%0 Journal Article %1 nguyen2019field %A Nguyen, Phan-Minh %D 2019 %K approximate dynamic generalization optimization probability readings %T Mean Field Limit of the Learning Dynamics of Multilayer Neural Networks %U http://arxiv.org/abs/1902.02880 %X Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet simplifies away a major part of their complexities? In this work, we uncover a phenomenon in which the behavior of these complex networks -- under suitable scalings and stochastic gradient descent dynamics -- becomes independent of the number of neurons as this number grows sufficiently large. We develop a formalism in which this many-neurons limiting behavior is captured by a set of equations, thereby exposing a previously unknown operating regime of these networks. While the current pursuit is mathematically non-rigorous, it is complemented with several experiments that validate the existence of this behavior.

@article{nguyen2019field, abstract = {Can multilayer neural networks -- typically constructed as highly complex structures with many nonlinearly activated neurons across layers -- behave in a non-trivial way that yet simplifies away a major part of their complexities? In this work, we uncover a phenomenon in which the behavior of these complex networks -- under suitable scalings and stochastic gradient descent dynamics -- becomes independent of the number of neurons as this number grows sufficiently large. We develop a formalism in which this many-neurons limiting behavior is captured by a set of equations, thereby exposing a previously unknown operating regime of these networks. While the current pursuit is mathematically non-rigorous, it is complemented with several experiments that validate the existence of this behavior.}, added-at = {2019-09-26T15:19:44.000+0200}, author = {Nguyen, Phan-Minh}, biburl = {https://www.bibsonomy.org/bibtex/22447daf1e1385709874418fba5f1ee28/kirk86}, description = {[1902.02880] Mean Field Limit of the Learning Dynamics of Multilayer Neural Networks}, interhash = {0cbce0c85ba68fe2dfaff4142aff4fd4}, intrahash = {2447daf1e1385709874418fba5f1ee28}, keywords = {approximate dynamic generalization optimization probability readings}, note = {cite arxiv:1902.02880}, timestamp = {2019-09-26T15:22:21.000+0200}, title = {Mean Field Limit of the Learning Dynamics of Multilayer Neural Networks}, url = {http://arxiv.org/abs/1902.02880}, year = 2019 }