arXiv subjects

Yin Cai

Publications and source records attributed to Yin Cai.

At least 19 recordsLinked to original sources

arXiv2026

Critical Gaussian Multiplicative Chaos on the Circle Is Rajchman

We prove that the Fourier coefficients of the canonical critical Gaussian multiplicative chaos on the circle vanish almost surely at infinity. More precisely, let $M_\phi^{\mathrm{crit}}$ be the canonical critical chaos associated with the centered circle field $\phi$ of covariance $\mathbb{E}[\phi(\theta)\phi(\theta')] = \log\frac{1}{\lvert e^{i\theta}-e^{i\theta'}\rvert}$. Then, almost surely, $\widehat{M_\phi^{\mathrm{crit}}}(n)\longrightarrow0$ as $\lvert n\rvert\to\infty$. This resolves the almost-sure critical Rajchman problem for the canonical circle field. Since critical chaos has Fourier dimension zero almost surely, no positive polynomial Fourier-decay rate can hold; the theorem therefore exhibits qualitative Fourier cancellation beyond the regime of positive Fourier dimension. The proof addresses two coupled difficulties: the heavy, nonuniform cell masses of critical chaos and the need to control exponentially many frequencies in each dyadic annulus. For an auxiliary periodized compact-range star-scale field, a derivative-rooted Bessel regression yields weighted small-cell summability and moving-tail control of exceptional large cells. After conditioning at a coarse scale below the Fourier scale, finite-range independence and conditional Bernstein concentration reduce uniform control of the terminal Fourier coefficients over each dyadic annulus to a spatial-variation estimate for a coarse predictable measure. A smooth positive-definite covariance correction and critical-chaos uniqueness then transfer the Rajchman property to the canonical critical chaos of the exact circle field.

math.PR↗

arXiv2026

SchemaGUI: A Schema-Driven Benchmark for Controllable GUI Generation Evaluation

Large language models (LLMs) have demonstrated strong potential in graphical user interface (GUI) generation, but reliable evaluation remains challenging due to uncontrolled data distributions, noisy annotations, and limited layout scenario coverage. To address this, we propose SchemaGUI, a template-based benchmark for controllable GUI generation evaluation. By synthesizing paired natural language instructions and deterministic function-call references from parameterized interface schemas, SchemaGUI can generate thousands of deterministically annotated tasks in seconds without human labeling. Based on 1,000 evaluated instances per scenario and language across six representative bilingual scenarios, we benchmark five mainstream models, including the Qwen3.5 family, Qwen3-Coder-30B, and DeepSeek-R1. Our extensive analysis reveals three key insights. First, precise geometric spatial control remains an important bottleneck; while scaling Qwen3.5 from 4B to 27B improves Schema Feasibility from 91.56% to 99.63%, the Geometry score improves more modestly (from 67.05% to 75.30%). Second, generation difficulty is highly sensitive to layout complexity, with current LLMs excelling at simple sequential arrangements but suffering severe coordinate drift in dense grids and multi-region compositions. Third, thinking mode increases token consumption while generally reducing GUI Score, particularly for smaller models.

cs.CL↗

arXiv2026

Canonical Mandelbrot Cascades on Curves Are Rajchman

We settle the Rajchman problem for canonical scalar dyadic Mandelbrot cascades at the minimal Kahane--Peyri\`ere integrability threshold. If $\mu$ is the cascade on $[0,1]$, then $\widehat{\mu}(\xi)\to 0$ as $|\xi|\to\infty$, almost surely on non-extinction. For every fixed nondegenerate $C^2$ embedded arc $\gamma:[0,1]\to\mathbb{R}^2$, the pushforward $\gamma_\#\mu$ is likewise Rajchman almost surely on non-extinction. The analogous conclusion holds for the scalar cascade on the parameter circle pushed forward by any fixed nondegenerate $C^2$ Jordan curve. No moment condition of order strictly greater than one is imposed; in particular, the results include the regime $\mathbb{E}[W^q]=\infty$ for every $q>1$. The proof combines a spine-based lower-deviation principle, adaptive terminal approximation, and predictable capping to obtain almost-sure estimates uniform over large frequency annuli without higher moments. For curved pushforwards, an endpoint-safe phase decomposition controls direction-dependent stationary regions, including those meeting the endpoints of an arc, and couples the geometric and probabilistic arguments through a common dyadic kernel. Combined with the exact Fourier-dimension formulas for the corresponding models, the theorems show that Rajchman decay persists at zero Fourier dimension.

