The beneficial role of noise-injection in learning is a consolidated concept in the field of artificial neural networks, suggesting that even biological systems might take advantage of similar mechanisms to optimize their performance. The training-with-noise algorithm proposed by Gardner and collaborators is an emblematic example of a noise-injection procedure in recurrent networks, which can be used to model biological neural systems. We show how adding structure to noisy training data can substantially improve the algorithm performance, allowing the network to approach perfect retrieval of the memories and wide basins of attraction, even in the scenario of maximal injected noise. We also prove that the so-called Hebbian Unlearning rule coincides with the training-with-noise algorithm when noise is maximal and data are stable fixed points of the network dynamics.

翻译：噪声注入在学习中的积极作用是人工神经网络领域的一个成熟概念，表明生物系统也可能利用类似机制优化其表现。Gardner及其合作者提出的带噪训练算法是循环网络中噪声注入方法的典范案例，可用于模拟生物神经系统的建模。我们证明，向训练数据添加结构化噪声能显著提升算法性能——即使在最大噪声注入场景下，网络也能接近完美的记忆检索并形成宽泛的吸引域。同时，我们证实所谓Hebbian遗忘规则与带噪训练算法在噪声最大且数据为网络动力学稳定不动点条件下完全等价。