Hebbian Learning
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Hebbian Learning |
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Introduction to Neural Networks: one of the most important concepts in the history of connectionism.
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Elsewhere on the Web
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• Polyworld simulator
• An Idiot's Guide to Neural Networks
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One of the most fascinating and almost magic-like feature of Neural Networks is that they are not programmed like conventional computers, but are literally trained to produce desired results: they learn. Scientists seeking new NN designs were always trying to copy the most successful learning system - the brain. That's the reason why one of the most influential works in connectionism's history came from a neuropsychologist, and not from a neural network researcher. Donald O. Hebb proposed his model for biological learning in 1949, founding a theory of behavior based as much as possible on the physiology of the nervous system. The main goal of his research was to understand how neurons in the brain change when learning occurs. The most important result that emerged from Hebb's research was formulated in a statement known as a Hebb's law (rule, postulate). The original statement, as published in his seminal work The Organization of Behaviour, reads as follows:
When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased.
This simple statement has remarkable implications. Within the AI context, this rule is used as an unsupervised training algorithm in which the synaptic weight between two neurons is increased if both the source neuron and target neuron are active at the same time. After appropriate training has occured, the target neuron will become more "sensitive" to the source neuron's stimulus. However, if we are to use Hebb's law as the learning rule for actual NN implementations, several modifications are necessary. The weight vectors must be normalized (that is, constrained to the fixed length) to avoid the uncontrollable growth and make the computer simulation of such networks computationally manageable. Both positive and negative (excitatory and inhibitory) interconnect weights must also be provided. The expression
wij = ai aj
essentially says that the weight change is equal to the product of activations of the neurons it connects. If both units are on (1) or off (-1) than the strength of the weight increases, otherwise it is decreased.
There are several interesting and less restrictive variations of the original law, making it more universal and suited for real-world applications. Stephen Grossberg developed one such extension, naming it neo-hebbian learning, which later served as a basis for his outstar learning paradigm. It expands the original postulate by introducing the learning and forgetting constants, making it more similar to the biological learning systems. More specifically, connection weights are computed using the expression
Weightt+1 = Weightt - F*OriginalRule + N*OriginalRule
where F and N are constants between 0 and 1, defining how quickly to "forget" and learn, working on the original Hebb's rule. However neo-hebian learning doesn't resolve the essential problems of the original concept, although it provides an important mathematical framework. Differential hebbian learning, on the other hand, takes into account the product of the rates of change - referring to the derivative of a neuron's output over time in mathematical terms. Drive reinforcement theory takes it even further, allowing some temporal learning to occur in the system.
Hebbian learning works well as long as all the input patterns are orthogonal, which in essence means that they do not overlap and are completely distinct. Real-world problems are rarely orthogonal, and this fact severely limits the effectiveness of the original law. However, differential hebbian learning and similar approaches are often used as a basis for the new learning algorithms, although rarely in the pure form described here. More powerful learning rules will be discussed in the following articles in this series.
In the meantime, I would like to suggest an excellent, interactive source of information on Neural Networks. "Connectionist Models of Cognition" created by Simon Dennis and Devin McAuley, is a Web-based textbook designed to introduce the key concepts in the area of neural networks. It provides hands-on modeling experience with a variety of standard architectures and the opportunity to begin developing your own models. A background in connectionist theory is not required! The BrainWave connectionist simulator is embedded within the materials, allowing you to interact with the figures as you work through the exercises. This Java simulator employs a graphical, direct manipulation interface - much like a drawing program - making it easy to use.