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Hongyu Chen

Publications and source records attributed to Hongyu Chen.

At least 19 recordsLinked to original sources
arXiv2026

Positive solutions of Yamabe-type equations with general potentials

Let $(M^n,g)$ be a smooth closed connected Riemannian manifold of dimension $n\ge3$, and let $ψ\in C^\infty(M,\mathbb R)$. We prove that the equation $$ -\frac{4(n-1)}{n-2}Δ_g u+ψu=u^{\frac{n+2}{n-2}} $$ has a smooth positive solution if and only if its linear part has positive first eigenvalue. In dimensions $n\ge6$, the proof combines an energy estimate under exact local mass constraints with an intersection argument for finite cycles of atomic measures; dimensions $3\le n\le5$ follow from the theorem of Bahri and Brezis.

math.AP↗
arXiv2026

Complete conformal metrics of constant positive scalar curvature with prescribed isolated singularities

Let $(M^n,g)$ be a smooth closed connected Riemannian manifold of dimension $n\ge3$ with positive Yamabe constant. For any prescribed finite set $Λ\subset M$ containing at least two points, we construct a complete metric on $M\setminusΛ$, conformal to $g$, with scalar curvature $n(n-1)$. At each singularity, the local geometric term in the reduced action comes from the first nonzero homogeneous metric term of degree at most $(n-2)/2$ in finite conformal normal coordinates, or from the mass of the Green function metric when all such terms vanish. We completely solve Schoen's conjecture about singular Yamabe problem.

math.DG↗
arXiv2026

Continuation and convergence for the higher dimensional conformal Chern--Calabi flow

We study the volume-normalized gradient flow of the squared Chern scalar curvature on compact Hermitian manifolds of complex dimension $n\ge3$. The flow extends smoothly past a finite time if the spatial supremum of Chern scalar curvature belongs to $L^2$ in time. A uniform curvature bound in the evolving $L^p$ norm, for one fixed $p>n$, gives global existence and smooth convergence of the whole trajectory to a constrained critical metric. On Chern scalar-flat backgrounds, small initial $L^p$ curvature gives exponential convergence to the background. A corresponding condition on the trace-free first Chern--Ricci form gives exponential convergence on Chern--Ricci-flat Hermitian and positive Kähler--Einstein backgrounds. The smallness thresholds are independent of the initial higher derivatives. We also construct constant Chern scalar curvature backgrounds of either sign with arbitrarily small smooth perturbations whose solutions, if global, cannot converge back to the background.

math.CV↗
arXiv2026

MGE-PO: Entropy-Aware Credit Assignment for Mathematical Reasoning

GRPO assigns the same group-relative advantage to equally rewarded responses within a question, leaving their generation uncertainty unused. We introduce MGE-PO, centered on four-quadrant (4Q) advantage shaping that combines verified correctness with rollout generation entropy. Correctness determines the sign of an additional correction, while entropy controls its magnitude: lower-entropy successes receive larger bonuses and higher-entropy failures receive larger penalties. An online entropy-based question curriculum supports this credit rule using cached rollout measurements. At the final checkpoint after eight training epochs on Qwen3-8B-Base, adding 4Q across three policy optimization settings yields absolute gains of 3.23-3.69% in six-benchmark macro avg@32 and 4.24-11.06% in macro pass@32. On Qwen2.5-7B-Base, the complete configuration raises four-benchmark macro avg@32 from 41.5% to 45.4%.

cs.CL↗
arXiv2026

Every Batch Is Its Own Validation Set: Leave-One-Out Gradient Matching for Online Data Selection in LLM Fine-Tuning

