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• Convolutional Neural Networks can be improved in terms of the classification performance and robustness by using variable weight structures. • Analysis of different data processing methods, models' robustness and statistical properties. • Comparative analysis of variable weight convolutional neural networks and other widely used machine learning techniques. • Medical applications to the classification of seizure phases and types. Deep learning techniques have recently achieved impressive results and raised expectations in the domains of medical diagnosis and physiological signal processing. The widely adopted methods include convolutional neural networks (CNNs) and recurrent neural networks (RNNs). However, the existing models possess static connection weights between layers, which might limit the generalization capability and the classification performance of the models as the weights of different layers are fixed after training. Furthermore, to deal with a large amount of data, a neural network with a sufficiently large size is required. This paper proposes the variable weight convolutional neural networks (VWCNNs), which are a type of network structure employing dynamic weights instead of static weights in their convolutional layers and fully-connected layers. VWCNNs are able to adapt to different characteristics of input data and can be viewed as an infinite number of traditional, fixed-weight CNNs. We will show that the proposed VWCNN structure outperforms the conventional CNN in terms of the classification accuracy, generalization capability, and robustness when the inputs are contaminated by noise. In this paper, VWCNNs are applied to the classification of three seizure phases (seizure-free, pre-seizure and seizure) based on measured electroencephalography (EEG) data. VWCNNs achieve 100% test accuracy and show strong robustness in the classification of the three seizure phases, and thus show the potential to be a useful classification tool for medical diagnosis. Furthermore, the classification of seven types of seizures is investigated in this paper using the world's largest open source database of seizure recordings, TUH EEG seizure corpus. Comparisons with conventional CNNs, RNN, MobileNet, ResNet, DenseNet and traditional machine learning methods including random forest, decision tree, support vector machine, K-nearest neighbours, standard neural networks, and Naïve Bayes are being conducted using realistic test data sets. The results demonstrate that VWCNNs have advantages over other classifiers in terms of classification accuracy and robustness. [ABSTRACT FROM AUTHOR]