A Convexity-Dependent Two-Phase Training Algorithm for Deep Neural Networks

Tomas Hrycej, Bernhard Bermeitinger, Massimo Pavone, Götz-Henrik Wiegand, Siegfried Handschuh

2025

Abstract

The key task of machine learning is to minimize the loss function that measures the model fit to the training data. The numerical methods to do this efficiently depend on the properties of the loss function. The most decisive among these properties is the convexity or non-convexity of the loss function. The fact that the loss function can have, and frequently has, non-convex regions has led to a widespread commitment to non-convex methods such as Adam. However, a local minimum implies that, in some environment around it, the function is convex. In this environment, second-order minimizing methods such as the Conjugate Gradient (CG) give a guaranteed superlinear convergence. We propose a novel framework grounded in the hypothesis that loss functions in real-world tasks swap from initial non-convexity to convexity towards the optimum - a property we leverage to design an innovative two-phase optimization algorithm. The presented algorithm detects the swap point by observing the gradient norm dependence on the loss. In these regions, non-convex (Adam) and convex (CG) algorithms are used, respectively. Computing experiments confirm the hypothesis that this simple convexity structure is frequent enough to be practically exploited to substantially improve convergence and accuracy.

Paper Citation

in Harvard Style

Hrycej T., Bermeitinger B., Pavone M., Wiegand G. and Handschuh S. (2025). A Convexity-Dependent Two-Phase Training Algorithm for Deep Neural Networks. In Proceedings of the 17th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR; ISBN , SciTePress, pages 78-86. DOI: 10.5220/0013696100004000

in Bibtex Style

@conference{kdir25,
author={Tomas Hrycej and Bernhard Bermeitinger and Massimo Pavone and Götz-Henrik Wiegand and Siegfried Handschuh},
title={A Convexity-Dependent Two-Phase Training Algorithm for Deep Neural Networks},
booktitle={Proceedings of the 17th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR},
year={2025},
pages={78-86},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013696100004000},
isbn={},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR
TI - A Convexity-Dependent Two-Phase Training Algorithm for Deep Neural Networks
SN -
AU - Hrycej T.
AU - Bermeitinger B.
AU - Pavone M.
AU - Wiegand G.
AU - Handschuh S.
PY - 2025
SP - 78
EP - 86
DO - 10.5220/0013696100004000
PB - SciTePress