An associative memory is an artificial neural network model designed to store and recall input-output patterns pairs by association. A new method for obtaining two associative memories +M and -M is presented in this article, which uses a framework focused on two new binary operations boxplus and boxminus, and a unary operation called projection. The conditions to obtaining perfect recovery and the noise boundaries that the memories can tolerate are studied. Memories +M and -M are robust to additive and subtractive noise, respectively, both types converge in one-step and operate in heteroassociative and autoassociative modes. The performance of the proposed memories is tested against other memory models under identical conditions using the gamma binary distance for measuring similarity between binary patterns. The computer simulation results based on the average of 500 trials with the binary set of 26 lowercase letters of 7x7 pixel size, showed that the proposed memories in autoassociative mode exhibited a gamma binary distance of above .8, .75 and .7 by distorting up to 10 pixels by additive, subtractive, and mixed noise, respectively, which implied that the recovered images had a high similarity. In absence of noise the performance was excellent, i.e., the 100% of the recovered images were identical.

中文翻译：

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构建联想记忆模型的新方法


联想记忆是一种人工神经网络模型，旨在通过关联来存储和回忆输入输出模式对。本文提出了一种获取两个联想记忆+M和-M的新方法，该方法使用一个专注于两个新的二元运算boxplus和boxminus以及称为投影的一元运算的框架。研究了获得完美恢复的条件以及存储器可以容忍的噪声边界。存储器+M和-M分别对加性和减性噪声具有鲁棒性，两种类型一步收敛，并以异关联和自关联模式运行。在相同条件下，使用伽玛二进制距离来测量二进制模式之间的相似性，对所提出的存储器的性能与其他存储器模型进行测试。基于对 7x7 像素大小的 26 个小写字母的二进制集进行 500 次平均试验的计算机模拟结果表明，所提出的自联想模式存储器通过扭曲向上表现出高于 0.8、0.75 和 0.7 的伽玛二进制距离。通过加性噪声、减性噪声和混合噪声分别达到 10 个像素，这意味着恢复的图像具有很高的相似性。在没有噪声的情况下，性能非常出色，即恢复的图像 100% 相同。