Abstract
The boolean \(\Sigma \) \(\Pi \)-neuron is a biologically inspired formal model for logical information processing. The boolean \(\Sigma \) \(\Pi \)-neuron model adequately reflects information processing processes in the cerebral cortex and in the dendritic trees of neurons. The advantage of the boolean \(\Sigma \) \(\Pi \)-neuron model is the ability to accurately represent any boolean function and the possibility of constructive learning (direct construction) in a single pass of the training sample. Another possibility is the direct construction of an ensemble of boolean \(\Sigma \) \(\Pi \)-neurons that function correctly on the training sample. This article discusses a new algorithm for constructing an ensemble of boolean \(\Sigma \) \(\Pi \)-neurons in parameterized form. This form can also be easily represented as a single boolean \(\Sigma \) \(\Pi \)-network with a hidden layer of linear and threshold linear units. In some cases, this makes it easier to retrain on new inputs by setting the appropriate control parameter values.
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Notes
- 1.
\((s)_{+}=\max \{s,0\}\).
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Shibzukhov, Z.M., Belov, O. (2025). Constructive Learning of Parameterized Boolean \(\Sigma \) \(\Pi \)-networks. In: Redko, V., Yudin, D., Dunin-Barkowski, W., Kryzhanovsky, B., Tiumentsev, Y. (eds) Advances in Neural Computation, Machine Learning, and Cognitive Research VIII. NI 2024. Studies in Computational Intelligence, vol 1179. Springer, Cham. https://doi.org/10.1007/978-3-031-80463-2_3
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DOI: https://doi.org/10.1007/978-3-031-80463-2_3
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