There is a correlation as they are bioinspired. The neurons in your brain are connected to other neurons through synapses, and neurons in your brain tend to fire when they receive sufficient excitatory input from other nearby neurons. That is, if you have a neuron connected to a few other neurons via synapses, and those few neurons fire, the connected neuron may also fire depending on the relative strength of the synaptic connections and whether the combined input exceeds the neuron’s firing threshold. The act of that neuron firing will then contribute to the input of some other neurons, which influences other neurons, and so on. This complex web of synaptic connections forms a network of neurons, called a neural network.
Contemporary Artificial Neural Networks are modeled on biology but are dramatically simpler in structure and connectivity than biological networks. There is no one kind of ANN. They have different structures depending on what kind of network they are, with the simplest in my opinion being static layers of fully connected neurons which are usually visualized as chains of neurons lined up next to each other, with all neurons in a chain connected to every neuron in the next chain. By analogy, neurons in the early layers contribute to the activation of the neurons in the next layers based on the strength of their synaptic connections. This is done through simple multiply-accumulate-add operations that are extremely well-studied in computer hardware. So we can create an artificial and emulated version of a biological neural network (be it one found in a human brain, mouse brain, or insect brain), but with a much simpler functional mechanism and connectivity suitable for computer hardware, that can still achieve some strong artificial intelligence capabilities.
Again it doesn’t have to have one particular structure. There are also neural networks that are more closely informed by biology, like Spiking Neural Networks. There are neural gases, that are not static and dynamically change the number of neurons. But nearly anything that is based on the concept of neurons connected to each other through some kind of web falls under the umbrella of neural networks, and usually, they can “learn” by re-organizing or evolving their state in response to stimulus.
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