The Gripon-Berrou neural network (GBNN) is a recently invented recurrent neural network embracing a LDPC-like sparse encoding setup which makes it extremely resilient to noise and errors. A natural use of GBNN is as an associative memory. There are two activation rules for the neuron dynamics, namely sum-of-sum and sum-of-max. The latter outperforms the former in terms of retrieval rate by a huge margin. In prior discussions and experiments, it is believed that although sum-of-sum may lead the network to oscillate, sum-of-max always converges to an ensemble of neuron cliques corresponding to previously stored patterns. However, this is not entirely correct. In fact, sum-of-max often converges to bogus fixed points where the ensemble only comprises a small subset of the converged state. By taking advantage of this overlooked fact, we can greatly improve the retrieval rate. We discuss this particular issue and propose a number of heuristics to push sum-of-max beyond these bogus fixed points. To tackle the problem directly and completely, a novel post-processing algorithm is also developed and customized to the structure of GBNN. Experimental results show that the new algorithm achieves a huge performance boost in terms of both retrieval rate and run-time, compared to the standard sum-of-max and all the other heuristics.
There are three important concepts to describe the quality of an associative memory: diversity (the number of paired patterns that the network can store), capacity (the maximum amount of stored information in bits) and efficiency (the ratio between the capacity and the amount of information that the network can store when the diversity reaches its maximum). @cite_9 , Gripon and Berrou have shown that, given the same amount of storage, GBNN outperforms the conventional Hopfield network in all of them, while decreasing the retrieval error rate. The initial retrieval rule used in @cite_9 was . Later in @cite_28 , the same authors also interpret GBNN using the formalism of error correcting codes, and propose a second retrieval rule which further decreases the error rate. We will discuss the mechanics of both rules in . Jiang al @cite_23 modify GBNN to learn long sequences by incorporating directed links. Aliabadi al @cite_15 extend GBNN to learn sparse messages.
@cite_28 @cite_9 @cite_23 @cite_15
2037808679 1553143087 2101055774 1666036116
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. Associative memories store content in such a way that the content can be later retrieved by presenting the memory with a small portion of the content, rather than presenting the memory with an address as in more traditional memories. Associative memories are used as building blocks for algorithms within database engines, anomaly detection systems, compression algorithms, and face recognition systems. A classical example of an associative memory is the Hopfield neural network. Recently, Gripon and Berrou have introduced an alternative construction which builds on ideas from the theory of error correcting codes and which greatly outperforms the Hopfield network in capacity, diversity, and efficiency. In this paper we implement a variation of the Gripon-Berrou associative memory on a general purpose graphical processing unit (GPU). The work of Gripon and Berrou proposes two retrieval rules, sum-of-sum and sum-of-max. The sum-of-sum rule uses only matrix-vector multiplication and is easily implemented on the GPU. The sum-of-max rule is much less straightforward to implement because it involves non-linear operations. However, the sum-of-max rule gives significantly better retrieval error rates. We propose a hybrid rule tailored for implementation on a GPU which achieves a 880-fold speedup without sacrificing any accuracy. The task of a neural associative memory is to retrieve a set of previously memorized patterns from their noisy versions by using a network of neurons. Hence, an ideal network should be able to 1) gradually learn a set of patterns, 2) retrieve the correct pattern from noisy queries and 3) maximize the number of memorized patterns while maintaining the reliability in responding to queries. We show that by considering the inherent redundancy in the memorized patterns, one can obtain all the mentioned properties at once. This is in sharp contrast with previous work that could only improve one or two aspects at the expense of the others. More specifically, we devise an iterative algorithm that learns the redundancy among the patterns. The resulting network has a retrieval capacity that is exponential in the size of the network. Lastly, by considering the local structures of the network, the asymptotic error correction performance can be made linear in the size of the network. The Gripon-Berrou neural network (GBNN) is a recently invented recurrent neural network embracing a LDPC-like sparse encoding setup which makes it extremely resilient to noise and errors. A natural use of GBNN is as an associative memory. There are two activation rules for the neuron dynamics, namely sum-of-sum and sum-of-max. The latter outperforms the former in terms of retrieval rate by a huge margin. In prior discussions and experiments, it is believed that although sum-of-sum may lead the network to oscillate, sum-of-max always converges to an ensemble of neuron cliques corresponding to previously stored patterns. However, this is not entirely correct. In fact, sum-of-max often converges to bogus fixed points where the ensemble only comprises a small subset of the converged state. By taking advantage of this overlooked fact, we can greatly improve the retrieval rate. We discuss this particular issue and propose a number of heuristics to push sum-of-max beyond these bogus fixed points. To tackle the problem directly and completely, a novel post-processing algorithm is also developed and customized to the structure of GBNN. Experimental results show that the new algorithm achieves a huge performance boost in terms of both retrieval rate and run-time, compared to the standard sum-of-max and all the other heuristics.