Neural networks are networks of nerve cells in the brains of humans and animals. The human brain has about 100 billion nerve cells. We humans owe our intelligence and our ability to learn various motor and intellectual capabilities to the brain's complex relays and adaptivity. For many centuries biologists, psychologists, and doctors have tried to understand how the brain functions. Around 1900 came the revolutionary realization that these tiny physical building blocks of the brain, the nerve cells and their connections, are responsible for awareness, associations, thoughts, consciousness, and the ability to learn.
The first big step toward neural networks in AI was made 1943 by McCulloch and Pitts in an article entitled "A logical calculus of the ideas immanent in nervous activity". They were the first to present a mathematical model of the neuron as the basic switching element of the brain. This article laid the foundation for the construction of artificial neural networks and thus for this very important branch of AI.
We could consider the field of modeling and simulation of neural networks to be the bionics branch within AI.1 Nearly all areas of AI attempt to recreate cognitive processes, such as in logic or in probabilistic reasoning. However, the tools used for modeling - namely mathematics, programming languages, and digital computers - have very little in common with the human brain. With artificial neural networks, the approach is different. Starting from knowledge about the function of natural neural networks, we attempt to model, simulate, and even reconstruct them in hardware. Every researcher in this area faces the fascinating and exciting challenge of comparing results with the performance of humans.
In this chapter we will attempt to outline the historical progression by defining a model of the neuron and its interconnectivity, starting from the most important biological insights. Then we will present several important and fundamental models: the Hopfield model, two simple associative memory models, and the - exceedingly important in practice - backpropagation algorithm.
Fig. 9.1 Two stages of the modeling of a neural network. Above a biological model and below a formal model with neurons and directed connections between them.
From Biology to Simulation
Each of the roughly 100 billion neurons in a human brain has, as shown in a simplified representation in Fig. 9.1, the following structure and function. Besides the cell body, the neuron has an axon, which can make local connections to other neurons over the dendrites. The axon can, however, grow up to a meter long in the form of a nerve fiber through the body.
The cell body of the neuron can store small electrical charges, similarly to a capacitor or battery. This storage is loaded by incoming electrical impulses from other neurons. The more electric impulse comes in, the higher the voltage. If the voltage exceeds a certain threshold, the neuron will fire. This means that it unloads its store, in that it sends a spike over the axon and the synapses. The electrical current divides and reaches many other neurons over the synapses, in which the same process takes place.
Now the question of the structure of the neural network arises. Each of the roughly 1011 neurons in the brain is connected to roughly 1000 to 10 000 other neurons, which yields a total of over 1014 connections. If we further consider that this gigantic number of extremely thin connections is made up of soft, three-dimensional tissue and that experiments on human brains are not easy to carry out, then it becomes clear why we do not have a detailed circuit diagram of the brain. Presumably we will never be capable of completely understanding the circuit diagram of our brain, based solely on its immense size.
From today's perspective, it is no longer worth even trying to make a complete circuit diagram of the brain, because the structure of the brain is adaptive. It changes itself on the fly and adapts according to the individual's activities and environmental influences. The central role here is played by the synapses, which create the connection between neurons. At the connection point between two neurons, it is as if two cables meet. However, the two leads are not perfectly conductively connective, rather there is a small gap, which the electrons cannot directly jump over. This gap is filled with chemical substances, so-called neurotransmitters. These can be ionized by an applied voltage and then transport a charge over the gap. The conductivity of this gap depends on many parameters, for example the concentration and the chemical composition of the neurotransmitter. It is enlightening that the function of the brain reacts very sensitively to changes of this synaptic connection, for example through the influence of alcohol or other drugs.
How does learning work in such a neural network? The surprising thing here is that it is not the actual active units, namely the neurons, which are adaptive, rather it is the connections between them, that is, the synapses. Specifically, this can change their conductivity. We know that a synapse is made stronger by however much more electrical current it must carry. Stronger here means that the synapse has a higher conductivity. Synapses which are used often obtain an increasingly higher weight. For synapses which are used infrequently or are not active at all, the conductivity continues to decrease. This can even lead to them dying off.
All neurons in the brain work asynchronously and in parallel, but, compared to a computer, at very low speed. The time for a neural impulse takes about a millisecond, exactly the same as the time for the ions to be transported over the synaptic gap. The clock frequency of the neuron then is under one kilohertz and is thus lower than that of modern computers by a factor of 106. This disadvantage, however, is more than compensated for in many complex cognitive tasks, such as image recognition, by the very high degree of parallel processing in the network of nerve cells.
The connection to the outside world comes about through sensor neurons, for example on the retina in the eyes, or through nerve cells with very long axons which reach from the brain to the muscles and thus can carry out actions such as the movement of a leg.
However, it is still unclear how the principles discussed make intelligent behavior possible. Just like many researchers in neuroscience, we will attempt to explain using simulations of a simple mathematical model how cognitive tasks, for example pattern recognition, become possible.
About the Author
Dr. Wolfgang Ertel is a professor at the Institute for Artificial Intelligence at the Ravensburg-Weingarten University of Applied Sciences, Germany.
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