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Yifeng Yu

Publications and source records attributed to Yifeng Yu.

At least 19 recordsLinked to original sources
arXiv2026

$L^\infty$ Variational Approximation of the Aubry Set

Let $H\in C^\infty(\mathbb R^n\times\mathbb T^n)$ be a periodic Tonelli Hamiltonian with critical value $c$. For each $k\in\mathbb N$, let $u_k$ be the normalized minimizer of the variational functional introduced by Evans[7], \[ I_k[w]=\int_{\mathbb T^n} e^{kH(Dw,x)}\,dx, \qquad \int_{\mathbb T^n}w\,dx=0. \] If $u_\infty$ is a uniform limit of a subsequence of $\{u_k\}$ and the Mather quotient $({A}_M,\delta_M)$ satisfies $H^1( A_M,\delta_M)=0$, then $u_\infty$ is a critical subsolution that is strict outside ${{A}}$ and \[ {A} = \{x\in\mathbb T^n\,:\,Du_\infty(x)\ \text{exists and }H(Du_\infty(x),x)=c\}=\{x\in\mathbb T^n\,:\,u_\infty(x)=u_{-}(x)\}, \] where ${A}$ is the projected Aubry set and $u_{-}$ is the backward weak KAM solution associated with $u_\infty$. In particular, by the theorem of Fathi--Figalli--Rifford[10], this conclusion holds for all smooth Tonelli Hamiltonians on $\mathbb T^n$ when $n\leq3$. This characterization also suggests a natural numerical localization principle for approximating the entire Aubry set through near-contact sets between $u_k$ and its large-time backward Lax--Oleinik evolution.

math.AP↗
arXiv2026

Diffusion Quasi-Monte Carlo

We study high-dimensional numerical integration with respect to complex target measures using diffusion-based transport maps and randomized quasi-Monte Carlo (RQMC). Score-based diffusion models induce a deterministic probability flow ODE that transports a simple prior to the target, suggesting a principled way to transform low-discrepancy points on the unit cube into informative samples. We construct a cube-to-target map by composing a Gaussian base transformation (the component-wise inverse Gaussian CDF) with an Euler-discretized probability flow ODE. To retain unbiasedness under transport approximation, we formulate integration as importance sampling (IS) on the cube. Our main result provides verifiable conditions under which the resulting IS integrand satisfies the boundary growth condition, implying an $O(N^{-1+\epsilon})$ RMSE for scrambled nets. We then establish these conditions for diffusion probability-flow transport under mild bounded-derivative assumptions on the learned vector field, explicitly controlling the boundary singularities introduced by the inverse Gaussian CDF. Experiments range from a 2D mixture to 784D images and a 40,960D conditional vorticity-assimilation task; in the latter, blocked scrambled Sobol' sampling reduces the randomization standard deviation of nonlinear accuracy metrics at essentially unchanged online denoising cost. Together, these results give a theoretical and empirical foundation for combining diffusion generative modeling with high-precision RQMC integration.

math.NA↗
arXiv2026

Turbulent Flame Speed Can Increase under Curvature Smoothing

Curvature effects are expected to smooth flame-front wrinkles and thereby reduce turbulent flame speed. We construct a smooth three-dimensional periodic shear flow for which introducing Markstein curvature diffusivity instead increases the effective flame speed predicted by the level-set G-equation. This gives the first counterexample, within this model, to monotone slowdown under curvature smoothing and contrasts with the rigorous monotonicity result for two-dimensional shear flows. The example reveals a genuinely multidimensional mechanism in which local curvature smoothing can enhance, rather than suppress, large-scale front propagation.

