The present paper considers an open problem of setting hyperparameters for convolutional neural networks aimed at image classification. Since selecting filter spatial extents for convolutional layers is a topical problem, it is approximately solved by accumulating statistics of the neural network performance. The network architecture is taken on the basis of the MNIST database experience. The eight-layered architecture having four convolutional layers is nearly best suitable for classifying small and medium size images. Image databases are formed of grayscale images whose size range is 28 × 28 to 64 × 64 by step 2. Except for the filter spatial extents, the rest of those eight layer hyperparameters are unalterable, and they are chosen scrupulously based on rules of thumb. A sequence of possible filter spatial extents is generated for each size. Then sets of four filter spatial extents producing the best performance are extracted. The rule of this extraction that allows selecting the best filter spatial extents is formalized with two conditions. Mainly, difference between maximal and minimal extents must be as minimal as possible. No unit filter spatial extent is recommended. The secondary condition is that the filter spatial extents should constitute a non-increasing set. Validation on MNIST and CIFAR- 10 databases justifies such a solution, which can be extended for building convolutional neural network classifiers of colour and larger images.
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