Scalable GPU-Accelerated Euler Characteristic Curves: Optimization and Differentiable Learning for PyTorch

• URL: http://arxiv.org/abs/2510.20271v1
• Date: Thu, 23 Oct 2025 06:59:07 GMT
• Title: Scalable GPU-Accelerated Euler Characteristic Curves: Optimization and Differentiable Learning for PyTorch
• Authors: Udit Saxena,
• Abstract summary: We present optimized GPU kernels for the Euler Characteristic Curve (ECC) achieving 16-2000"O speedups over prior GPU implementations on synthetic grids.<n>We introduce a differentiable PyTorch layer enabling end-to-end learning.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Topological features capture global geometric structure in imaging data, but practical adoption in deep learning requires both computational efficiency and differentiability. We present optimized GPU kernels for the Euler Characteristic Curve (ECC) computation achieving 16-2000\"O speedups over prior GPU implementations on synthetic grids, and introduce a differentiable PyTorch layer enabling end-to-end learning. Our CUDA kernels, optimized for Ampere GPUs use 128B-coalesced access and hierarchical shared-memory accumulation. Our PyTorch layer learns thresholds in a single direction via a Differentiable Euler Characteristic Transform-style sigmoid relaxation. We discuss downstream relevance, including applications highlighted by prior ECC work, and outline batching/multi-GPU extensions to broaden adoption.

Related papers

• GPU-Accelerated Algorithms for Graph Vector Search: Taxonomy, Empirical Study, and Research Directions [54.570944939061555]
  We present a comprehensive study of GPU-accelerated graph-based vector search algorithms.<n>We establish a detailed taxonomy of GPU optimization strategies and clarify the mapping between algorithmic tasks and hardware execution units.<n>Our findings offer clear guidelines for designing scalable and robust GPU-powered approximate nearest neighbor search systems.
  arXiv  Detail & Related papers  (2026-02-10T16:18:04Z)
• A User's Guide to $\texttt{KSig}$: GPU-Accelerated Computation of the Signature Kernel [12.111848705677138]
  The signature kernel is a positive definite kernel for sequential and temporal data.<n>In this chapter, we give a short introduction to $textttKSig$, a $textttScikit-Learn$ compatible Python package that implements various GPU-accelerated algorithms for computing signature kernels.
  arXiv  Detail & Related papers  (2025-01-13T09:11:13Z)
• Fully-fused Multi-Layer Perceptrons on Intel Data Center GPUs [3.7101665559244874]
  This paper presents a SYCL implementation of Multi-formedLayer Perceptrons (MLPs) for the Intel Data Center GPU Max 1550. We show with a simple model that this results in a significant increase in arithmetic intensity, leading to improved performance, especially for inference.
  arXiv  Detail & Related papers  (2024-03-26T11:38:39Z)
• Accelerating Machine Learning Primitives on Commodity Hardware [0.0]
  We present an extensive study of the Sliding Window convolution technique as a more efficient alternative to the commonly used General Matrix multiplication (GEMM) based convolution in Deep Neural Networks (DNNs) Our results suggest that the Sliding Window computation kernels can outperform GEMM-based convolution on a CPU and even on dedicated hardware accelerators. This could promote a wider adoption of AI on low-power and low-memory devices without the need for specialized hardware.
  arXiv  Detail & Related papers  (2023-10-08T16:26:18Z)
• GloptiNets: Scalable Non-Convex Optimization with Certificates [61.50835040805378]
  We present a novel approach to non-cube optimization with certificates, which handles smooth functions on the hypercube or on the torus. By exploiting the regularity of the target function intrinsic in the decay of its spectrum, we allow at the same time to obtain precise certificates and leverage the advanced and powerful neural networks.
  arXiv  Detail & Related papers  (2023-06-26T09:42:59Z)
• ParaGraph: Weighted Graph Representation for Performance Optimization of HPC Kernels [1.304892050913381]
  We introduce a new graph-based program representation for parallel applications that extends the Abstract Syntax Tree. We evaluate our proposed representation by training a Graph Neural Network (GNN) to predict the runtime of an OpenMP code region. Results show that our approach is indeed effective and has normalized RMSE as low as 0.004 to at most 0.01 in its runtime predictions.
  arXiv  Detail & Related papers  (2023-04-07T05:52:59Z)
• Efficient Graph Field Integrators Meet Point Clouds [59.27295475120132]
  We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds.
  arXiv  Detail & Related papers  (2023-02-02T08:33:36Z)
• Efficient Dataset Distillation Using Random Feature Approximation [109.07737733329019]
  We propose a novel algorithm that uses a random feature approximation (RFA) of the Neural Network Gaussian Process (NNGP) kernel. Our algorithm provides at least a 100-fold speedup over KIP and can run on a single GPU. Our new method, termed an RFA Distillation (RFAD), performs competitively with KIP and other dataset condensation algorithms in accuracy over a range of large-scale datasets.
  arXiv  Detail & Related papers  (2022-10-21T15:56:13Z)
• Accelerating Genetic Programming using GPUs [0.0]
  Genetic Programming (GP) has multiple applications in machine learning such as curve fitting, data modelling, feature selection, classification etc. This paper describes a GPU accelerated stack-based variant of the generational GP algorithm which can be used for symbolic regression and binary classification.
  arXiv  Detail & Related papers  (2021-10-15T06:13:01Z)
• Adaptive Elastic Training for Sparse Deep Learning on Heterogeneous Multi-GPU Servers [65.60007071024629]
  We show that Adaptive SGD outperforms four state-of-the-art solutions in time-to-accuracy. We show experimentally that Adaptive SGD outperforms four state-of-the-art solutions in time-to-accuracy.
  arXiv  Detail & Related papers  (2021-10-13T20:58:15Z)
• Efficient and Generic 1D Dilated Convolution Layer for Deep Learning [52.899995651639436]
  We introduce our efficient implementation of a generic 1D convolution layer covering a wide range of parameters. It is optimized for x86 CPU architectures, in particular, for architectures containing Intel AVX-512 and AVX-512 BFloat16 instructions. We demonstrate the performance of our optimized 1D convolution layer by utilizing it in the end-to-end neural network training with real genomics datasets.
  arXiv  Detail & Related papers  (2021-04-16T09:54:30Z)
• Kernel methods through the roof: handling billions of points efficiently [94.31450736250918]
  Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems. Recent advances have shown the benefits of a number of algorithmic ideas, for example combining optimization, numerical linear algebra and random projections. Here, we push these efforts further to develop and test a solver that takes full advantage of GPU hardware.
  arXiv  Detail & Related papers  (2020-06-18T08:16:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.