Online batch selection fine-tunes a language model on the most useful part of each candidate batch. Selectors that match the gradient of the candidate batch are attractive because they need no held-out data, yet they rarely beat training on the whole batch. We show why. In-sample gradient matching uses every example as part of its own target, so its objective credits each example with its own gradient noise. This is the covariance penalty that makes training error optimistic, now sitting on the diagonal of the gradient Gram matrix: it steers selection toward the noisiest examples and makes the full batch the best solution the objective can reach. The fix costs nothing. For each example, the other candidates form an independent sample of the data distribution, so removing the diagonal turns the matching objective into an unbiased estimate of the update's error with respect to the population gradient. The minimizer of this leave-one-out objective weights examples by their gradient signal-to-noise ratio (SNR), and whenever per-example SNR is heterogeneous enough, half of a batch yields a lower-error update than the whole batch; we give the exact condition. We build \method{} on this principle. It computes the Gram matrix in the metric of the Adam preconditioner during the ordinary backward pass, selects a weighted subset greedily with a $(1-e^{-γ})$ guarantee, and uses no held-out data. Across four fine-tuning tasks and seven backbones from 1.5B to 8B parameters, LOOM improves on full-batch training by 2.3 and 2.4 points on Llama-3.1-8B and Qwen2.5-7B, exceeds every in-sample gradient matcher by 2.4 points and the validation-guided GREATS and OPUS by 1.6--2.0, and selects injected label noise at under a fifth of its base rate.

cs.LG↗
arXiv2026

Quantum Fidelity Landscape-Guided Prior Calibration for Single-Circuit QGAN Image Generation

Quantum Generative Adversarial Networks (QGANs) have emerged as representative generative models in the Noisy Intermediate-Scale Quantum (NISQ) era and have attracted increasing attention in quantum machine learning. However, most existing QGAN methods rely on patch-based decomposition strategies, which weaken the global consistency of generated images and increase quantum resource overhead. In this work, we investigate a simpler approach: pixel-level, end-to-end image generation using a single-quantum-circuit QGAN. By analyzing the structural matching relationship between the quantum prior and the target data distribution in Hilbert space, we provide a new theoretical perspective for understanding the training behavior of naive end-to-end QGANs. Specifically, we introduce the Quantum Fidelity Landscape (QFL), defined as the pairwise-fidelity structure induced by an ensemble of quantum states and preserved under shared unitary transformations of the quantum generation process. We show that, under a fixed Lipschitz readout, this invariant imposes a one-sided bound on decoded sample separation, motivating calibration of the prior-induced QFL before adversarial training. To validate this theoretical insight, we propose BasicQGAN, a QGAN framework incorporating quantum prior calibration. Before adversarial optimization, BasicQGAN aligns the prior-induced QFL with the data-induced QFL. Experimental results on small-scale grayscale image datasets show that BasicQGAN achieves stable and effective end-to-end pixel-level image generation while requiring fewer qubits and trainable parameters than representative patch-based quantum generators. Furthermore, experiments with different initial quantum-state ensembles show that QFL-calibrated ensembles achieve better generative performance.

quant-ph↗
arXiv2026

Collaborative Principle Evolution via Evidence Transfer for Scientific Discovery

Large Language Model (LLM)-based agents promise to automate scientific discovery, yet exploring the vast hypothesis space remains costly. Existing principle-evolution methods accelerate this loop, but operate sequentially, which caps exploration breadth and wastes wall-clock time on challenging problems. To address this, we formulate collaborative scientific discovery as evidence transfer between parallel principle-evolution branches. We present COEVOLVE, which realizes this transfer through a coordination core over parallel branches. By integrating value-of-information-gated routing and context-discounted likelihood injection, COEVOLVE enables branches to collaborate through shared measurements while keeping their principle posteriors separate. Across six scientific-discovery tasks under a matched evaluation budget, COEVOLVE attains a mean solution quality of 66.5% versus 57.0% for single-branch principle evolution, with a 1.80x mean wall-clock speedup on the GPT-5.6-Terra backbone; on five auto-research tasks delegated to an autonomous research harness, it is the only arm whose mean stays above the published SOTA anchor on every task. These results establish when evidence sharing accelerates parallel discovery and when transfer safeguards are necessary to limit negative or inert transfers

cs.LG↗
arXiv2026

Sustained Orbital Motion Driven by Circularly Polarized Light in Nanoscale Stator-Rotor Architectures

