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In classical mechanics, motion is often described through relationships between spatial coordinates and time. A car moving along a straight highway with constant acceleration serves as a simple case where velocity is an explicit function of time. This scenario results in a linear equation, enabling straightforward analysis using basic differentiation techniques.In contrast, a satellite in circular orbit follows a path defined by an implicit function. The position of the satellite is constrained...
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Curves defined implicitly, where variables cannot be separated algebraically, require specialized techniques for analysis. The conchoid of Nicomedes exemplifies such a case. Its equation links x and y in a way that prevents isolation of one variable, making implicit differentiation essential to determine the slope and behavior at any point on the curve.The implicit form of the conchoid can be expressed as:To differentiate this equation, y is treated as a function of x, and the chain rule is...
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Deep Neural Networks for Image-Based Dietary Assessment
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GPU-Accelerated Adjoint Algorithmic Differentiation.

Felix Gremse1, Andreas Höfter2, Lukas Razik1

  • 1Experimental Molecular Imaging, RWTH Aachen University, Germany ; Software and Tools for Computational Engineering, RWTH Aachen University, Germany.

Computer Physics Communications
|March 5, 2016
PubMed
Summary
This summary is machine-generated.

Adjoint algorithmic differentiation (AAD) on GPUs faces memory and parallelization challenges. Vectorizing cost functions using GPU-accelerated operations significantly reduces memory use and speeds up gradient computation.

Keywords:
Adjoint Algorithmic DifferentiationGPU Programming

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Area of Science:

  • Computational Science
  • Numerical Analysis
  • Computer Science

Background:

  • Gradient-based optimization is crucial for scientific problems like classifier training and medical image reconstruction.
  • Adjoint algorithmic differentiation (AAD) automates gradient computation but can require excessive memory for storing intermediate derivatives.
  • Parallelization in AAD is challenging, especially on many-core architectures like GPUs, due to synchronization needs and memory constraints.

Purpose of the Study:

  • To investigate methods for mitigating memory and parallelization limitations in AAD on GPUs.
  • To evaluate the performance of vectorized cost functions using GPU-accelerated operations within an AAD framework.
  • To compare vectorized AAD implementations with naive and vectorized CPU approaches.

Main Methods:

  • Implemented AAD software that recognizes GPU-accelerated vector and matrix operations as intrinsic functions.
  • Developed vectorized cost functions for AAD, enabling the use of optimized parallel libraries.
  • Compared memory consumption and gradient computation times of naive, vectorized CPU, and vectorized GPU AAD implementations using four cost functions.

Main Results:

  • Vectorization substantially reduced memory consumption for both CPU and GPU implementations compared to the naive approach, in some cases by an order of magnitude.
  • Vectorized implementations leveraged optimized parallel libraries, yielding significant speedups for the CPU version over the naive reference.
  • The GPU version achieved an additional speedup of 7.5 ± 4.4, demonstrating effective utilization of GPU processing power for AAD.

Conclusions:

  • Expressing cost functions using GPU-accelerated operations is an effective strategy to overcome memory and parallelization limitations in AAD.
  • Vectorized AAD offers substantial performance improvements in both memory efficiency and computation time, particularly on GPUs.
  • The developed AAD approach is extensible to more complex scientific problems, including nonlinear reconstruction tasks.