AI 中文总结
该研究将学习规则扩展至复值自旋，提出的规则优于赫布学习，证明了Diederich和Opper结果的复值扩展，并测试了振荡器网络对不同模式的联想记忆性能。
AI 中文摘要
在本文中，我们将学习规则从实值二元自旋扩展到复值自旋。这种表述可稳健且自然地表示灰度模式，其中自旋表现为多状态神经元，可存储在复值权重矩阵中。我们描述了一种规则，其性能优于标准方法（如赫布学习），能以适合振荡器网络进行模式检索的形式编码信息。由于神经网络中需要局部且增量的学习规则，我们用复值自旋表述证明了Diederich和Opper的一项结果的扩展。随后，我们在不同场景下测试了振荡器系统的联想记忆行为，分别针对实值、复值相关及随机模式。
英文摘要
In this article, we extend learning rules from real binary to complex-valued spins. This formulation allows for a robust and natural representation of grayscale patterns, where spins behave as multi-state neurons and can be stored in a complex-valued weight matrix. We describe a rule that performs better than standard methods, such as Hebbian learning, to encode information in a suitable form for pattern retrieval with networks of oscillators. Since in neural networks it is of interest to have local and incremental learning rules, we prove the extension of a result by Diederich and Opper with our complex-valued spin formulation. We then test the behavior of the associative memory for the system of oscillators under different circumstances for both real-valued, as well as complex-valued correlated and random patterns.
Comments18 pages, 11 figures
