mlsanityData to 7 Oct 2026

Acceleration via Symplectic Discretization of High-Resolution Differential Equations

arXiv 1902.03694 ↗First posted 11 Feb 2019math.OC cs.LG cs.NAcited by 27

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Abstract (arXiv)

We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization schemes: an explicit Euler scheme, an implicit Euler scheme, and a symplectic scheme. We show that the optimization algorithm generated by applying the symplectic scheme to a high-resolution ODE proposed by Shi et al. [2018] achieves an accelerated rate for minimizing smooth strongly convex functions. On the other hand, the resulting algorithm either fails to achieve acceleration or is impractical when the scheme is implicit, the ODE is low-resolution, or the scheme is explicit.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Feb 2019.

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Citing papers per year: 2021: 9; 2022: 6; 2023: 5; 2024: 4; 2025: 2; 2026: 1.

27 papers.

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  1. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  2. 2021A Continuized View on Nesterov Acceleration for Stochastic Gradient Descent and Randomized Gossipcited by 15
  3. 2021Provable Convergence of Nesterov's Accelerated Gradient Method for Over-Parameterized Neural Networkscited by 7
  4. 2021Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimizationcited by 6
  5. 2022Proximal Subgradient Norm Minimization of ISTA and FISTAcited by 6
  6. 2024Accelerated Preference Optimization for Large Language Model Alignmentcited by 5
  7. 2021First-Order Methods for Convex Optimizationcited by 4
  8. 2021A Contraction Theory Approach to Optimization Algorithms from Acceleration Flowscited by 3
  9. 2022Losing momentum in continuous-time stochastic optimisationcited by 2
  10. 2022NAG-GS: Semi-Implicit, Accelerated and Robust Stochastic Optimizercited by 2
  11. 2022Linear Convergence of ISTA and FISTAcited by 2
  12. 2023On the connections between optimization algorithms, Lyapunov functions, and differential equations: theory and insightscited by 2
15 more
  1. 2023A Variational Perspective on High-Resolution ODEscited by 2
  2. 2021A Discrete Variational Derivation of Accelerated Methods in Optimizationcited by 1
  3. 2021Fast symplectic integrator for Nesterov-type acceleration methodcited by 1
  4. 2022Resonance in Weight Space: Covariate Shift Can Drive Divergence of SGD with Momentumcited by 1
  5. 2023Linear convergence of forward-backward accelerated algorithms without knowledge of the modulus of strong convexitycited by 1
  6. 2025Learning by solving differential equationscited by 1
  7. 2025Accelerating Optimization via Differentiable Stopping Timecited by 1
  8. 2026Second Order Drifting Modelscited by 1
  9. 2021A More Stable Accelerated Gradient Method Inspired by Continuous-Time Perspectivecited by 0
  10. 2022Whiplash Gradient Descent Dynamicscited by 0
  11. 2023Reducing Discretization Error in the Frank-Wolfe Methodcited by 0
  12. 2023Accelerated Optimization Landscape of Linear-Quadratic Regulatorcited by 0
  13. 2024A General Continuous-Time Formulation of Stochastic ADMM and Its Variantscited by 0
  14. 2024Symplectic Bregman divergencescited by 0
  15. 2024Generalized Continuous-Time Models for Nesterov's Accelerated Gradient Methodscited by 0