math.AP↗
arXiv2026

On the Limits of Latent Reuse in Diffusion Models

Diffusion models are often trained in low-dimensional latent spaces, which are then reused for related but shifted datasets. In this work, we study when such latent reuse remains reliable under distribution shift. We consider a source-target setting in which both datasets are approximately low-dimensional but may lie near different subspaces. We show that freezing and reusing a source latent space induces a target-domain score error governed by two quantities: the principal-angle misalignment between the source and target subspaces, and the target ambient noise amplified by the diffusion time scale. Motivated by these limits, we further study mixed source-target training and characterize how the required shared latent dimension depends on the relative geometry of the two distributions. Our results provide theoretical guidance on when latent reuse is reliable and when learning a shared representation may be necessary.

stat.ML↗
arXiv2026

Nonexistence of vanishing-viscosity limits for mechanical Hamiltonian ergodic problems

For $\varepsilon>0$, let $\phi^\varepsilon$ be the solution of the ergodic problem \[ \frac12 |D\phi^\varepsilon|^2+F(x)-\varepsilon\Delta\phi^\varepsilon=c(\varepsilon) \qquad \text{on } \mathbb{T}^n, \] normalized by $\phi^\varepsilon(0)=0$. We construct a one-dimensional example with $F\in C^3$ for which the vanishing-viscosity limit $\lim_{\varepsilon\to0}\phi^\varepsilon$ does not exist. This gives a negative answer to a problem proposed by Jauslin, Kreiss, and Moser [10].

math.AP↗
arXiv2026

BubbleSpec: Turning Long-Tail Bubbles into Speculative Rollout Drafts for Synchronous Reinforcement Learning

Reinforcement Learning (RL) has become a cornerstone for improving the performance of Large Language Models (LLMs). However, its rollout phase constitutes a significant efficiency bottleneck, mainly arising from the long-tail bubbles across data parallel ranks, particularly in long-context scenarios where faster GPUs remain idle while waiting for stragglers. Existing solutions, such as partial rollout or asynchronous RL, mitigate these bubbles by compromising the algorithm's strict synchronous nature. Instead, we propose BubbleSpec, a novel framework that accelerates RL rollouts while strictly keeping the mathematical exactness. Instead of attempting to eliminate bubbles, BubbleSpec exploits them. We exploit the idle time windows of faster ranks to pre-generate rollout results for subsequent steps, serving as drafts for speculative decoding. Unlike prior speculative methods that rely on historical epoch similarity and warm-ups, BubbleSpec is agnostic to dataset size and provides immediate acceleration from the onset of training. Extensive evaluations demonstrate that BubbleSpec reduces decoding steps by 50% and increases rollout throughput by up to 1.8x. Critically, BubbleSpec is seamlessly compatible with various RL frameworks and strategies as it sustains the strict synchronous property of RL algorithms.

cs.LG↗
arXiv2026

InfoLaw: Information Scaling Laws for Large Language Models with Quality-Weighted Mixture Data and Repetition

Upweighting high-quality data in LLM pretraining often improves performance, but in datalimited regimes, especially under overtraining, stronger upweighting increases repetition and can degrade performance. However, standard scaling laws do not reliably extrapolate across mixture recipes or under repetitions, making the selection for optimal data recipes at scaling underdetermined. To solve this, we introduce InfoLaw (Information Scaling Laws), a data-aware scaling framework that predicts loss from consumed tokens, model size, data mixture weights, and repetition. The key idea is to model pretraining as information accumulation, where quality controls information density and repetition induces scaledependent diminishing returns. We first collect the model performance after training on datasets that vary in scale, quality distribution, and repetition level. Then we build up the modeling for information so that information accurately predicts those model performance. InfoLaw predicts performance on unseen data recipes and larger scale runs (up to 7B, 425B tokens) with 0.15% mean and 0.96% max absolute error in loss, and it extrapolates reliably across overtraining levels, enabling efficient data-recipe selection under varying compute budgets.

cs.CL↗
arXiv2026

Sharp global and almost everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations

