# How Far is Adam from Natural Gradient Descent?

Published: 2026-10-02 · Updated: 2026-10-02 · Category: Research

Source page: https://www.sipply.dev/story/how-far-is-adam-from-natural-gradient-descent-ae3cd7c8 · 中文: https://www.sipply.dev/zh/story/how-far-is-adam-from-natural-gradient-descent-ae3cd7c8

## Summary

A recent study published on arXiv delves into the performance of the Adam optimizer in comparison to natural gradient descent (NGD). The research highlights that while Adam is effective in minimizing loss across various loss landscapes, it diverges significantly from NGD, particularly in ill-conditioned scenarios. This divergence suggests that Adam's success may be attributed more to its momentum smoothing capabilities rather than its alignment with the natural gradient, raising questions about its optimization efficiency in challenging conditions.

## Key takeaways

- Adam optimizer shows strong performance but deviates from natural gradient descent.
- The effectiveness of Adam may stem from momentum smoothing rather than optimal gradient alignment.
- Ill-conditioned settings reveal significant geometric differences between Adam and NGD.

## Why it matters

Understanding the limitations of popular optimizers like Adam is crucial for developing more efficient training algorithms in machine learning. This research could lead to improved optimization techniques that better handle complex loss landscapes.

- **Product managers:** Product managers should be aware of the implications of optimizer performance on model training efficiency, as this can directly impact product development timelines and resource allocation.
- **Developers:** For developers and engineers, this study underscores the importance of selecting the right optimization algorithms based on the characteristics of the loss landscape, which can enhance model training outcomes.
- **Students and job seekers:** Students and job-seekers should recognize the significance of understanding various optimization techniques, as this knowledge is essential for building robust machine learning models and can enhance their employability in the field.

## Sources

- [How Far is Adam from Natural Gradient Descent?](https://arxiv.org/abs/2610.00004) (arXiv cs.LG, 2026-10-02)

## 中文

### Adam与自然梯度下降的距离有多远？

一项最近在arXiv上发布的研究探讨了Adam优化器与自然梯度下降（NGD）的性能比较。研究强调，尽管Adam在各种损失景观中有效地最小化损失，但在病态条件下，它与NGD的偏离显著。这种偏离表明，Adam的成功可能更多归因于其动量平滑能力，而非与自然梯度的一致性，这引发了对其在挑战性条件下优化效率的质疑。

**要点：**

- Adam优化器表现强劲，但偏离自然梯度下降。
- Adam的有效性可能源于动量平滑，而非最佳梯度对齐。
- 病态设置揭示了Adam与NGD之间显著的几何差异。

**为什么重要：** 理解像Adam这样的流行优化器的局限性对于开发更高效的机器学习训练算法至关重要。这项研究可能导致更好的优化技术，以更好地处理复杂的损失景观。

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