Analyzing Monotonic Linear Interpolation in Neural Network Loss Landscapes

04/22/2021 ∙ by James Lucas, et al. ∙ 5

Linear interpolation between initial neural network parameters and converged parameters after training with stochastic gradient descent (SGD) typically leads to a monotonic decrease in the training objective. This Monotonic Linear Interpolation (MLI) property, first observed by Goodfellow et al. (2014) persists in spite of the non-convex objectives and highly non-linear training dynamics of neural networks. Extending this work, we evaluate several hypotheses for this property that, to our knowledge, have not yet been explored. Using tools from differential geometry, we draw connections between the interpolated paths in function space and the monotonicity of the network - providing sufficient conditions for the MLI property under mean squared error. While the MLI property holds under various settings (e.g. network architectures and learning problems), we show in practice that networks violating the MLI property can be produced systematically, by encouraging the weights to move far from initialization. The MLI property raises important questions about the loss landscape geometry of neural networks and highlights the need to further study their global properties.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 2

page 15

page 33

page 34

page 35

page 36

Code Repositories

mli-release

Public source code for the paper "Analyzing Monotonic Linear Interpolation in Neural Network Loss Landscapes"


view repo
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.