 
Summary: IEEE TRANSACTIONS ON NEURAL. NEIWOKKS. Vol. 4. N O I . JANL'AKY lW.3 117
An Analog Feedback Associative Memory
Amir Atiya, Mcmher, IEEE, and Yaser S. AbuMostafa
Abstruct Most of the neural network associative memory
models deal with the storage of binary vectors. We consider the
Hopfield continuoustime network, and develop a new method
for the storage of analog vectors, i.e., vectors whose components
are realvalued. An important requirement is that each memory
vector has to be an asymptotically stable (i.e., attractive) equi
librium of the network. We point out some of the limitations
of the continuous Hopfield model on the set of vectors that
can be stored. These limitations can be relieved by choosing
a network containing visible as well as hidden units. We have
chosen an architecture consisting of several hidden layers and
a visible layer, connected in a circular fashion. We prove that
the twolayer case of such an architecture is guaranteed to store
any number of given analog vectors provided their number
does not exceed 1 + the number of neurons in the hidden
layer. We have developed a learning algorithm, which results
in correctly adjusting the locations of the equilibria, as well
