ABSTRACT The information capacity of Kanerva's Sparse, Distributed Memory (SDM) and Hopfield-type neural networks is investigated. Under the approximations used here, it is shown that the total information stored in these systems is proportional to the number connections in the network. The proportionality constant is the same for the SDM and HopJreld-type models independent of the particular model, or the order of the model. The approximations are checked numerically. This same analysis can be used to show that the SDM can store sequences of spatiotemporal patterns, and the addition of time-delayed connections allows the retrieval of context dependent temporal patterns. A minor modification of the SDM can be used to store correlated patterns. INTRODUCTION Many different models of memory and thought have been proposed by scientists over the years. The learning rule considered here uses the outer-product of patterns of Is and -Is.

THE CAPACITY OF THE KANERVA ASSOCIATIVE MEMORY IS EXPONENTIAL P. A. Chou CA 94305 ABSTRACT The capacity of an associative memory is defined as the maximum number of vords that can be stored and retrieved reliably by an address vithin a given sphere of attraction. It is shown by sphere packing arguments that as the address length increases. This exponential grovth in capacity can actually be achieved by the Kanerva associative memory. Formulas for these op.timal values are provided. The exponential grovth in capacity for the Kanerva associative memory contrasts sharply vith the sub-linear grovth in capacity for the Hopfield associative memory.

This paper describes an approach to 2-dimensional object recognition. Complex-log conformal mapping is combined with a distributed associative memory to create a system which recognizes objects regardless of changes in rotation or scale. Recalled information from the memorized database is used to classify an object, reconstruct the memorized version of the object, and estimate the magnitude of changes in scale or rotation. The system response is resistant to moderate amounts of noise and occlusion. Several experiments, using real, gray scale images, are presented to show the feasibility of our approach. Introduction The challenge of the visual recognition problem stems from the fact that the projection of an object onto an image can be confounded by several dimensions of variability such as uncertain perspective, changing orientation and scale, sensor noise, occlusion, and nonuniform illumination.

REFLEXIVE ASSOCIATIVE MEMORIES Hendrlcus G. Loos Laguna Research Laboratory, Fallbrook, CA 92028-9765 ABSTRACT In the synchronous discrete model, the average memory capacity of bidirectional associative memories (BAMs) is compared with that of Hopfield memories, by means of a calculat10n of the percentage of good recall for 100 random BAMs of dimension 64x64, for different numbers of stored vectors. The memory capac1ty Is found to be much smal1er than the Kosko upper bound, which Is the lesser of the two dimensions of the BAM. On the average, a 64x64 BAM has about 68 % of the capacity of the corresponding Hopfield memory with the same number of neurons. The memory capacity limitations are due to spurious stable states, which arise In BAMs In much the same way as in Hopfleld memories. Occurrence of spurious stable states can be avoided by replacing the thresholding in the backlayer of the BAM by another nonl1near process, here called "Dominant Label Selection" (DLS).

Recently, many modifications to the McCulloch/Pitts model have been proposed where both learning and forgetting occur. Given that the network never saturates (ceases to function effectively due to an overload of information), the learning updates can continue indefinitely. For these networks, we need to introduce performance measmes in addition to the information capacity to evaluate the different networks. We mathematically define quantities such as the plasticity of a network, the efficacy of an information vector, and the probability of network saturation. From these quantities we analytically compare different networks.

ABSTRACT The information capacity of Kanerva's Sparse, Distributed Memory (SDM) and Hopfield-type neural networks is investigated. Under the approximations used here, it is shown that the total information stored in these systems is proportional to the number connections in the network. The proportionality constant is the same for the SDM and HopJreld-type models independent of the particular model, or the order of the model. The approximations are checked numerically. This same analysis can be used to show that the SDM can store sequences of spatiotemporal patterns, and the addition of time-delayed connections allows the retrieval of context dependent temporal patterns. A minor modification of the SDM can be used to store correlated patterns. INTRODUCTION Many different models of memory and thought have been proposed by scientists over the years. The learning rule considered here uses the outer-product of patterns of Is and -Is.

THE CAPACITY OF THE KANERVA ASSOCIATIVE MEMORY IS EXPONENTIAL P. A. Chou CA 94305 ABSTRACT The capacity of an associative memory is defined as the maximum number of vords that can be stored and retrieved reliably by an address vithin a given sphere of attraction. It is shown by sphere packing arguments that as the address length increases. This exponential grovth in capacity can actually be achieved by the Kanerva associative memory. Formulas for these op.timal values are provided. The exponential grovth in capacity for the Kanerva associative memory contrasts sharply vith the sub-linear grovth in capacity for the Hopfield associative memory.

ABSTRACT The information capacity of Kanerva's Sparse, Distributed Memory (SDM) and Hopfield-type neural networks is investigated. Under the approximations used here, it is shown that the total informationstored in these systems is proportional to the number connections in the network. Theproportionality constant is the same for the SDM and HopJreld-type models independent ofthe particular model, or the order of the model. The approximations are checked numerically. This same analysis can be used to show that the SDM can store sequences ofspatiotemporal patterns, and the addition of time-delayed connections allows the retrieval of context dependent temporal patterns. A minor modification of the SDM can be used to store correlated patterns. INTRODUCTION Many different models of memory and thought have been proposed by scientists over the years.

Invariant Object Recognition Using a Distributed Associative Memory Harry Wechsler and George Lee Zimmerman Department or Electrical Engineering University or Minnesota Minneapolis, MN 55455 Abstract This paper describes an approach to 2-dimensional object recognition. Complex-log conformal mappingis combined with a distributed associative memory to create a system which recognizes objects regardless of changes in rotation or scale. Recalled information from the memorized database is used to classify an object, reconstruct the memorized version ofthe object, and estimate the magnitude of changes in scale or rotation. The system response is resistant to moderate amounts of noise and occlusion. Several experiments, using real,gray scale images, are presented to show the feasibility of our approach. Introduction The challenge of the visual recognition problem stems from the fact that the projection of an object onto an image can be confounded by several dimensions of variability such as uncertain perspective, changing orientation and scale, sensor noise, occlusion, and nonuniform illumination.

The memory capac1ty Is found to be much smal1er than the Kosko upper bound, which Is the lesser of the two dimensions of the BAM. On the average, a 64x64 BAM has about 68 %of the capacity of the corresponding Hopfield memory with the same number of neurons.