Light-induced forces and torques offer a versatile strategy for remotely actuating microscopic objects, enabling breakthroughs including optical trapping and light-driven nanomachines. Extending such optical actuation to sustained cyclic motion, however, requires fundamentally distinct designs and, in particular, forces capable of delivering nonzero mechanical work over repeated cycles. Here, we demonstrate via simulations a nanoscale stator-rotor architecture, which achieves persistent orbital motion of a spherical rotor under circularly polarized plane-wave illumination. An off-center rotor displacement defines a stator-rotor structural polarity. Optical helicity coupled to this polarity generates a tangential force perpendicular to the instantaneous stator-rotor direction; as the rotor moves around the stator, the force direction rotates with it. Electrodynamic symmetry analysis identifies this response as arising from antisymmetric, nonconservative forces that produce nonzero closed-cycle work, whereas linear polarization yields symmetric, conservative responses with zero closed-cycle work. Material screening and Bayesian optimization identify an Ag-nanoshell design region, while Pareto analysis balances tangential actuation and radial confinement. A balanced candidate is predicted to lower the maximum steady-state temperature rise from 56.2 to 20.9 K relative to Au at the same light intensity. Brownian-dynamics simulations further show confined, helicity-defined orbital motion, with all 32 trajectories retaining the same circulation direction. These results establish a symmetry-guided route toward sustained cyclic optical actuation at the nanoscale.

physics.optics↗
arXiv2026

Pogorelov interior estimates and a Liouville theorem for the complex Monge--Ampère equation

We prove a Pogorelov interior estimate for strictly plurisubharmonic solutions of the complex Monge-Ampère equation $\det(u_{i\bar{j}})=1$ with homogeneous Dirichlet data under the condition that, for some constant $κ\geq 1$, $(κu_{i\bar{j}}-u_{is}u^{s\bar{t}}u_{\overline{tj}})$ is non-negative definite. For $κ=1$, this gives the estimate for real convex solutions. The estimate depends only on the dimension, $κ$, and the $C^0$ and $C^1$ norms of the solution. As an application, every smooth entire convex solution of $\det(u_{i\bar{j}})=1$ on $\mathbb{C}^n$ is a real quadratic polynomial. The same conclusion holds if real convexity is assumed only outside a compact subset of $\mathbb{C}^n$.

math.AP↗
arXiv2026

Higher-Order Topological States with Cleavage-Dependent Dirac Mass

Topological quantum chemistry based on local charge profiles lacks predictive power for the crystalline cleavage of higher-order topological insulators (HOTIs). By cleaving an obstructed atomic insulator, we discover a topological phase characterized by e/2-fractional charges localized at precisely half of the corners, while the remaining empty corners host complementary vacancies of interstice charge. These zero-energy charge vacancies and topological corners form a spatially balanced geometry, separately localized at four corners. Crucially, we demonstrate that the emergence of corner zero modes dictates that specific dangling bonds acting as the mass of a Dirac fermion-must explicitly expose in, and subtly slope toward, the corner regions. This strict directionality is verified by the anisotropic evolution of the mass term within a (2+1) dimensional parameter space. Moreover, we find that the topological corners acquire lower entanglement entropy compared to the bulk, a behavior opposite to that of the real-space energy distribution which forms an energy-entropy compensation, essentially derived from the topological charge compensation. Our work paves the way for the local chemical environment at topological boundaries, and demonstrates the higher order quantum transport counterparts for high energy Dirac physics.

cond-mat.mes-hall↗
arXiv2026

AI-Generated Measurements for Identification and Inference with Missing Data: A Weak Shadow Variable Approach

