论文标题
连接神经网络和宇宙动力学的双重性
A duality connecting neural network and cosmological dynamics
论文作者
论文摘要
我们证明，通过梯度下降训练的神经网络的动力学以及平坦，真空能量主导的宇宙中标量场的动力学在结构上是密切相关的。这种二元性为这些系统之间的协同作用提供了一个框架，以理解和解释神经网络动态以及模拟和描述早期宇宙模型的新方法。在神经网络的连续时间限制下工作，我们在分析上与平均背景的动力学和平均磁场周围的小扰动的动力学匹配，突出了单独限制中的潜在差异。我们对该分析描述进行经验测试，并定量地显示了有效的现场理论参数对神经网络超参数的依赖性。由于这种二元性，宇宙常数与梯度下降更新中的学习率成反比。
We demonstrate that the dynamics of neural networks trained with gradient descent and the dynamics of scalar fields in a flat, vacuum energy dominated Universe are structurally profoundly related. This duality provides the framework for synergies between these systems, to understand and explain neural network dynamics and new ways of simulating and describing early Universe models. Working in the continuous-time limit of neural networks, we analytically match the dynamics of the mean background and the dynamics of small perturbations around the mean field, highlighting potential differences in separate limits. We perform empirical tests of this analytic description and quantitatively show the dependence of the effective field theory parameters on hyperparameters of the neural network. As a result of this duality, the cosmological constant is matched inversely to the learning rate in the gradient descent update.
