Shaping schedules as a method for accelerated learning

In psychology, shaping is defined as the process of building new responses by reinforcing successive approximations to a desired response [1]. The notion of shaping was developed by behavioral psychologists for training emimah and is used as an analogy for supervised neural network "training. ~ Shaping is a schedule of learning that begins with presenting associatious that are simple to learn. As the simple associations are learned, progressively more difficult associations are used in the training. This incremental approach to learning can dramatically decrease the time required to learn complex associations, and can be used to bias how a neural network carries out an association. The authors have been experimenting with classification problems using the back-propagation learning algorithm [2]. This is a supervised learning paradigm in which a feed-forward neural network learns to associate a set of input patterns with a set of output patterns. TypicMly a set of exemplars, input/output pattern pa~s to be associated, are presented. Real world pattern classification problems may require a huge number of exemplars because of the difficulty of the task they model. If a large number of highly varied exemplars are used, the largely varied patterns create large contradictory error signals that may cause a bark-propagation network to either learn very slowly or to stabilize to an undesirable "local m i n i m a ~ (such as cla~siying all input pa t t e rns a~ being in the same class). An al ternat ive to present ing a huge number of exemplars all at once is to use shaping. First a subset of the exemplars is presented. W hen the network can correctly classify the first set of pa t terns , more members of the exemplar set are added. This processes continues unt i l all of the members of the complete exemplar set are used to t ra in the network. A shaping schedule is a heirarchical approach to learning. The neural network can be viewed as learning a high dimensional decision surface that partitions the input space [3]. The first stages of shaping allow the network to quickly find simple coarse partitions of the input space. These partitions are stretched, bent and further refined in the later stages of the shaping schedule. Therefore, a shaping schedule is most effective when a classification problem requires a complex decision surface. An analogous way of thinking of shaping is that it is directing, and therefore limiting, the search involved in the learning process. The objective in developing a shaping schedule is to maintain a large directed gradient such that the learning can asurf~ through error space. Shaping was used to teach a neural network to distinguish between images of A's, B's, C's, D's, and blank images independent of rotation, brightness, and contrast, in the presence large amounts of added noise [4]. The learning time for this task with shaping was approximately four times faster than learning the same task without the shaping schedule. The authors' present work includes other emperical studies and analytical studies to determine how to best design a shaping schedule for a particular classification problem.