math.PR↗

arXiv2026

Exact Fourier dimensions of dyadic Mandelbrot cascades on curves of nonvanishing curvature under minimal integrability

We prove exact Fourier-dimension formulas for scalar dyadic Mandelbrot cascades pushed forward to fixed nondegenerate $C^2$ embedded arcs and fixed nondegenerate $C^2$ Jordan curves in $\mathbb R^2$. Let $W$ be in the minimal Kahane--Peyriere regime. For each fixed nondegenerate $C^2$ embedded arc $\gamma:[0,1]\to\mathbb R^2$, the pushforward $\mu_\gamma$ of the interval cascade satisfies, almost surely on non-extinction, \[ \dim_{\mathrm F}(\mu_\gamma)=A_{\mathrm{loc}}(W), \] where \[ A_{\mathrm{loc}}(W) = \sup_{q>1} \max\left\{ 0,\, \frac{q-1-\log_2\mathbb E[W^q]}{q} \right\}, \] with the $q$-term interpreted as $0$ when $\mathbb E[W^q]=\infty$. The analogous formula holds for scalar circle cascades pushed forward by fixed nondegenerate $C^2$ Jordan curves $\gamma:\mathbb T\to\mathbb R^2$, with the pushforward denoted by $\mu_\gamma^{\mathbb T}$. This extends the scalar circle endpoint formula from the canonical circle to fixed parametrized arcs and Jordan curves. The main new issue beyond the canonical circle is the loss of the explicit trigonometric phase and, for arcs, the presence of endpoint stationary regimes. We prove the arc lower bound by a finite-$r$ annular Fourier theorem based on an endpoint-safe phase decomposition, phase-bin coefficient estimates, predictable capping, complex Freedman concentration, and an $r$-tail compensator. The Jordan lower bound follows by first-generation dyadic cutting into two fixed arcs. The matching upper bounds use deterministic curved-support obstructions together with the scalar-circle minimum lower local-dimension theorem.

math.PR↗

arXiv2026

Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability

We determine the Fourier dimension of dyadic Mandelbrot cascades under the minimal Kahane-Peyriere integrability condition. The interval theorem is proved in a vector-valued dyadic cascade model in which sibling weights may have arbitrary dependence. For every balanced energy-admissible vector law, almost surely on non-extinction, dim_F(mu)=dim_E(mu)=dim_2(mu)=D_E(X). In the canonical scalar case, under W>=0, E W=1, E[W log_2^+ W] 1} max{0, (q-1-log_2 E[W^q])/q}. The interval and circle formulas share a light-tail/heavy-tail dichotomy but have different mechanisms: energy dimension for the interval, and minimum lower local dimension for the circle. The circle lower bound follows from a finite-moment annular Fourier theorem.

math.PR↗

arXiv2026

Deep Research as Rubric for Reinforcement Learning

Open-ended reasoning and long-form generation tasks lack reliable automatic verification signals for reward-based policy optimization. Rubrics offer a promising alternative, but existing approaches treat them as given artifacts -- either hand-crafted or prompt-generated -- and often miss the task-specific, knowledge-intensive dimensions that matter most, distorting the reward signal. Our key observation is that rubric construction is itself a research problem: identifying what makes a response correct or insightful requires discovering and synthesizing external knowledge. We propose Deep Research as Rubric (DR-rubric), a two-stage framework for constructing such rubrics. Stage I elicits domain facts, structural constraints, and failure modes through iterative multi-turn agentic search; Stage II distills this evidence into atomic, independently verifiable constraints for GRPO-based policy optimization. Because the model under training can serve as its own rubric generator, DR-rubric-8B supports bootstrap rubric generation without frontier-model assistance. We evaluate on 6 benchmarks spanning agentic research and expert reasoning. Experiments show that DR-Rubric achieves strong competitive performance with only 1K -- 3K training instances, where GPT-5-generated rubrics particularly benefit breadth coverage on agentic tasks, Gemini-generated rubrics yield the most balanced performance across agentic and expert reasoning tasks, and bootstrap rubrics exhibit a specialization-to-rebalancing evolution achieving the best overall performance at the third iteration. Results demonstrate that reframing rubric construction from static evaluation templates into an evidence-driven research process yields more scalable, fine-grained reward signals for open-ended tasks.