Across business and social science applications, outcomes are often missing in ways that depend on the unobserved outcomes themselves. In service systems, for example, whether a customer submits a rating depends on the rating they would have provided. Such missing-not-at-random (MNAR) mechanisms make population quantities difficult to identify without strong assumptions on the observation process. Meanwhile, rich unstructured data, such as customer interaction histories, are increasingly available and can be used to construct structured measurements using tools such as large language models (LLMs). In this work, we develop an assumption-lean partial identification framework that uses such measurements as weak shadow variables, defined as outcome-informative proxies that are conditionally independent of missingness given the true outcome and observed covariates. Importantly, they need not accurately predict missing outcomes or satisfy the completeness requirement in the classical shadow variable literature. For identification, we characterize sharp bounds on population quantities through a pair of linear programs. For estimation and inference, we propose a localized penalized estimator that remains feasible under sampling error, and a subsampling algorithm for constructing confidence intervals. In semi-synthetic experiments using real customer-service dialogues, weak-shadow-variable intervals are about 89\% narrower than those without auxiliary information, while their midpoints have around 41\% lower estimation error than classical MNAR methods.

stat.ML↗
arXiv2026

CoQui: A Coordinate-Conditioned Quantum Implicit Generative Adversarial Network for End-to-End Image Generation

Quantum generative adversarial networks (QGANs) have attracted increasing attention for image generation using parameterized quantum circuits. Existing amplitude-based approaches face two key limitations: pixel locations are typically encoded by computational-basis indices or address qubits, causing quantum resources to grow with image resolution; meanwhile, jointly decoding many pixels from normalized quantum states introduces probability competition among pixels and limits precise pixel-wise control. To address these issues, we reformulate quantum image generation as coordinate-conditioned implicit function learning. Our method takes spatial coordinates and latent variables as inputs, uses a classical embedding network to generate input-dependent circuit parameters, and evaluates a variational quantum circuit at each coordinate. Pixel intensities are directly obtained from the expectation value of a dedicated color qubit, and a complete image is generated by querying all spatial coordinates. This design decouples image resolution from address-qubit requirements and avoids shared probability-normalization constraints across pixels. We further design a specialized variational quantum circuit to provide structural inductive bias for coordinate-conditioned generation. Simulated experiments on two benchmark datasets show that our method outperforms FRQI-based generation and PQWGAN in visual and quantitative quality while using fewer qubits, and also achieves better generation quality than the corresponding classical baseline.

quant-ph↗
arXiv2026

SVR: Self-Verifying Refinement via Joint Verdict-Confidence Reinforcement Learning for Adaptive Test-Time Compute

Scaling test-time computation can improve language-model reasoning, but uniform budgets waste computation on easy inputs, while verifier-guided refinement relies on external feedback. We introduce Self-Verifying Refinement (SVR), an oracle-free multi-turn reinforcement learning framework that learns to use self-verification as a compute-control policy. At each turn, the model produces a solution together with a discrete correctness verdict and a confidence score; it retains the current answer only when the verdict is Correct and confidence exceeds a threshold, and otherwise continues refinement using its own self-verification. Ground-truth correctness is used only to construct training rewards and is never exposed to the policy through refinement prompts or required at inference. SVR is trained with GRPO on fixed-horizon trajectories using rewards that promote solution correctness, calibration-aware self-verification, and stop-ready correct states; adaptive stopping is activated only at inference. On seven mathematical reasoning benchmarks with Qwen3.5-2B, SVR achieves a macro-average accuracy of 0.563 with only 2.99 inference turns on average. In the evaluated complete-system comparison, it exceeds standard GRPO, strong multi-turn baselines, and a fixed-budget oracle-guided score-feedback reference while requiring substantially fewer turns than fixed ten-turn inference. These results demonstrate that learned self-verification can serve as an effective internal control signal for answer retention and adaptive test-time compute allocation.