We study the periodic homogenization of the viscous Hamilton--Jacobi equation \[ u_t^\varepsilon + \frac{1}{2}|Du^\varepsilon|^2 + V\!\left(\frac{x}{\varepsilon}\right) = \frac{\varepsilon}{2}\Delta u^\varepsilon \qquad \text{in } \mathbb{R}^n \times (0,\infty), \] with initial datum $g \in W^{1,\infty}(\mathbb{R}^n)$, where $V$ is Lipschitz continuous and $\mathbb{Z}^n$-periodic. We prove the sharp global estimate \[ |u^\varepsilon(x,t)-u(x,t)| \leq \varepsilon\!\left(C+\frac{n}{2}\log\!\left(\frac{\max\{t,\varepsilon\}}{\varepsilon}\right)\right) \qquad \text{for all } (x,t)\in \mathbb{R}^n \times [0,\infty), \] where $\varepsilon \in (0,1]$, $u$ solves the limiting (homogenized) equation and $C>0$ is a constant depending only on $\|Dg\|_{L^\infty(\mathbb{R}^n)}$, $\|DV\|_{L^\infty(\mathbb{R}^n)}$, and $n$. We further show that if $g$ is locally semiconcave, then \[|u^\varepsilon(x,t)-u(x,t)| \leq C_{x,t}\varepsilon \qquad \text{for a.e. } (x,t)\in \mathbb{R}^n \times (0,\infty),\] where $C_{x,t}$ depends on $(x,t)$, $\|Dg\|_{L^\infty(\mathbb{R}^n)}$, and $\|DV\|_{L^\infty(\mathbb{R}^n)}$. More precisely, the above improved rate holds at every point $(x,t)$ where $u(\cdot,t)$ is twice differentiable at $x$. In particular, this occurs for a.e. $x\in \mathbb{R}^n$, since $u(\cdot,t)$ is locally semiconcave. We conclude by raising the open problem of whether the same $O(\varepsilon |\log \varepsilon|)$ rate remains valid for general strictly convex Hamiltonians or general periodic diffusions.

math.AP↗
arXiv2026

Evaluating AI Grading on Real-World Handwritten College Mathematics: A Large-Scale Study Toward a Benchmark

Grading in large undergraduate STEM courses often yields minimal feedback due to heavy instructional workloads. We present a large-scale empirical study of AI grading on real, handwritten single-variable calculus work from UC Irvine. Using OCR-conditioned large language models with structured, rubric-guided prompting, our system produces scores and formative feedback for thousands of free-response quiz submissions from nearly 800 students. In a setting with no single ground-truth label, we evaluate performance against official teaching-assistant grades, student surveys, and independent human review, finding strong alignment with TA scoring and a large majority of AI-generated feedback rated as correct or acceptable across quizzes. Beyond calculus, this setting highlights core challenges in OCR-conditioned mathematical reasoning and partial-credit assessment. We analyze key failure modes, propose practical rubric- and prompt-design principles, and introduce a multi-perspective evaluation protocol for reliable, real-course deployment. Building on the dataset and evaluation framework developed here, we outline a standardized benchmark for AI grading of handwritten mathematics to support reproducible comparison and future research.

cs.LG↗
arXiv2026

Geometry of the Minimal Level Set of the Effective Hamiltonian in Two Dimensions

In this paper, we characterize the geometric structure of the boundary of the minimal level set $F_0$ of the effective Hamiltonian $\overline{H}$ associated with the mechanical Hamiltonian \[ H(p,x)=\frac12|p|^2+V(x) \] in dimension $n=2$, where $V$ on $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$ has a unique maximum and Hessian at this maximizer has two distinct negative eigenvalues. For $n=2$, the geometry of the level sets of $\overline{H}$ strictly above the minimum has been largely understood since the 1990s, mainly through the equivalent formulation in terms of stable norms; we fill the remaining gap at the minimal level by providing an explicit, verifiable characterization of $\partial F_0$. In particular, we show that $p \in \partial F_0$ does not lie on any flat edge if and only if $\partial F_0$ is differentiable at $p$ and its outer normal direction is irrational, except possibly at one exceptional pair of points $\pm p_0$. Consequently, flat edges are dense along $\partial F_0$. We also construct an example demonstrating that this exceptional pair can occur, showing the result is sharp.