cs.CL↗

arXiv2026

Scaling Behavior of Single LLM-Driven Multi-Agent Systems

The burgeoning field of LLM-based Multi-Agent Systems (MAS) promises to tackle complex tasks through collaborative intelligence, yet fundamental questions regarding their scaling behavior and intrinsic collective dynamics remain underexplored. This paper systematically investigates how the performance of a homogeneous MAS evolves as the number of agents increases, isolating the variable of collaboration from model or knowledge heterogeneity. We propose the Sequential Iterative Multi-Agent System (SIMAS) framework, a minimalist architecture centered on sequential inter-agent communication, to clearly observe scaling effects. Through extensive experiments across diverse tasks and model scales, we establish that MAS performance does not scale monotonically with agent count but follows a pattern of diminishing returns, governed by a trade-off between collaborative synergy and coordination overhead. Our findings reveal that effective MAS requires a sufficiently capable base LLM, that task type critically modulates the optimal agent count, and that collective intelligence is an emergent property contingent on strategic interaction design rather than a guaranteed outcome of agent plurality. The performance degradation stems coordination overhead rather than merely long-context failure, and the scaling tendency generalizes across interaction architectures like structured debate topologies. This work provides a foundational understanding of MAS scaling laws, offering practical guidance for designing efficient collaborative systems and challenging the prevailing assumption that more agents invariably lead to better performance.

cs.MA↗

arXiv2026

MARO: Learning Stronger Reasoning from Social Interaction

Humans face countless scenarios that require reasoning and judgment in daily life. However, existing large language model training methods primarily allow models to learn from existing textual content or solve predetermined problems, lacking experience in real scenarios involving interaction, negotiation, and competition with others. To address this, this paper proposes Multi-Agent Reward Optimization (MARO), a method that enables large language models (LLMs) to acquire stronger reasoning abilities by learning and practicing in multi-agent social environments. Specifically, MARO first addresses the sparse learning signal problem by decomposing final success or failure outcomes into each specific behavior during the interaction process; second, it handles the uneven role distribution problem by balancing the training sample weights of different roles; finally, it addresses environmental instability issues by directly evaluating the utility of each behavior. Experimental results demonstrate that MARO not only achieves significant improvements in social reasoning capabilities, but also that the abilities acquired through social simulation learning can effectively transfer to other tasks such as mathematical reasoning and instruction following. This reveals the tremendous potential of multi-agent social learning in enhancing the general reasoning capabilities of LLMs.

cs.AI↗

arXiv2025

AgentGroupChat-V2: Divide-and-Conquer Is What LLM-Based Multi-Agent System Need

Large language model based multi-agent systems have demonstrated significant potential in social simulation and complex task resolution domains. However, current frameworks face critical challenges in system architecture design, cross-domain generalizability, and performance guarantees, particularly as task complexity and number of agents increases. We introduces AgentGroupChat-V2, a novel framework addressing these challenges through three core innovations: (1) a divide-and-conquer fully parallel architecture that decomposes user queries into hierarchical task forest structures enabling dependency management and distributed concurrent processing. (2) an adaptive collaboration engine that dynamically selects heterogeneous LLM combinations and interaction modes based on task characteristics. (3) agent organization optimization strategies combining divide-and-conquer approaches for efficient problem decomposition. Extensive experiments demonstrate AgentGroupChat-V2's superior performance across diverse domains, achieving 91.50% accuracy on GSM8K (exceeding the best baseline by 5.6 percentage points), 30.4% accuracy on competition-level AIME (nearly doubling other methods), and 79.20% pass@1 on HumanEval. Performance advantages become increasingly pronounced with higher task difficulty, particularly on Level 5 MATH problems where improvements exceed 11 percentage points compared to state-of-the-art baselines. These results confirm that AgentGroupChat-V2 provides a comprehensive solution for building efficient, general-purpose LLM multi-agent systems with significant advantages in complex reasoning scenarios. Code is available at https://github.com/MikeGu721/AgentGroupChat-V2.

cs.CL↗

arXiv2025

MIRAGE: Exploring How Large Language Models Perform in Complex Social Interactive Environments

