The "Eleven Dimensional" Brain? Topology of Neural Networks

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2021-07-02 13:30:03

The Human Brain Can Create Structures in Up to 11 Dimensions The human brain sees the world as an 11-dimensional multiverse Scientists find mysterious shapes and structures in the brain with up to ELEVEN dimensions

The paper , published in Frontiers in Computational Neuroscience , comes from the lab of Henry Markram, one of the world's most powerful neuroscientists. As well as being head of the Blue Brain Project at the École Polytechnique Fédérale de Lausanne, Markram founded the € 1 billion Human Brain Project and co-founder of scientific publishing giant Frontiers . The new paper is fascinating. But the headlines were completely misleading: this paper has nothing to do with multiverses and very little to do with anything 11-dimensional. The paper is actually all about "cliques" of neurons. A clique is simply a group of neurons, each of which is connected to all of the others. Here's a diagram (graph) showing a hypothetical clique of 5 neurons:

If these were real neurons, they would of course occupy 3-dimensional space, just like everything else in the universe. Now, mathematicians refer to a clique of 5 neurons as having a dimension of 4. This doesn't mean that five connected neurons occupy some mysterious fourth dimension. It just means that the graph of the connections could be depicted as a 4-dimensional object . But we could equally well depict it as a 2-dimensional diagram (seen above.) In general, a clique containing n nodes has a dimension of n-1. The nodes could be neurons or anything else. So where did the wacky multi-dimensional media coverage come from? It seems to have been prompted by the hype-filled Frontiers press release on this paper, called "Blue Brain Team Discovers a Multi-Dimensional Universe in Brain Networks." If you look beyond the headlines, the paper is actually pretty interesting, although it raises more questions than it answers. The big claim is that neural networks in the brain contain an unexpectedly high number of cliques, including large ones with a dimension of 7 (not 11, though.)