Martin Klimo

Martin Klimo, Ondrej Such

In our work we propose implementing fuzzy logic using memristors. Min and max operations are done by antipodally configured memristor circuits that may be assembled into computational circuits. We discuss computational power of such circuits with respect to m-efficiency and experimentally observed behavior of memristive devices. Circuits implemented with real devices are likely to manifest learning behavior. The circuits presented in the work may be applicable for instance in fuzzy classifiers.

Martin Klimo, Lubomir Kralik

Pattern recognition systems implemented using deep neural networks achieve better results than linear models. However, their drawback is the black box property. This property means that one with no experience utilising nonlinear systems may need help understanding the outcome of the decision. Such a solution is unacceptable to the user responsible for the final decision. He must not only believe in the decision but also understand it. Therefore, recognisers must have an architecture that allows interpreters to interpret the findings. The idea of post-hoc explainable classifiers is to design an interpretable classifier parallel to the black box classifier, giving the same decisions as the black box classifier. This paper shows that the explainable classifier completes matching classification decisions with the black box classifier on the MNIST and FashionMNIST databases if Zadeh`s fuzzy logic function forms the classifier and DeconvNet importance gives the truth values. Since the other tested significance measures achieved lower performance than DeconvNet, it is the optimal transformation of the feature values to their truth values as inputs to the fuzzy logic function for the databases and recogniser architecture used.

Ondrej Such, Ondrej Skvarek, Martin Klimo

We consider the ability of a very simple feed-forward neural network to discriminate phonemes based on just relative power spectrum. The network consists of two neurons with symmetric nonlinear response over a spectral range. The output of the neurons is subsequently fed to a comparator. We show that often this is enough to achieve complete separation of data. We compare the performance of found discriminants with that of more general neurons. Our conclusion is that not much is gained in passing to real-valued weights. More likely higher number of neurons and preprocessing of input will yield better discrimination results. The networks considered are directly amenable to hardware (neuromorphic) designs. Other advantages include interpretability, guarantees of performance on unseen data and low Kolmogorov complexity.