Large Language Models (LLMs) have shown remarkable capabilities in environmental perception, reasoning-based decision-making, and simulating complex human behaviors, particularly in interactive role-playing contexts. This paper introduces the Multiverse Interactive Role-play Ability General Evaluation (MIRAGE), a comprehensive framework designed to assess LLMs' proficiency in portraying advanced human behaviors through murder mystery games. MIRAGE features eight intricately crafted scripts encompassing diverse themes and styles, providing a rich simulation. To evaluate LLMs' performance, MIRAGE employs four distinct methods: the Trust Inclination Index (TII) to measure dynamics of trust and suspicion, the Clue Investigation Capability (CIC) to measure LLMs' capability of conducting information, the Interactivity Capability Index (ICI) to assess role-playing capabilities and the Script Compliance Index (SCI) to assess LLMs' capability of understanding and following instructions. Our experiments indicate that even popular models like GPT-4 face significant challenges in navigating the complexities presented by the MIRAGE. The datasets and simulation codes are available in \href{https://github.com/lime728/MIRAGE}{github}.

cs.CL↗

arXiv2024

AgentGroupChat: An Interactive Group Chat Simulacra For Better Eliciting Emergent Behavior

Language significantly influences the formation and evolution of Human emergent behavior, which is crucial in understanding collective intelligence within human societies. Considering that the study of how language affects human behavior needs to put it into the dynamic scenarios in which it is used, we introduce AgentGroupChat in this paper, a simulation that delves into the complex role of language in shaping collective behavior through interactive debate scenarios. Central to this simulation are characters engaging in dynamic conversation interactions. To enable simulation, we introduce the Verbal Strategist Agent, utilizing large language models to enhance interaction strategies by incorporating elements of persona and action. We set four narrative scenarios based on AgentGroupChat to demonstrate the simulation's capacity to mimic complex language use in group dynamics. Evaluations focus on aligning agent behaviors with human expectations and the emergence of collective behaviors within the simulation. Results reveal that emergent behaviors materialize from a confluence of factors: a conducive environment for extensive information exchange, characters with diverse traits, high linguistic comprehension, and strategic adaptability. During discussions on ``the impact of AI on humanity'' in AgentGroupChat simulation, philosophers commonly agreed that ``AI could enhance societal welfare with judicious limitations'' and even come to a conclusion that ``the essence of true intelligence encompasses understanding the necessity to constrain self abilities''. Additionally, in the competitive domain of casting for primary roles in films in AgentGroupChat, certain actors were ready to reduce their remuneration or accept lesser roles, motivated by their deep-seated desire to contribute to the project.

cs.AI↗

arXiv2024

Hear $π$ from Quantum Galperin Billiards

Galperin introduced an interesting method to learn the digits of $π$ by counting the collisions of two billiard balls and a hard wall. This paper studies two quantum versions of the Galperin billiards. It is shown that the digits of $π$ can be observed in the phase shifts of the quantum models.

quant-ph↗

arXiv2023

Direct Manipulation of quantum entanglement from the non-Hermitian nature of light-matter interaction

Biphoton process is an essential benchmark for quantum information science and technologies, while great efforts have been made to improve the coherence of the system for better quantum correlations. Nevertheless, we find that the non-Hermitian features induced by the atomic quantum interference could be well employed for the direct control of entanglement. We report the demonstration of exceptional point (EP) in biphotons by measuring the light-atom interaction as a natural non-Hermitian system, in which the electromagnetically induced transparency regime provides a powerful mechanism to precisely tune the non-Hermitian coupling strength. Such biphoton correlation is tuned within an unprecedented large range from Rabi oscillation to antibunching-exponential-decay, also indicating high-dimensional entanglement within the strong and weak light-matter coupling regimes. The EP at the transition point between the two regimes is clearly observed with the biphoton quantum correlation measurements, exhibiting a single exponential decay and manifesting the coalesced single eigenstate. Our results provide a unique method to realize the controllability of natural non-Hermitian processes without the assistance of artificial photonic structures, and paves the way for quantum control by manipulating the non-Hermitian features of the light-matter interaction.

quant-ph↗

arXiv2023

Effective potential engineering by emergent anisotropy in a tunable open-access microcavity

