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Subspace Levenberg-Marquardt Algorithms Boost Neural Network Training

M. Duc Hoang· September 2, 2026 View original

Key takeaways

  • Classical Levenberg-Marquardt (LM) offers strong convergence but is costly for large NNs.
  • Subspace LM methods (KSLM, HSLM) address LM's scalability issues.
  • These methods provide more efficient second-order optimization for neural networks.
  • They offer a robust alternative to first-order optimizers like SGD and Adam.

Who benefits

AI DevelopmentScientific ComputingMachine Learning ResearchRoboticsData Analytics

Summary

This research evaluates subspace Levenberg-Marquardt (LM) algorithms, such as KSLM and HSLM, for training neural networks on regression and classification tasks. These methods address the high computational and memory costs of classical LM, offering more efficient second-order optimization compared to first-order methods like SGD and Adam.

Researchers have conducted an evaluation of subspace Levenberg-Marquardt (LM) algorithms, including Krylov subspace LM (KSLM) and hybrid subspace LM (HSLM), for their application in training neural networks. The classical Levenberg-Marquardt algorithm is renowned for its rapid convergence and robustness, particularly in smaller to medium-sized networks. However, its computational and memory demands escalate significantly with an increasing number of network parameters, limiting its scalability for larger models. Subspace methods were developed to overcome these limitations, making second-order optimization algorithms more efficient. This study compares the performance of these subspace LM variants against the traditional LM method, as well as popular first-order optimizers like Stochastic Gradient Descent (SGD) and Adam, across various regression and classification tasks. The findings aim to demonstrate the improved efficiency and practical applicability of subspace LM algorithms for training neural networks, offering a viable alternative for scenarios where the benefits of second-order methods are desired without incurring prohibitive resource costs.

Why it matters

Optimizing neural network training is crucial for faster development cycles and more efficient resource utilization, especially for complex models where second-order methods can offer superior convergence properties.

How to implement this in your domain

  1. 1Review current neural network training pipelines and identify opportunities for optimizer improvements.
  2. 2Investigate subspace Levenberg-Marquardt algorithms (KSLM, HSLM) as alternatives to first-order optimizers like Adam or SGD.
  3. 3Benchmark the performance of subspace LM variants against existing optimizers on specific regression or classification tasks.
  4. 4Consider integrating these more efficient second-order methods into training frameworks for small to medium-sized neural networks.

Original post by M. Duc Hoang

"arXiv:2609.00789v1 Announce Type: new Abstract: The Levenberg-Marquardt (LM) algorithm is a well-known second-order method for rapid convergence and strong robustness when training small- to medium-sized neural networks (NNs). However, its computational and memory costs increase…"

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