuation for Robin problems with non-smooth potentials

In this work, we study the unique continuation properties of Robin boundary value problems with Robin potentials $η\in L_{d-1+\varepsilon}$. Our results generalize earlier ones in which $η$ was assumed to be either zero (Neumann problem) or differentiable.

math.AP↗
arXiv2024

Liouville Theorem with Boundary Conditions from Chern--Gauss--Bonnet Formula

The $σ_k(A_g)$ curvature and the boundary $\mathcal{B}^k_g$ curvature arise naturally from the Chern--Gauss--Bonnet formula for manifolds with boundary. In this paper, we prove a Liouville theorem for the equation $σ_k(A_g)=1$ in $\overline{\mathbb{R}^n_+}$ with the boundary condition $\mathcal{B}^k_g=c$ on $\partial\mathbb{R}^n_+$, where $g=e^{2v}|dx|^2$ and $c$ is some nonnegative constant. This extends an earlier result of Wei, which assumes the existence of $\lim_{|x|\to\infty}(v(x)+2\log|x|)$. In addition, we establish a local gradient estimate for solutions of such equations, assuming an upper bound on the solution $v$.

math.AP↗
arXiv2024

Liouville theorems for conformally invariant fully nonlinear equations. I

A fundamental theorem of Liouville asserts that positive entire harmonic functions in Euclidean spaces must be constant. A remarkable Liouville-type theorem of Caffarelli-Gidas-Spruck states that positive entire solutions of $-Δu=u^{ {(n+2)}/{(n-2)} }$, $n\ge 3$, are unique modulo Möbius transformations. Far-reaching extensions were established for general fully nonlinear conformally invariant equations through the works of Chang-Gursky-Yang, Li-Li, Li, and Viaclovsky. In this paper, we derive necessary and sufficient conditions for the validity of such Liouville-type theorems. This leads to necessary and sufficient conditions for local gradient estimates of solutions to hold, assuming a one-sided bound on the solutions, for a wide class of fully nonlinear elliptic equations involving Schouten tensors. A pivotal advancement in proving these Liouville-type theorems is our enhanced understanding of solutions to such equations near isolated singularities. In particular, we utilize earlier results of Caffarelli-Li-Nirenberg on lower- and upper-conical singularities. For general conformally invariant fully nonlinear elliptic equations, we prove that a viscosity super- (sub-)solution can be extended across an isolated singularity if and only if it is a lower- (upper-)conical singularity. We also provide necessary and sufficient conditions for lower- (upper-)conical behavior of a function near isolated singularities in terms of its conformal Hessian. As an application of our Liouville theorems and local gradient estimates, we establish new existence and compactness results for conformal metrics on a closed Riemannian manifold with prescribed symmetric functions of the Schouten (Ricci) tensor, allowing the scalar curvature of the conformal metrics to have varying signs.

math.AP↗
arXiv2023

Asymptotic expansions for harmonic functions at conical boundary points

We prove three theorems about the asymptotic behavior of solutions $u$ to the homogeneous Dirichlet problem for the Laplace equation at boundary points with tangent cones. First, under very mild hypotheses, we show that the doubling index of $u$ either has a unique finite limit, or goes to infinity; in other words, there is a well-defined order of vanishing. Second, under more quantitative hypotheses, we prove that if the order of vanishing of $u$ is finite at a boundary point $0$, then locally $u(x) = |x|^m ψ(x/|x|) + o(|x|^m)$, where $|x|^m ψ(x/|x|)$ is a homogeneous harmonic function on the tangent cone. Finally, we construct a convex domain in three dimensions where such an expansion fails at a boundary point, showing that some quantitative hypotheses are necessary in general. The assumptions in all of the results only involve regularity at a single point, and in particular are much weaker than what is necessary for unique continuation, monotonicity of Almgren's frequency, Carleman estimates, or other related techniques.

math.AP↗
arXiv2023

On the uniqueness of variable coefficient Schrödinger equations

We prove unique continuation properties for linear variable coefficient Schrödinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any cubic exponential rate at two different times must be identically zero. Assuming a transversally anisotropic type condition, we recover the sharp Gaussian (quadratic exponential) rate in the series of works by Escauriaza-Kenig-Ponce-Vega [14, 17, 18].

math.AP↗
arXiv2023

Asymptotics of harmonic functions in the absence of monotonicity formulas

In this article, we study the asymptotics of harmonic functions. A typical method is by proving monotonicity formulas of a version of rescaled Dirichlet energy, and use it to study the renormalized solution -- the Almgren's blowup. However, such monotonicity formulas require strong smoothness assumptions on domains and operators. We are interested in the cases when monotonicity formulas are not available, including variable coefficient equations with unbounded lower order terms, Dirichlet problems on rough (non-$C^1$) domains, and Robin problems with rough Robin potentials.

math.AP↗
arXiv2022

Quantitative unique continuation for Robin boundary value problems on $C^{1,1}$ domains

In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on $C^{1,1}$ domains. The first one is a sharp vanishing order estimate of Robin problems with Lipschitz coefficients and differentiable, sign-changing potentials. This generalizes the result for the "Robin eigenfunctions" in [26], which deals with the case with constant potentials. The second result is a unique continuation result from the boundary -- any non-trivial solution cannot vanish at infinite order from the boundary or vanish on an open subset on the boundary. Such result generalizes the one in [1] for the Laplace equation on $C^{1,1}$ domains with zero Neumann boundary conditions.

math.AP↗
arXiv2021

Optimal regularity of mixed Dirichlet-conormal boundary value problems for parabolic operators

We obtain the regularity of solutions in Sobolev spaces for the mixed Dirichlet-conormal problem for parabolic operators in cylindrical domains with time-dependent separations, which is the first of its kind. Assuming the boundary of the domain to be Reifenberg-flat and the separation to be locally sufficiently close to a Lipschitz function of $m$ variables, where $m=0,\ldots,d-2$, with respect to the Hausdorff distance, we prove the unique solvability for $p\in (2(m+2/(m+3),2(m+2)/(m+1)))$. In the case when $m=0$, the range $p\in(4/3,4)$ is optimal in view of the known results for Laplace equations.

math.AP↗
arXiv2021

The Dirichlet-conormal problem for the heat equation with inhomogeneous boundary conditions

We consider the mixed Dirichlet-conormal problem for the heat equation on cylindrical domains with a bounded and Lipschitz base $Ω\subset \mathbb{R}^d$ and a time-dependent separation $Λ$. Under certain mild regularity assumptions on $Λ$, we show that for any $q>1$ sufficiently close to 1, the mixed problem in $L_q$ is solvable. In other words, for any given Dirichlet data in the parabolic Riesz potential space $\mathcal{L}_q^1$ and the Neumann data in $L_q$, there is a unique solution and the non-tangential maximal function of its gradient is in $L_q$ on the lateral boundary of the domain. When $q=1$, a similar result is shown when the data is in the Hardy space. Under the additional condition that the boundary of the domain $Ω$ is Reifenberg-flat and the separation is locally sufficiently close to a Lipschitz function of $m$ variables, where $m=0,\ldots,d-2$, with respect to the Hausdorff distance, we also prove the unique solvability result for any $q\in(1,(m+2)/(m+1))$. In particular, when $m=0$, i.e., $Λ$ is Reifenberg-flat of co-dimension $2$, we derive the $L_q$ solvability in the optimal range $q\in (1,2)$. For the Laplace equation, such results were established in [6, 5, 7] and [14].

math.AP↗