Paper
Neural network optimization strategies and the topography of the loss landscape
Authors
Jianneng Yu, Alexandre V. Morozov
Abstract
Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in machine learning is the performance of trained neural networks on previously unseen test data. Here, we investigate neural network training by stochastic gradient descent (SGD) - a non-convex global optimization algorithm which relies only on the gradient of the objective function. We contrast SGD solutions with those obtained via a non-stochastic quasi-Newton method, which utilizes curvature information to determine step direction and Golden Section Search to choose step size. We use several computational tools to investigate neural network parameters obtained by these two optimization methods, including kernel Principal Component Analysis and a novel, general-purpose algorithm for finding low-height paths between pairs of points on loss or energy landscapes, FourierPathFinder. We find that the choice of the optimizer profoundly affects the nature of the resulting solutions. SGD solutions tend to be separated by lower barriers than quasi-Newton solutions, even if both sets of solutions are regularized by early stopping to ensure adequate performance on test data. When allowed to fit extensively on the training data, quasi-Newton solutions occupy deeper minima on the loss landscapes that are not reached by SGD. These solutions are less generalizable to the test data however. Overall, SGD explores smooth basins of attraction, while quasi-Newton optimization is capable of finding deeper, more isolated minima that are more spread out in the parameter space. Our findings help understand both the topography of the loss landscapes and the fundamental role of landscape exploration strategies in creating robust, transferrable neural network models.
Metadata
Related papers
Fractal universe and quantum gravity made simple
Fabio Briscese, Gianluca Calcagni • 2026-03-25
POLY-SIM: Polyglot Speaker Identification with Missing Modality Grand Challenge 2026 Evaluation Plan
Marta Moscati, Muhammad Saad Saeed, Marina Zanoni, Mubashir Noman, Rohan Kuma... • 2026-03-25
LensWalk: Agentic Video Understanding by Planning How You See in Videos
Keliang Li, Yansong Li, Hongze Shen, Mengdi Liu, Hong Chang, Shiguang Shan • 2026-03-25
Orientation Reconstruction of Proteins using Coulomb Explosions
Tomas André, Alfredo Bellisario, Nicusor Timneanu, Carl Caleman • 2026-03-25
The role of spatial context and multitask learning in the detection of organic and conventional farming systems based on Sentinel-2 time series
Jan Hemmerling, Marcel Schwieder, Philippe Rufin, Leon-Friedrich Thomas, Mire... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.21276v1</id>\n <title>Neural network optimization strategies and the topography of the loss landscape</title>\n <updated>2026-02-24T17:49:13Z</updated>\n <link href='https://arxiv.org/abs/2602.21276v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.21276v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in machine learning is the performance of trained neural networks on previously unseen test data. Here, we investigate neural network training by stochastic gradient descent (SGD) - a non-convex global optimization algorithm which relies only on the gradient of the objective function. We contrast SGD solutions with those obtained via a non-stochastic quasi-Newton method, which utilizes curvature information to determine step direction and Golden Section Search to choose step size. We use several computational tools to investigate neural network parameters obtained by these two optimization methods, including kernel Principal Component Analysis and a novel, general-purpose algorithm for finding low-height paths between pairs of points on loss or energy landscapes, FourierPathFinder. We find that the choice of the optimizer profoundly affects the nature of the resulting solutions. SGD solutions tend to be separated by lower barriers than quasi-Newton solutions, even if both sets of solutions are regularized by early stopping to ensure adequate performance on test data. When allowed to fit extensively on the training data, quasi-Newton solutions occupy deeper minima on the loss landscapes that are not reached by SGD. These solutions are less generalizable to the test data however. Overall, SGD explores smooth basins of attraction, while quasi-Newton optimization is capable of finding deeper, more isolated minima that are more spread out in the parameter space. Our findings help understand both the topography of the loss landscapes and the fundamental role of landscape exploration strategies in creating robust, transferrable neural network models.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.LG'/>\n <category scheme='http://arxiv.org/schemas/atom' term='stat.ML'/>\n <published>2026-02-24T17:49:13Z</published>\n <arxiv:comment>12 pages in the main text + 5 pages in the supplement. 6 figures + 1 table in the main text, 4 figures and 1 table in the supplement</arxiv:comment>\n <arxiv:primary_category term='cs.LG'/>\n <author>\n <name>Jianneng Yu</name>\n </author>\n <author>\n <name>Alexandre V. Morozov</name>\n </author>\n </entry>"
}