Photonic spin-orbit (SO) coupling is an important physical mechanism leading to numerous interesting phenomena in the systems of microcavity photons and exciton-polaritons. We report the effect of SO coupling in a tunable open-access microcavity embedded with anisotropic active media. The SO coupling associated with the TE-TM splitting results in an emergent anisotropy, which further leads to fine energy splittings allowing clear observation of the full set of eigenstates, in sharp contrast with the isotropic situation which leads to the isotropic eigenstates of spin vortices. We show that the photonic potential can be engineered by playing with the relation between the emergent anisotropy and the cavity ellipticity. All the experimental results are well reproduced by the degenerate perturbation theory. Our results constitute a significant extension to the research field of microcavity spinoptronics, with potential applications in polarization control and optical property measurement of photonic devices and materials.

physics.optics↗

arXiv2023

Direct generation of time-energy-entangled W triphotons in atomic vapor

Sources of entangled multiphotons are not only essential for fundamental tests of quantum foundations, but are also the cornerstone of a variety of optical quantum technologies today. Over past three decades, tremendous efforts have been devoted to creating multiphoton entanglement by multiplexing existing biphoton sources with linear optics and postselections. Different from all previous protocols, here we report, for the first time, the observation of continuous-mode time-energy-entangled W-class triphotons with an unprecedented generation rate directly through the process of spontaneous six-wave mixing (SSWM) in a four-level triple-Lambda atomic vapor cell. Facilitated by electromagnetically induced transparency and coherence control, our SSWM scheme enables versatile narrowband triphoton generation with many intriguing properties including long temporal coherence and controllable waveforms, ideal for implementing long-distance quantum communications, networking, and information processing by interfacing photons and atoms. Most importantly, our work paves a way for the development of a reliable and efficient genuine triphoton source, thus making the research on multiphoton entanglement within easy reach.

quant-ph↗

arXiv2022

Atomic Coherence Assisted Multipartite Entanglement Generation with DELC Four-Wave Mixing

Multipartite entanglement plays an important role in quantum information processing and quantum metrology. Here, the dressing-energy-level-cascaded (DELC) four-wave mixing (FWM) processes are proposed to generate all-optical controlled multipartite entanglement within a single device. The entanglement characteristics of the produced states of light are characterized by applying the Duan criterion and the positivity under partial transposition criterion. Moreover, by using an internal dressing field to modulate atomic coherence, multiple quantum coherent channels of FWM are simultaneously constructed, which result in a great extension of entanglement mode number and quantum information capacity. We find that the violation of the entanglement criteria inequalities is coherent-channel dependent, and the produced states can be directly modulated via atomic coherence. Our system can integrate the generation and modulation of the entangled states in one process. It may help provide a compact method for realizing large scale quantum networks.

quant-ph↗

arXiv2022

Geodesic photon coupling and non-Hermitian exceptional point of microcavities on topologically curved space

Asymmetric microcavities supporting Whispering-gallery modes (WGMs) are of great significance for on-chip optical information processing. We define asymmetric microcavities on topologically curved surfaces, where the geodesic light trajectories completely reconstruct the cavity mode features. The quality factors of the lossy chaotic and island modes in flat cavities can be increased by up to ~200 times by the space curvature. Strong and weak coupling between modes of very different origins occur when the space curvature brings them into resonance, leading to a fine tailoring of the cavity photon energy and lifetime. Finally, we prove that by varying the overall loss, an exceptional point can be clearly observed at which both the cavity photon energy and lifetime become degenerate. Our work is at the crosspoint of optical chaotic dynamics, non-Hermitian physics and geodesic optical devices, and would open the novel area of geodesic microcavity photonics.

physics.optics↗

arXiv2021

Hierarchy of Nonlinear Entanglement Dynamics for Continuous Variables

The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate high-order Hamiltonians remains unclear. Here, we derive a hierarchy of sufficient and necessary conditions for the positive-partial-transposition separability of bipartite nonlinear quantum states. The proposed criteria detect the nonpositive-partial-transposition inseparability of higher-order moments of states, which provides a systematic framework for the characterization of this kind of entanglement. Through numerical simulation of cubic and quartic Hamiltonians, we demonstrate the existence and competition of a hierarchy of entanglement witnesses, revealing the mechanism underlying such entanglement. Our results may provide a new direction in continuous variable quantum information processing.

quant-ph↗