# Logical Information Cells I

arXiv: https://arxiv.org/abs/2108.04751 · HTML: https://mlsanity.com/paper/2108.04751/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 10 Aug 2021.

## Builds on (most cited first, 4 of 4)

- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Deep Learning Enabled Semantic Communication Systems](https://mlsanity.com/paper/2006.10685/) (2020)
- [Topos and Stacks of Deep Neural Networks](https://mlsanity.com/paper/2106.14587/) (2021)

## Abstract (arXiv)

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 measure of the logical value for collections of such cells. The logical score growths with the depth of the layer, i.e. the information on the output decision increases, which confirms a kind of bottleneck principle. Then we study a bit more complex tasks, a priori involving predicate logic. We compare the logic and the measured weights. This shows, for groups of neurons, a neat correlation between the logical score and the size of the weights. It exhibits a form of sparsity between the layers. The most spectacular result concerns the triples which can conclude for all conditions: when applying their weight matrices to their logical matrix, we recover the classification. This shows that weights precisely perform the proofs.