aiqbench analysis
This paper applies optimal control theory to ResNets, proving that joint loss optimization creates a "turnpike" phenomenon where network depth becomes less critical for early-exit performance. The work provides theoretical grounding for using intermediate layer outputs as regularization and inference shortcuts, directly addressing efficiency-accuracy trade-offs in deep learning architectures.
Towards an Optimal Control Foundation of Early Exits - Turnpikes and ResNets
arXiv:2611.05120v1 Announce Type: new Abstract: The feed-forward propagation through neural networks is crucial for training and inference. To trade off efficiency and accuracy, it has been proposed to consider intermediate outputs of hidden states as data-dependent regularization during training and, ultimately, as early-exits during inference. In this work, we analyze the joint optimization of loss functions computed for the output layer and intermediate layers using optimal control theory. We prove that ResNets trained in this joint fashion exhibit the so-called turnpike phenomenon, this implies that the number of layers required to reach a prescribed loss level is bounded from above independently of the overall network depth. This induces a similarity property across the internal representations of early-exiting networks of varying depths. We connect the turnpike to the overthinking phenomenon, and provide theoretical insights into the success of early-exit criteria derived from softmax probabilities, specifically entropy and max-probability. In a range of experiments, we demonstrate the existence and effect of turnpikes and the resulting similarity in the early-exit performance for ResNets of varying depths.
Abstract:The feed-forward propagation through neural networks is crucial for training and inference. To trade off efficiency and accuracy, it has been proposed to consider intermediate outputs of hidden states as data-dependent regularization during training and, ultimately, as early-exits during inference. In this work, we analyze the joint optimization of loss functions computed for the output layer and intermediate layers using optimal control theory. We prove that ResNets trained in this joint fashion exhibit the so-called turnpike phenomenon, this implies that the number of layers required to reach a prescribed loss level is bounded from above independently of the overall network depth. This induces a similarity property across the internal representations of early-exiting networks of varying depths. We connect the turnpike to the overthinking phenomenon, and provide theoretical insights into the success of early-exit criteria derived from softmax probabilities, specifically entropy and max-probability. In a range of experiments, we demonstrate the existence and effect of turnpikes and the resulting similarity in the early-exit performance for ResNets of varying depths.
Machine Learning (cs.LG); Systems and Control (eess.SY)
arXiv:2611.05120 [cs.LG]
(or arXiv:2611.05120v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.05120 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 266 words