将神经元突触可塑性与噪声梯度下降关联，证明其快速收敛到最活跃的前驱神经元。
Spike-timing-dependent Hebbian learning as noisy gradient descent
- 将脉冲时间依赖型可塑性建模为在概率单纯形上的噪声梯度下降
- 在非凸损失函数下仍实现指数级快速收敛，识别出活动最强的前驱神经元
- 揭示生物学习机制背后的优化本质，适合神经科学与类脑计算研究者
海布学习是生物神经网络学习的核心原则。本文将一种脉冲时间依赖的海布可塑性规则，与在概率单纯形上针对非凸损失函数的噪声梯度下降相联系。尽管持续存在噪声且优化问题非凸，但可严格证明该海布学习动态能识别出活动最高的前驱神经元，且收敛速度随迭代次数呈指数级加快。这与通常情况不同：固定噪声水平下的噪声梯度下降仅能收敛至一个噪声导致动态在极小值附近波动的稳态。
原文摘要 · Abstract (English)
Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a non-convex loss function on the probability simplex. Despite the constant injection of noise and the non-convexity of the underlying optimization problem, one can rigorously prove that the considered Hebbian learning dynamic identifies the presynaptic neuron with the highest activity and that the convergence is exponentially fast in the number of iterations. This is non-standard and surprising as typically noisy gradient descent with fixed noise level only converges to a stationary regime where the noise causes the dynamic to fluctuate around a minimiser.
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