Rolling Ball Optimizer: Learning by ironing out loss landscape wrinkles

• URL: http://arxiv.org/abs/2505.19527v3
• Date: Fri, 24 Oct 2025 04:55:44 GMT
• Title: Rolling Ball Optimizer: Learning by ironing out loss landscape wrinkles
• Authors: Mohammed Djameleddine Belgoumri, Mohamed Reda Bouadjenek, Hakim Hacid, Imran Razzak, Sunil Aryal,
• Abstract summary: Training large neural networks (NNs) requires optimizing high-dimensional data-dependent loss functions.<n>These functions are often highly complex and textured, even fractal-like.<n>Noise in the training data can propagate forward and give rise to unrepresentative small-scale geometry.
• Score: 19.667068548957143
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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