Logical Information Cells I
Jean-Claude Belfiore, Daniel Bennequin, Xavier Giraud

TL;DR
This paper investigates how simple artificial neural networks spontaneously develop logical reasoning capabilities, linking neuron activity patterns to semantic information and demonstrating that weights perform logical proofs.
Contribution
It introduces a measure of logical value for neural cells, showing how network depth enhances logical information and that weights encode logical proofs, revealing new insights into neural reasoning.
Findings
Neuron activities become more quantized and informative with depth.
Logical scores correlate with weight sizes, indicating sparsity.
Weights perform logical proofs, enabling classification through logical matrices.
Abstract
In this study we explore the spontaneous apparition of visible intelligible reasoning in simple artificial networks, and we connect this experimental observation with a notion of semantic information. We start with the reproduction of a DNN model of natural neurons in monkeys, studied by Neromyliotis and Moschovakis in 2017 and 2018, to explain how "motor equivalent neurons", coding only for the action of pointing, are supplemented by other neurons for specifying the actor of the action, the eye E, the hand H, or the eye and the hand together EH. There appear inner neurons performing a logical work, making intermediary proposition, for instance E V EH. Then, we remarked that adding a second hidden layer and choosing a symmetric metric for learning, the activities of the neurons become almost quantized and more informative. Using the work of Carnap and Bar-Hillel 1952, we define a…
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Taxonomy
TopicsFractal and DNA sequence analysis · Machine Learning in Bioinformatics · Neural Networks and Applications
