The problem of neural network association is to retrieve a previously memorized pattern from its noisy version using a network of neurons. An ideal neural network should include three components simultaneously: a learning algorithm, a large pattern retrieval capacity and resilience against noise. Prior works in this area usually improve one or two aspects at the cost of the third. Our work takes a step forward in closing this gap. More specifically, we show that by forcing natural constraints on the set of learning patterns, we can drastically improve the retrieval capacity of our neural network. Moreover, we devise a learning algorithm whose role is to learn those patterns satisfying the above mentioned constraints. Finally we show that our neural network can cope with a fair amount of noise.
Due to the low capacity of Hopfield networks, extension of associative memories to non-binary neural models has also been explored in the past. Hopfield addressed the case of continuous neurons and showed that similar to the binary case, neurons with states between @math and @math can memorize a set of random patterns, albeit with less capacity @cite_11 . In @cite_8 the authors investigated a multi-state complex-valued neural associative memories for which the estimated capacity is @math . Under the same model but using a different learning method, @cite_6 showed that the capacity can be increased to @math . However the complexity of the weight computation mechanism is prohibitive. To overcome this drawback, a Modified Gradient Descent learning Rule (MGDR) was devised in @cite_7 .
@cite_8 @cite_7 @cite_6 @cite_11
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Associative memories retrieve stored information given partial or erroneous input patterns. Recently, a new family of associative memories based on Clustered-Neural-Networks (CNNs) was introduced that can store many more messages than classical Hopfield-Neural Networks (HNNs). In this paper, we propose hardware architectures of such memories for partial or erroneous inputs. The proposed architectures eliminate winner-take-all modules and thus reduce the hardware complexity by consuming 65 fewer FPGA lookup tables and increase the operating frequency by approximately 1.9 times compared to that of previous work. We consider the problem of neural association for a network of non-binary neurons. Here, the task is to recall a previously memorized pattern from its noisy version using a network of neurons whose states assume values from a finite number of non-negative integer levels. Prior works in this area consider storing a finite number of purely random patterns, and have shown that the pattern retrieval capacities (maximum number of patterns that can be memorized) scale only linearly with the number of neurons in the network. In our formulation of the problem, we consider storing patterns from a suitably chosen set of patterns, that are obtained by enforcing a set of simple constraints on the coordinates (such as those enforced in graph based codes). Such patterns may be generated from purely random information symbols by simple neural operations. Two simple neural update algorithms are presented, and it is shown that our proposed mechanisms result in a pattern retrieval capacity that is exponential in terms of the network size. Furthermore, using analytical results and simulations, we show that the suggested methods can tolerate a fair amount of errors in the input. A model of a multivalued associative memory is presented. This memory has the form of a fully connected attractor neural network composed of multistate complex-valued neurons. Such a network is able to perform the task of storing and recalling gray-scale images. It is also shown that the complex-valued fully connected neural network may be considered as a generalization of a Hopfield network containing real-valued neurons. A computational energy function is introduced and evaluated in order to prove network stability for asynchronous dynamics. Storage capacity as related to the number of accessible neuron states is also estimated. The Hopfield model for a neural network is studied in the limit when the number @math of stored patterns increases with the size @math of the network, as @math . It is shown that, despite its spin-glass features, the model exhibits associative memory for @math , @math . This is a result of the existence at low temperature of @math dynamically stable degenerate states, each of which is almost fully correlated with one of the patterns. These states become ground states at @math . The phase diagram of this rich spin-glass is described.