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Hao Yu

Publications and source records attributed to Hao Yu.

3 recordsLinked to original sources

arXiv2026

Spectral convergence of random feature method in one dimension

We first prove the spectral convergence of the random feature method (RFM) when used to solve second-order elliptic equations and eigenvalue problems in one dimension, provided that the solutions belong to Gevrey classes or Sobolev spaces. Second, we derive the convergence rate of RFM when integrated with the Partition of Unity Method (PUM) in terms of the patch size. Finally, we show that the singular values of the resulting random feature matrix decay exponentially, leading to exponential growth of the condition number. We also prove that PUM can mitigate this excessive singular-value decay.

math.NA↗

arXiv2026

H-Scale: Hessian-Guided Scale Refinement for NVFP4 Sub-Byte LLM Inference

The NVIDIA Blackwell architecture, with native support for the ultra-fine-grained NVFP4 format, opens new opportunities for accelerating large language model (LLM) inference. NVFP4's micro-block design, such as a group size of 16, offers strong representational flexibility for capturing local weight distributions and isolating outliers, but it also introduces a large and highly sensitive space of per-group scaling factors. Existing post-training quantization (PTQ) methods primarily focus on refining quantized weight values, leaving this scale-selection step underexplored. To address this gap, we propose \textbf{H-Scale}, a lightweight post-processing method for NVFP4 per-group scale refinement. Instead of minimizing plain weight reconstruction error, H-Scale selects hardware-valid group scales using a diagonal second-order proxy derived from calibration activations, thereby targeting layer output perturbation more directly. It is designed as a drop-in replacement for RTN-style scale selection in diverse NVFP4 pipelines, requires only modest offline calibration, and introduces strictly zero overhead at inference time. Under a fixed evaluation protocol, experiments on mainstream LLMs show that H-Scale generally improves a broad range of NVFP4 baselines and brings several variants closer to the BF16 reference.

cs.CL↗

arXiv2024

Generalization Error Estimates of Machine Learning Methods for Solving High Dimensional Schrödinger Eigenvalue Problems

We propose a machine learning method for computing eigenvalues and eigenfunctions of the Schrödinger operator on a $d$-dimensional hypercube with Dirichlet boundary conditions. The cut-off function technique is employed to construct trial functions that precisely satisfy the homogeneous boundary conditions. This approach eliminates the error caused by the standard boundary penalty method, improves the overall accuracy of the method, as demonstrated by the typical numerical examples. Under the assumption that the eigenfunctions belong to a spectral Barron space, we derive an explicit convergence rate of the generalization error of the proposed method, which does not suffer from the curse of dimensionality. We verify the assumption by proving a new regularity shift result for the eigenfunctions when the potential function belongs to an appropriate spectral Barron space. Moreover, we extend the generalization error bound to the normalized penalty method, which is widely used in practice.

math.NA↗