An artificial neural network that creates its own connections

I read about the advancement of artificial neural networks (ANNs), and as a rule, they need training to change their weights in order to achieve the desired result. They will also always get the same result when they get the same input after tuning (biological networks are optional).

Then I started reading about evolutionary neural networks. However, evolution usually involves recombining the genomes of two parents into a new genome, there is no “learning”, but it actually recombines and checks using a fitness test.

I thought the human brain controls its own connections. It creates bonds, strengthens some and weakens others.

Is there a neural network topology that allows this? In cases where a neural network that has a bad reaction, or adjusts its weight accordingly, and possibly creates random new connections (I'm not sure how the brain creates new connections, but even if I did not, an accidental mutation a new connection could would make it easier). A good reaction will strengthen these bonds.

I believe this type of topology is known as a neural network of type Turing type B, but I have not seen any coded examples or documents.

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This article, Adaptive Peak Neural Network with Hebbian Learning , is specifically designed to create new neurons and synapses. From the introduction:

Traditional speed-based neural networks and new neural networks, which seem to be very effective for some tasks, but they have problems with long-term training and “catastrophic forgetting”. Once a network learns to complete a task, it is difficult to adapt to new applications. To do this correctly, you can simulate the processes that occur in the human brain: neurogenesis and synaptogenesis, or the birth and death of both neurons and synapses. To be effective, this must be achieved while maintaining current memories.

If you do a Google search using the keyword neurogenesis "neural networks" or similar, you will find more articles. There is also a similar question at cogsci.stackexchange.com.

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neat networks as well as cascading ones to add their own connections / neurons to solve problems by creating structures to create specific responses to stimuli

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