Authors:
Tomas Hrycej
1
;
Bernhard Bermeitinger
2
;
Massimo Pavone
1
;
Götz-Henrik Wiegand
1
and
Siegfried Handschuh
1
Affiliations:
1
Institute of Computer Science, University of St.Gallen (HSG), St. Gallen, Switzerland
;
2
Institute of Computer Science in Vorarlberg, University of St. Gallen (HSG), Dornbirn, Austria
Keyword(s):
Conjugate Gradient, Convexity, Adam, Computer Vision, Vision Transformer.
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 gradien
t 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.
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