math.AP↗
arXiv2026

Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guarantees

Score-based diffusion models have become a powerful framework for generative modeling, with score estimation as a central statistical bottleneck. Existing guarantees for score estimation largely focus on light-tailed targets or rely on restrictive assumptions such as compact support, which are often violated by heavy-tailed data in practice. In this work, we study conventional (Gaussian) score-based diffusion models when the target distribution is heavy-tailed and belongs to a Sobolev class with smoothness parameter $\beta>0$. We consider both exponential and polynomial tail decay, indexed by a tail parameter $\gamma$. Using kernel density estimation, we derive sharp minimax rates for score estimation, revealing a qualitative dichotomy: under exponential tails, the rate matches the light-tailed case up to polylogarithmic factors, whereas under polynomial tails the rate depends explicitly on $\gamma$. We further provide sampling guarantees for the associated continuous reverse dynamics. In total variation, the generated distribution converges at the minimax optimal rate $n^{-\beta/(2\beta+d)}$ under exponential tails (up to logarithmic factors), and at a $\gamma$-dependent rate under polynomial tails. Whether the latter sampling rate is minimax optimal remains an open question. These results characterize the statistical limits of score estimation and the resulting sampling accuracy for heavy-tailed targets, extending diffusion theory beyond the light-tailed setting.

math.ST↗
arXiv2025

SingMOS-Pro: An Comprehensive Benchmark for Singing Quality Assessment

Singing voice generation progresses rapidly, yet evaluating singing quality remains a critical challenge. Human subjective assessment, typically in the form of listening tests, is costly and time consuming, while existing objective metrics capture only limited perceptual aspects. In this work, we introduce SingMOS-Pro, a dataset for automatic singing quality assessment. Building on our preview version SingMOS, which provides only overall ratings, SingMOS-Pro extends the annotations of the additional data to include lyrics, melody, and overall quality, offering broader coverage and greater diversity. The dataset contains 7,981 singing clips generated by 41 models across 12 datasets, spanning from early systems to recent state-of-the-art approaches. Each clip is rated by at least five experienced annotators to ensure reliability and consistency. Furthermore, we investigate strategies for effectively utilizing MOS data annotated under heterogeneous standards and benchmark several widely used evaluation methods from related tasks on SingMOS-Pro, establishing strong baselines and practical references for future research. The dataset is publicly available at https://huggingface.co/datasets/TangRain/SingMOS-Pro.

cs.SD↗
arXiv2025

RLHGNN: Reinforcement Learning-driven Heterogeneous Graph Neural Network for Next Activity Prediction in Business Processes

Next activity prediction represents a fundamental challenge for optimizing business processes in service-oriented architectures such as microservices environments, distributed enterprise systems, and cloud-native platforms, which enables proactive resource allocation and dynamic service composition. Despite the prevalence of sequence-based methods, these approaches fail to capture non-sequential relationships that arise from parallel executions and conditional dependencies. Even though graph-based approaches address structural preservation, they suffer from homogeneous representations and static structures that apply uniform modeling strategies regardless of individual process complexity characteristics. To address these limitations, we introduce RLHGNN, a novel framework that transforms event logs into heterogeneous process graphs with three distinct edge types grounded in established process mining theory. Our approach creates four flexible graph structures by selectively combining these edges to accommodate different process complexities, and employs reinforcement learning formulated as a Markov Decision Process to automatically determine the optimal graph structure for each specific process instance. RLHGNN then applies heterogeneous graph convolution with relation-specific aggregation strategies to effectively predict the next activity. This adaptive methodology enables precise modeling of both sequential and non-sequential relationships in service interactions. Comprehensive evaluation on six real-world datasets demonstrates that RLHGNN consistently outperforms state-of-the-art approaches. Furthermore, it maintains an inference latency of approximately 1 ms per prediction, representing a highly practical solution suitable for real-time business process monitoring applications. The source code is available at https://github.com/Joker3993/RLHGNN.

