标题： 学习霍普菲尔德神经网络中的记忆与遗忘：分岔机制、吸引子和盆地 显示英文标题

标题： Memorisation and forgetting in a learning Hopfield neural network: bifurcation mechanisms, attractors and basins

摘要： 尽管基于人工神经网络（ANNs）的人工智能出现了爆炸性增长，但这些网络被用作“黑箱”，因为在学习过程中，它们如何形成记忆或产生不需要的特征，包括虚假记忆和灾难性遗忘，尚不清楚。 关于学习ANNs的孤立方面有大量研究，但由于其高维度和非线性，全面分析仍是一个挑战。 在ANNs中，知识被认为存在于连接权重或吸引子盆地中，但这两种范式并未明确联系。 在此，我们通过揭示导致吸引子形成和破坏及其盆地边界分岔的机制，全面分析了在Hebbian学习下81个神经元Hopfield网络中的记忆形成机制。 我们表明，施加的刺激通过影响连接权重的演化，诱导出一个分叉，然后是鞍点分叉的级联，创建新的吸引子及其盆地，这些盆地可以编码真实或虚假的记忆，并导致旧记忆的突然消失（灾难性遗忘）。 在成功学习的情况下，新类别由新诞生的点吸引子的盆地表示，其边界由新鞍点的稳定流形表示。 通过这种方式，记忆和遗忘代表了同一机制的两种表现形式。 我们分析高维学习ANNs的策略是通用的，适用于任何形式的循环ANNs。 所展示的记忆形成和灾难性遗忘的机制为更广泛的循环ANNs的操作提供了见解，并可能有助于开发减轻其缺陷的方法。 显示英文摘要

摘要： Despite explosive expansion of artificial intelligence based on artificial neural networks (ANNs), these are employed as "black boxes'', as it is unclear how, during learning, they form memories or develop unwanted features, including spurious memories and catastrophic forgetting. Much research is available on isolated aspects of learning ANNs, but due to their high dimensionality and non-linearity, their comprehensive analysis remains a challenge. In ANNs, knowledge is thought to reside in connection weights or in attractor basins, but these two paradigms are not linked explicitly. Here we comprehensively analyse mechanisms of memory formation in an 81-neuron Hopfield network undergoing Hebbian learning by revealing bifurcations leading to formation and destruction of attractors and their basin boundaries. We show that, by affecting evolution of connection weights, the applied stimuli induce a pitchfork and then a cascade of saddle-node bifurcations creating new attractors with their basins that can code true or spurious memories, and an abrupt disappearance of old memories (catastrophic forgetting). With successful learning, new categories are represented by the basins of newly born point attractors, and their boundaries by the stable manifolds of new saddles. With this, memorisation and forgetting represent two manifestations of the same mechanism. Our strategy to analyse high-dimensional learning ANNs is universal and applicable to recurrent ANNs of any form. The demonstrated mechanisms of memory formation and of catastrophic forgetting shed light on the operation of a wider class of recurrent ANNs and could aid the development of approaches to mitigate their flaws.