arXiv subjects

Ruoxiang Xu

Publications and source records attributed to Ruoxiang Xu.

3 recordsLinked to original sources

arXiv2026

FlashPDE: A Drop-In Fused Triton Operator Library for Neural PDE Solvers

Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators. We present FlashPDE, a drop-in fused operator library for grid-based scientific machine learning. FlashPDE replaces fragmented PyTorch finite-difference execution with differentiable Triton kernels. Each operator integrates fused stencil evaluation, an analytic discrete-adjoint backward pass, and boundary-gradient correction within a unified PyTorch autograd Function interface. The library provides 14 differentiable PDE operators covering 17 configurations across 1D--3D elliptic, parabolic, and Navier--Stokes systems, while remaining independent of neural architectures and training strategies. Experiments on an NVIDIA A100 GPU show that FlashPDE reduces peak memory usage by up to 37.0x compared with coordinate-based automatic differentiation and reduces CUDA kernel launches by up to 3.5x compared with eager PyTorch finite-difference implementations. Across six representative PDE benchmarks, FlashPDE achieves up to 2.30x end-to-end time-to-solution speedup and up to 19.2x kernel-level acceleration while maintaining numerical agreement with PyTorch finite-difference references. FlashPDE provides a hardware-efficient execution layer that bridges differentiable PDE solvers and GPU-optimized numerical computation within the PyTorch ecosystem.

cs.LG↗

arXiv2025

Vocabulary In-Context Learning in Transformers: Benefits of Positional Encoding

Numerous studies have demonstrated that the Transformer architecture possesses the capability for in-context learning (ICL). In scenarios involving function approximation, context can serve as a control parameter for the model, endowing it with the universal approximation property (UAP). In practice, context is represented by tokens from a finite set, referred to as a vocabulary, which is the case considered in this paper, \emph{i.e.}, vocabulary in-context learning (VICL). We demonstrate that VICL in single-layer Transformers, without positional encoding, does not possess the UAP; however, it is possible to achieve the UAP when positional encoding is included. Several sufficient conditions for the positional encoding are provided. Our findings reveal the benefits of positional encoding from an approximation theory perspective in the context of ICL.

cs.LG↗

arXiv2024

DAE-Fuse: An Adaptive Discriminative Autoencoder for Multi-Modality Image Fusion

In extreme scenarios such as nighttime or low-visibility environments, achieving reliable perception is critical for applications like autonomous driving, robotics, and surveillance. Multi-modality image fusion, particularly integrating infrared imaging, offers a robust solution by combining complementary information from different modalities to enhance scene understanding and decision-making. However, current methods face significant limitations: GAN-based approaches often produce blurry images that lack fine-grained details, while AE-based methods may introduce bias toward specific modalities, leading to unnatural fusion results. To address these challenges, we propose DAE-Fuse, a novel two-phase discriminative autoencoder framework that generates sharp and natural fused images. Furthermore, We pioneer the extension of image fusion techniques from static images to the video domain while preserving temporal consistency across frames, thus advancing the perceptual capabilities required for autonomous navigation. Extensive experiments on public datasets demonstrate that DAE-Fuse achieves state-of-the-art performance on multiple benchmarks, with superior generalizability to tasks like medical image fusion.

cs.CV↗