发表机构
Utrecht University; Institute for Theoretical Physics（乌得勒支大学; 理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究修改NN/QFT对偶性，构建(0+1)维格点规范理论框架，计算深度网络的神经元传播子与散射振幅，为研究深度网络的高阶关联及信息传播提供场论方法。
AI 中文摘要
我们修改了NN/QFT对偶性[1]，以纳入网络的逐层置换对称性，从而得到一个(0+1)维格点规范理论，其中N个神经元的每一层充当一个N分量格点位点，权重矩阵扮演着位于链路上的规范场的角色。在该框架中，我们计算树级神经元-神经元传播子，其描述网络中层方差的演化，并开发费曼图机制以计算1/N微扰展开中的相互作用。特别地，我们获得了O(1)阶精确传播子所有修正的递归表达式，代表网络系综中的统计涨落，包括介导前层相互作用的无穷多圈图。我们还给出了神经元散射振幅的初步分析，其贡献按1/N阶逐次展开，这为研究深度网络中的高阶关联及延伸的信息传播提供了场论框架。我们还讨论了神经网络与量子场论交叉领域的一些有趣未来研究方向。
英文摘要
We modify the NN/QFT duality [1] to incorporate the layerwise permutation symmetry of the network, resulting in a $(0\!+\!1)$-dimensional lattice gauge theory, in which each layer of $N$ neurons acts as an $N$-component lattice site, and the weight matrices play the role of gauge fields living on the links. In this framework, we compute the tree-level neuron-neuron propagator which describes the evolution of layer variance in the network, and develop the Feynman diagram machinery to compute interactions in the perturbative expansion in $1/N$. In particular, we obtain a recursive expression for all corrections to the exact propagator at $O(1)$, representing statistical fluctuations in the ensemble of networks, including infinitely-many loop diagrams mediating the interactions from previous layers. We also present a preliminary analysis of neuron scattering amplitudes that contribute order-by-order in $1/N$, which provides a field-theoretic framework for studying higher-point correlations, and by extension information propagation, in deep networks. We remark on some interesting directions for future work at the intersection of neural networks and quantum field theory.
Comments40 pages, infinite figures
