We study bi-directional associative neural networks that, exposed to noisy examples of an extensive number of random archetypes, learn the latter (with or without the presence of a teacher) when the supplied information is enough: in this setting, learning is heteroassociative -- involving couples of patterns -- and it is achieved by reverberating the information depicted from the examples through the layers of the network. By adapting Guerra's interpolation technique, we provide a full statistical mechanical picture of supervised and unsupervised learning processes (at the replica symmetric level of description) obtaining analytically phase diagrams, thresholds for learning, a picture of the ground-state in plain agreement with Monte Carlo simulations and signal-to-noise outcomes. In the large dataset limit, the Kosko storage prescription as well as its statistical mechanical picture provided by Kurchan, Peliti, and Saber in the eighties is fully recovered. Computational advantages in dealing with information reverberation, rather than storage, are discussed for natural test cases. In particular, we show how this network admits an integral representation in terms of two coupled restricted Boltzmann machines, whose hidden layers are entirely built of by grand-mother neurons, to prove that by coupling solely these grand-mother neurons we can correlate the patterns they are related to: it is thus possible to recover Pavlov's Classical Conditioning by adding just one synapse among the correct grand-mother neurons (hence saving an extensive number of these links for further information storage w.r.t. the classical autoassociative setting).

翻译：我们研究了双向联想神经网络，该网络在暴露于大量随机原型的噪声示例后，当提供足够的信息时（无论是否存在教师信号），能够学习这些原型：在该设定中，学习是异联想性的——涉及模式对——并且通过将示例中描绘的信息在网络层间来回回响来实现。通过改进Guerra的插值技术，我们提供了有监督和无监督学习过程的完整统计力学图像（在副本对称描述层次上），解析地得到了相图、学习阈值，以及基态的清晰描述，这些结果与蒙特卡洛模拟和信噪比结果高度一致。在大型数据集极限下，完全恢复了Kosko存储规则及其在八十年代由Kurchan、Peliti和Saber给出的统计力学描述。本文讨论了在处理信息回响（而非存储）时的计算优势，并辅以自然测试案例。特别地，我们展示了该网络如何通过两个耦合的限制玻尔兹曼机进行积分表示，其隐藏层完全由祖母神经元构建，从而证明仅通过耦合这些祖母神经元，我们就能关联它们所对应的模式：因此，只需在正确的祖母神经元之间添加一个突触，即可实现对巴甫洛夫经典条件反射的复现（从而相较于经典的自联想设定，节省了大量用于进一步信息存储的链接）。