ANALYSIS AND COMPARISON OF DIFFERENT LEARNING ALGORITHMS FOR PATTERN ASSOCIATION PROBLEMS J. Bernasconi Brown Boveri Research Center CH-S40S Baden, Switzerland ABSTRACT We investigate the behavior of different learning algorithms for networks of neuron-like units. As test cases we use simple pattern association problems, such as the XOR-problem and symmetry detection problems. The algorithms considered are either versions of the Boltzmann machine learning rule or based on the backpropagation of errors. We also propose and analyze a generalized delta rule for linear threshold units. We find that the performance of a given learning algorithm depends strongly on the type of units used.

ABSTRACT A novel network type is introduced which uses unit-length 2-vectors for local variables. As an example of its applications, associative memory nets are defined and their performance analyzed. Real systems corresponding to such'phasor' models can be e.g. INTRODUCTION Most neural network models use either binary local variables or scalars combined with sigmoidal nonlinearities. Rather awkward coding schemes have to be invoked if one wants to maintain linear relations between the local signals being processed in e.g.

We propose learning rules for recurrent neural networks with high-order interactions between some or all neurons. The designed networks exhibit the desired associative memory function: perfect storage and retrieval of pieces of information and/or sequences of information of any complexity.

ABSTRACT Advances in brain theory need two complementary approaches: Analytical investigations by in situ measurements and as well synthetic modelling supported by computer simulations to generate suggestive hypothesis on purposeful structures in the neural tissue. In this paper research of the second line is described: Starting from a neurophysiologically inspired model of stimulusresponse (SR) and/or associative memorization and a psychologically motivated ministructure for basic control tasks, preconditions and conditions are studied for cooperation of such units in a hierarchical organisation, as can be assumed to be the general layout of macrostructures in the brain. I. INTRODUCTION Theoretic modelling in brain theory is a highly speculative subject. However, it is necessary since it seems very unlikely to get a clear picture of this very complicated device by just analyzing the available measurements on sound and/or damaged brain parts only. As in general physics, one has to realize, that there are different levels of modelling: in physics stretching from the atomary level over atom assemblies till up to general behavioural models like kinematics and mechanics, in brain theory stretching from chemical reactions over electrical spikes and neuronal cell assembly cooperation till general human behaviour.

The net is defined as a set of units, each witb an activation, and weights between units which determine the activations. The algorithm uses a gradient descent technique to calculate the direction by which each weight should be changed in order to minimise the summed squared difference between the desired output and the actual output. Using this algorithm it is believed that a net can be trained to make an arbitrary nonlinear mapping of the input units onto the output units if given enough intermediate units. This'static' net can be used as part of a larger system with more complex behaviour. The static net has no memory for past inputs, but many problems require the context of the input in order to c.ompute the answer.

(June 1987).

The designed networks exhibit the desired associative memory function: perfect storage and retrieval of pieces of information and/or sequences of information of any complexity. INTRODUCTION In the field of information processing, an important class of potential applications of neural networks arises from their ability to perform as associative memories. Since the publication of J. Hopfield's seminal paper1, investigations of the storage and retrieval properties of recurrent networks have led to a deep understanding of their properties. The basic limitations of these networks are the following: - their storage capacity is of the order of the number of neurons; - they are unable to handle structured problems; - they are unable to classify non-linearly separable data. American Institute of Physics 1988 234 In order to circumvent these limitations, one has to introduce additional non-linearities. This can be done either by using "hidden", nonlinear units, or by considering multi-neuron interactions2. This paper presents learning rules for networks with multiple interactions, allowing the storage and retrieval, either of static pieces of information (autoassociative memory), or of temporal sequences (associative memory), while preventing an explosive growth of the number of synaptic coefficients. AUTOASSOCIATIVEMEMORY The problem that will be addressed in this paragraph is how to design an autoassociative memory with a recurrent (or feedback) neural network when the number p of prototypes is large as compared to the number n of neurons. We consider a network of n binary neurons, operating in a synchronous mode, with period t.

Serial Order: A Parallel Distributed Processing Approach.

ABSTRACT A novel network type is introduced which uses unit-length 2-vectors for local variables. As an example of its applications, associative memory nets are defined and their performance analyzed. Real systems corresponding to such'phasor' models can be e.g. INTRODUCTION Most neural network models use either binary local variables or scalars combined with sigmoidal nonlinearities. Rather awkward coding schemes have to be invoked if one wants to maintain linear relations between the local signals being processed in e.g.

In this paper research of the second line is described: Starting from a neurophysiologically inspired model of stimulusresponse (SR)and/or associative memorization and a psychologically motivated ministructure for basic control tasks, preconditions and conditions are studied for cooperation of such units in a hierarchical organisation, as can be assumed to be the general layout of macrostructures in the brain. I. INTRODUCTION Theoretic modelling in brain theory is a highly speculative subject. However, it is necessary since it seems very unlikely to get a clear picture of this very complicated device by just analyzing theavailable measurements on sound and/or damaged brain parts only. As in general physics, one has to realize, that there are different levels of modelling: in physics stretching from the atomary levelover atom assemblies till up to general behavioural models like kinematics and mechanics, in brain theory stretching from chemical reactions over electrical spikes and neuronal cell assembly cooperation till general human behaviour. The research discussed in this paper is located just above the direct study of synaptic cooperation of neuronal cell assemblies as studied e. g. in /Amari 1988/. It takes into account the changes of synaptic weighting, without simulating the physical details of such changes, and makes use of a general imitation of learning situation (stimuli) - response connections for building up trainable basic control loops, which allow dynamic SR memorization and which are themsel ves elements of some more complex behavioural loops.