Block-level Stiffness Analysis of Residual Networks

Eliska Kloberdanz, Wei Le

Keywords: resnets, stiffness, ordinary differential equations

TL;DR: In this paper we are the first ones to connect the concepts of stiffness and ResNets via the dynamical systems interpretation to propose that ResNets can be viewed as stiff ODEs.

Abstract: Residual Networks (ResNets) can be interpreted as dynamic systems, which are systems whose state changes over time and can be described with ordinary differential equations (ODEs). Specifically, the dynamic systems interpretation views individual residual blocks as ODEs. The solution to an ODE is an approximation; and therefore contains an error term. If an ODE is stiff it is likely that this error is amplified and becomes dominating in the solution calculations, which negatively affects the accuracy of the approximated solution. Therefore, stiff ODEs are often numerically unstable. In this paper we leverage the dynamic systems interpretation to perform a novel theoretical analysis of ResNets by leveraging findings and tools from numerical analysis of ODEs. Specifically, we perform block level stiffness analysis of ResNets. We find that residual blocks towards the end of ResNet models exhibit increased stiffness and that there is a significant correlation between stiffness and model accuracy and loss. Based on these findings, we propose that ResNets behave as stiff numerically unstable ODEs.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Theory (eg, control theory, learning theory, algorithmic game theory)