One-hot encoding is the prevalent method used in neural networks to represent multi-class categorical data. Its success stems from its ease of use and interpretability as a probability distribution when accompanied by a softmax activation function. However, one-hot encoding leads to very high dimensional vector representations when the categorical data’s cardinality is high. The Hamming distance in one-hot encoding is equal to two from the coding theory perspective, which does not allow detection or error-correcting capabilities. Binary coding provides more possibilities for encoding categorical data into the output codes, which mitigates the limitations of the one-hot encoding mentioned above. We propose a novel method based on Zadeh fuzzy logic to train binary output codes holistically. We study linear block codes for their possibility of separating class information from the checksum part of the codeword, showing their ability not only to detect recognition errors by calculating non-zero syndrome, but also to evaluate the truth-value of the decision. Experimental results show that the proposed approach achieves similar results as one-hot encoding with a softmax function in terms of accuracy, reliability, and out-of-distribution performance. It suggests a good foundation for future applications, mainly classification tasks with a high number of classes.

Pattern recognition systems always misclassify anomalies, which can be dangerous for uninformed users. Therefore, anomalies must be filtered out from each classification. The main challenge for the anomaly filter design is the huge number of possible anomaly samples compared with the number of samples in the training set. Tailoring the filter for the given classifier is just the first step in this reduction. Paper tests the hypothesis that the filter trained in avoiding “near” anomalies will also refuse the “far” anomalies, and the anomaly detector is then just a classifier distinguishing between “far real” and “near anomaly” samples. As a “far real” samples generator was used, a Generative Adversarial Network (GAN) fake generator that transforms normally distributed random seeds into fakes similar to the training samples. The paper proves the assumption that seeds unused in fake training will generate anomalies. These seeds are distinguished according to their Chebyshev norms. While the fakes have seeds within the hypersphere with a given radius, the near anomalies have seeds within the sphere near cover. Experiments with various anomaly test sets have shown that GAN-based anomaly detectors create a reliable anti-anomaly shield using the abovementioned assumptions. The proposed anomaly detector is tailored to the given classifier, but its limitation is due to the need for the availability of the database on which the classifier was trained.

Humans have rich experience applying linear models and logical thinking, but only experts understand the behaviour of non-linear systems. However, the deep neural network (DNN) implementation of non-linear systems outperforms optimal linear models. Therefore, the forward DNN (the pattern recognition system in this paper) attracts attention to the necessity of interpreting the results obtained by DNN. To preserve the high performance of DNN, we focus on a post hoc explanation; this approach means building an explainable model for the decision obtained by the black box. To avoid the interpretation of a set of millions of non-linear functions, we divide DNN into two parts: the feature extractor and the classifier. Following that, we argue for a specific interpretation of each of them. While for classifiers, we have several suitable explainable models (and we decided on the fuzzy logical function), we believe that feature interpretation is a creative scientific activity corresponding to the usual research. The paper presents a tool to help researchers and users understand extracted features not necessarily known in the specific application domain. Explanation of the new features is the way of learning from computers.

We present a new way to passively implement permutation circuits, a concept of importance in bit-oriented or line-oriented designs, used in communications, cryptography, field-programmable gate arrays or next-generation pulsed neural networks. We argue that the proposed implementation is more reliable and efficient than previous designs when the number of permuted signals is at least 16. It uses complementary resistive gates, which are natural extensions of the concept of a complementary resistive switch. When Ir/TaO _x /Ta stack is used for switching, the devices show abrupt transitions among a discrete number of states resulting in a complex input-output characteristic. This deviates significantly from the fuzzy logic model of such gates previously proposed on the basis of theoretical models.