cs.SE↗
arXiv2025

QuaDMix: Quality-Diversity Balanced Data Selection for Efficient LLM Pretraining

Quality and diversity are two critical metrics for the training data of large language models (LLMs), positively impacting performance. Existing studies often optimize these metrics separately, typically by first applying quality filtering and then adjusting data proportions. However, these approaches overlook the inherent trade-off between quality and diversity, necessitating their joint consideration. Given a fixed training quota, it is essential to evaluate both the quality of each data point and its complementary effect on the overall dataset. In this paper, we introduce a unified data selection framework called QuaDMix, which automatically optimizes the data distribution for LLM pretraining while balancing both quality and diversity. Specifically, we first propose multiple criteria to measure data quality and employ domain classification to distinguish data points, thereby measuring overall diversity. QuaDMix then employs a unified parameterized data sampling function that determines the sampling probability of each data point based on these quality and diversity related labels. To accelerate the search for the optimal parameters involved in the QuaDMix framework, we conduct simulated experiments on smaller models and use LightGBM for parameters searching, inspired by the RegMix method. Our experiments across diverse models and datasets demonstrate that QuaDMix achieves an average performance improvement of 7.2% across multiple benchmarks. These results outperform the independent strategies for quality and diversity, highlighting the necessity and ability to balance data quality and diversity.

cs.CL↗
arXiv2025

Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration

Score-based diffusion models have emerged as powerful tools in generative modeling, yet their theoretical foundations remain underexplored. In this work, we focus on the Wasserstein convergence analysis of score-based diffusion models. Specifically, we investigate the impact of various discretization schemes, including Euler discretization, exponential integrators, and midpoint randomization methods. Our analysis provides a quantitative comparison of these discrete approximations, emphasizing their influence on convergence behavior. Furthermore, we explore scenarios where Hessian information is available and propose an accelerated sampler based on the local linearization method. We demonstrate that this Hessian-based approach achieves faster convergence rates of order $\widetilde{\mathcal{O}}\left(\frac{1}{\varepsilon}\right)$ significantly improving upon the standard rate $\widetilde{\mathcal{O}}\left(\frac{1}{\varepsilon^2}\right)$ of vanilla diffusion models, where $\varepsilon$ denotes the target accuracy.

stat.ML↗
arXiv2024

Does Yakhot's growth law for turbulent burning velocity hold?

Using formal renormalization theory, Yakhot derived in ([32], 1988) an $O\left(\frac{A}{\sqrt{\log A}}\right)$ growth law of the turbulent flame speed with respect to large flow intensity $A$ based on the inviscid G-equation. Although this growth law is widely cited in combustion literature, there has been no rigorous mathematical discussion to date about its validity. As a first step towards unveiling the mystery, we prove that there is no intermediate growth law between $O\left(\frac{A}{\log A}\right)$ and $O(A)$ for two dimensional incompressible Lipschitz continuous periodic flows with bounded swirl sizes. In particular, we do not assume the non-degeneracy of critical points. Additionally, other examples of flows with lower regularity, Lagrangian chaos, and related phenomena are also discussed.

math.AP↗
arXiv2024

Muskits-ESPnet: A Comprehensive Toolkit for Singing Voice Synthesis in New Paradigm

This research presents Muskits-ESPnet, a versatile toolkit that introduces new paradigms to Singing Voice Synthesis (SVS) through the application of pretrained audio models in both continuous and discrete approaches. Specifically, we explore discrete representations derived from SSL models and audio codecs and offer significant advantages in versatility and intelligence, supporting multi-format inputs and adaptable data processing workflows for various SVS models. The toolkit features automatic music score error detection and correction, as well as a perception auto-evaluation module to imitate human subjective evaluating scores. Muskits-ESPnet is available at \url{https://github.com/espnet/espnet}.

cs.SD↗