AI summary

This paper introduces a hierarchical learning machine (HLM) and presents a method to describe the evolution of weights through an energy function, addressing the credit assignment problem (CAP). The method is applied to a hierarchical associative memory model, demonstrating the potential for learning and generalization through simulations on alphabetic character recognition.

Abstract

Threshold functions and related operators are widely used as basiC elements of adaptive and associative networks [Nakano 72, Amari 72, Hopfleld 821. There exist numerous learning rules for finding a set of weights to achieve a particular correspondence between input-output pairs. But early works in the field have shown that the number of threshold functions (or linearly separable functions) in N binary variables is small compared to the number of all possible boolean mappings in N variables, especially if N is large. This problem is one of the main limitations of most neural networks models where the state is fully specified by the environment during learning: they can only learn linearly separable functions of their Inputs. Moreover, a learning procedure which requires the outside world to specify the state of every neuron during the learning session can hardly be considered as a general learning rule because in real-world conditions, only a partial information on the "ideal" network state for each task is available from the environment. It is possible to use a set of so-called "hidden units" [Hinton,Sejnowski,Ackley. 84], without direct inter action with the enVironment, which can compute intermediate predicates. Unfortunately, the global response depends on the output of a particular hidden unit in a highly non-linear way, moreover the nature of this dependence is influenced by the states of the other cells. Thus, it is difficult to decide whether the output of a hidden unit is wrong for a particular input, and, consequently, how to modify its weights. This last problem has been referred to as the "credit aSSignment problem" (CAP) in [Hinton & aJ. 841. Attempts to find a learning rule taking into account hidden units and generating high order predicates failed until recently, which could explain for the decrease of interest in this field for the past 15 years [Minsky & Papert 681. In this paper, we consIder learning and associative memorIzation as dynamic processes and show how to describe the evolution of the weights through an "energy" function. This method will be used to solve the CAP and applied to a model of hierarchical associative memory called HLM (Hierarchical Learning Machine).