Geometry of learning: Visualizing the performance of neural network supervised training methods.

*(English)*Zbl 0898.68075Summary: The empirical comparison of numerical methods is of great importance in the development of improved training methods and in algorithm selection for problem solving since it is not always evident which algorithm is proper for a given class of applications. Questions concerning “the cost”, in terms of function evaluations, the speed of convergence, in terms of epochs and the sensitivity of an algorithm to initial conditions are usually addressed by practitioners of the field. To this end a software package for analyzing and visualizing the convergence behavior of training methods is introduced in this contribution. This package gives quantitative measures for the terms “cost”, “fast” and “sensitive”. Also it gives pieces of information and displays the geometry of basins of attraction for any training method. It displays also, using different colors, the regions of convergence to the minima for various training methods. Moreover, it indicates the rate of their convergence as well as the region of divergence of these methods. Furthermore, this package gives statistical information regarding the total convergence area in a specific domain for various minima.

##### MSC:

68T15 | Theorem proving (deduction, resolution, etc.) (MSC2010) |

##### Keywords:

problem solving##### Software:

OPTAC
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\textit{G. S. Androulakis} et al., Nonlinear Anal., Theory Methods Appl. 30, No. 7, 4539--4544 (1997; Zbl 0898.68075)

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##### References:

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