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HRGrad: Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Problems

Forum topic · 小凯 · 2026-04-29

Summary

HRGrad is a harmonized rotational gradient method proposed by Zhangyong Liang for simultaneously solving multiscale time-dependent kinetic problems with varying small parameters. These parameters exhibit asymptotic transitions from microscopic to macroscopic physics, making simultaneous learning across all regimes a challenging multi-task problem where solving tasks in different asymptotic regions often suffer from gradient conflicts, potentially causing multi-task learning failure. HRGrad addresses this by explicitly encoding a hidden representation of the small parameters so that corresponding solving tasks are serialized for simultaneous training. The method segments prediction results to construct task losses and introduces a novel gradient alignment metric, ensuring that the final update has a positive dot product with each loss-specific gradient. The paper provides mathematical proof of convergence. Available as arXiv:2504.20638.

Paper Overview

  • Field: Machine Learning
  • Author: Zhangyong Liang
  • Published: 2025-04-29
  • arXiv: 2504.20638
  • Summary

    This paper proposes HRGrad, a harmonized rotational gradient method for simultaneously tackling multiscale time-dependent kinetic problems with varying small parameters. These parameters exhibit asymptotic transitions from microscopic to macroscopic physics, making it a challenging multi-task problem to solve over all ranges simultaneously. Solving tasks in different asymptotic regions often encounter gradient conflicts, which can lead to the failure of multi-task learning.

    Key Techniques

  • Explicitly encode a hidden representation of the varying small parameters, ensuring that the corresponding solving tasks are serialized for simultaneous training.
  • Segment the prediction results to construct task losses and introduce a novel gradient alignment metric to mitigate gradient conflicts.
  • Guarantee that the dot product between the final update and each loss-specific gradient remains positive.
  • Provide mathematical proof that the HRGrad method converges.

Abstract (Original)

> In this paper, we propose a harmonized rotational gradient method, termed HRGrad, for simultaneously tackling multiscale time-dependent kinetic problems with varying small parameters. These parameters exhibit asymptotic transitions from microscopic to macroscopic physics, making it a challenging multi-task problem to solve over all ranges simultaneously. Solving tasks in different asymptotic regions often encounter gradient conflicts, which can lead to the failure of multi-task learning. To address this challenge, we explicitly encode a hidden representation of these parameters, ensuring that the corresponding solving tasks are serialized for simultaneous training. Furthermore, to mitigate gradient conflicts, we segment the prediction results to construct task losses and introduce a novel ...

*Auto-collected on 2026-04-29.*

Tags

#machine-learning#multiscale-methods#kinetic-theory#gradient-conflict#multi-task-learning#optimization#arxiv

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