← 研踪 PaperTrailarXiv:2611.05120 · v1
Towards an Optimal Control Foundation of Early Exits - Turnpikes and ResNets
首次提交 2026-11-04 00:08
版本更新 2026-11-04 00:08
雷达观测 2026-11-04 23:39
摘要
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.
作者备注：Accepted at NeurIPS 2026
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-04 00:08 · 最新观测版本
Towards an Optimal Control Foundation of Early Exits - Turnpikes and ResNets
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.
查看此版本解读 →查看此版本原文 ↗