# Rolling Ball Optimizer: Learning by ironing out loss landscape wrinkles

arXiv: https://arxiv.org/abs/2505.19527 · HTML: https://mlsanity.com/paper/2505.19527/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 26 May 2025.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Noether's Learning Dynamics: Role of Symmetry Breaking in Neural Networks](https://mlsanity.com/paper/2105.02716/) (2021)
- [Continuous Time Analysis of Momentum Methods](https://mlsanity.com/paper/1906.04285/) (2019)
- [Anomalous diffusion dynamics of learning in deep neural networks](https://mlsanity.com/paper/2009.10588/) (2020)
- [Modeling AdaGrad, RMSProp, and Adam with Integro-Differential Equations](https://mlsanity.com/paper/2411.09734/) (2024)
- [Evolution of Convolutional Neural Network (CNN): Compute vs Memory bandwidth for Edge AI](https://mlsanity.com/paper/2311.12816/) (2023)
- [There is a Singularity in the Loss Landscape](https://mlsanity.com/paper/2201.06964/) (2022)

## Abstract (arXiv)

Training large neural networks (NNs) requires optimizing high-dimensional data-dependent loss functions. The optimization landscape of these functions is often highly complex and textured, even fractal-like, with many spurious local minima, ill-conditioned valleys, degenerate points, and saddle points. Complicating things further is the fact that these landscape characteristics are a function of the data, meaning that noise in the training data can propagate forward and give rise to unrepresentative small-scale geometry. This poses a difficulty for gradient-based optimization methods, which rely on local geometry to compute updates and are, therefore, vulnerable to being derailed by noisy data. In practice,this translates to a strong dependence of the optimization dynamics on the noise in the data, i.e., poor generalization performance. To remediate this problem, we propose a new optimization procedure: Rolling Ball Optimizer (RBO), that breaks this spatial locality by incorporating information from a larger region of the loss landscape in its updates. We achieve this by simulating the motion of a rigid sphere of finite radius rolling on the loss landscape, a straightforward generalization of Gradient Descent (GD) that simplifies into it in the infinitesimal limit. The radius serves as a hyperparameter that determines the scale at which RBO sees the loss landscape, allowing control over the granularity of its interaction therewith. We are motivated by the intuition that the large-scale geometry of the loss landscape is less data-specific than its fine-grained structure, and that it is easier to optimize. We support this intuition by proving that our algorithm has a smoothing effect on the loss function. Evaluation against SGD, SAM, and Entropy-SGD, on MNIST and CIFAR-10/100 demonstrates promising results in terms of convergence speed, training accuracy, and generalization performance.