cs.AI↗
arXiv2026

Designing Service Systems from Textual Evidence

Designing service systems requires selecting among alternative configurations -- choosing the best chatbot variant, the optimal routing policy, or the most effective quality control procedure. In many service systems, the primary evidence of performance quality is textual -- customer support transcripts, complaint narratives, compliance review reports -- rather than the scalar measurements assumed by classical optimization methods. Large language models (LLMs) can read such textual evidence and produce standardized quality scores, but these automated judges exhibit systematic biases that vary across alternatives and evaluation instances. Human expert review remains accurate but costly. We study how to identify the best service configuration with high confidence while minimizing expensive human audits, given that automated evaluation is cheap but biased. We formalize this as a sequential decision problem where a biased proxy score is observed for every evaluation, and a verified outcome can be acquired selectively at additional cost. We prove that LLM-only selection fails under arm-dependent bias, and that naive selective-audit estimators can be asymptotically biased. We develop an estimator combining proxy scores with inverse-propensity-weighted residuals and construct anytime-valid confidence sequences. Our algorithm, PP-LUCB, jointly decides which alternatives to evaluate and whether to request human audits, concentrating reviews where the LLM judge is least reliable. We prove correctness and establish instance-dependent cost bounds showing near-optimal efficiency. On a customer support ticket classification task, our algorithm correctly identifies the best model in 40/40 trials while achieving 90\% audit cost reduction.

cs.LG↗
arXiv2026

NanoBTE: Fast Iterative Solution of the Phonon Boltzmann Transport Equation for Nanoscale Heat Transport

Nanoscale heat dissipation has become a critical challenge in advanced semiconductor devices, where phonon transport can strongly deviate from the classical Fourier description due to the boundary scattering and ballistic effects. In this work, we propose NanoBTE, a deterministic finite-volume solver for the non-gray phonon Boltzmann transport equation under the relaxation-time approximation. The solver supports complex two- and three-dimensional geometries, band-resolved phonon properties, discrete-ordinates angular quadrature, volumetric heat generation, and multiple phonon boundary conditions, including thermalizing, diffuse, and specular reflections. %To improve the efficiency of multiscale simulations, both sequential and synthetic iterative schemes are implemented, where the latter couples the microscopic phonon transport equation with a macroscopic diffusion-type temperature equation to accelerate convergence in near-diffusive regimes. Both sequential and synthetic iterative options are implemented for the steady-state solution. Furthermore, NanoBTE adopts a band-direction task decomposition strategy, enabling efficient MPI-based CPU parallelization and GPU acceleration of the dominant sparse transport operations.

cond-mat.mtrl-sci↗
arXiv2026

Regularity of Solutions to Monge-Ampère Equations on Stein Spaces

In this note, we study degenerate complex Monge-Ampère equations on singular Stein spaces with right-hand sides depending on the unknown. First, we prove continuity up to the boundary for solutions. Next, under a holomorphic peak-set condition, we prove local Hölder estimates on the regular locus, allowing the boundary datum to fail to be Hölder continuous at the singular boundary. This includes the case of finite singular boundary sets.

math.CV↗
arXiv2026

Position: Reasoning After Perception Means Reasoning Without Vision

A common belief in multimodal research is that the perceptual weaknesses of vision--language models can be compensated by stronger language reasoning (e.g., chain-of-thought, in-context learning, or external tools). We challenge this assumption. We argue that for a broad class of visual tasks hard to specify in language, failures stem from a structural fatality where the temporal decision of \textit{when} to reason strictly dictates the spatial constraint of \textit{where} reasoning takes place. When visual reasoning is deferred to language generation, current architectures do not merely delay computation; they displace it from the continuous visual representation to a discrete textual space. Consequently, the sequential ``Perception-then-Reasoning'' paradigm degenerates perception into a passive, one-off feature encoding process, rendering it functionally equivalent to ``Reasoning-in-Text-Space'', where task-critical spatial signals are collapsed before reasoning begins. We substantiate this claim with the Turing Eye Test (TET): tasks that must be resolved in \emph{visual space} and are hard to verbalize; results show text-only reasoning cannot remedy these perceptual failures. Our findings suggest rethinking the architectural divide: shifting from reasoning \textit{about} perception to reasoning \textit{within} perception. This facilitates actively reasoning-driven perception that operates directly on pixel-level visual representations, rather than within a collapsed textual space.

cs.CV↗