Over-parameterized Model Optimization with Polyak-{\L}ojasiewicz Condition

Yixuan Chen, Yubin Shi, Mingzhi Dong, Xiaochen Yang, Dongsheng Li, Yujiang Wang, Robert P. Dick, Qin Lv, Yingying Zhao, Fan Yang, Ning Gu, Li Shang

Keywords: Over-parameterized Model, Model Optimization, Polyak-{\L}ojasiewicz Condition.

TL;DR: This work proposes a new regularized risk minimization for over-parameterized models with a novel PL regularization and implements it via network pruning guided by PL-based condition number.

Abstract: This work pursues the optimization of over-parameterized deep models for superior training efficiency and test performance. We first theoretically emphasize the importance of two properties of over-parameterized models, i.e., the convergence gap and the generalization gap. Subsequent analyses unveil that these two gaps can be upper-bounded by the ratio of the Lipschitz constant and the Polyak-{\L}ojasiewicz (PL) constant, a crucial term abbreviated as the \emph{condition number}. Such discoveries have led to a structured pruning method with a novel pruning criterion. That is, we devise a gating network that dynamically detects and masks out those poorly-behaved nodes of a deep model during the training session. To this end, this gating network is learned via minimizing the \emph{condition number} of the target model, and this process can be implemented as an extra regularization loss term. Experimental studies demonstrate that the proposed method outperforms the baselines in terms of both training efficiency and test performance, exhibiting the potential of generalizing to a variety of deep network architectures and tasks.

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: Deep Learning and representational learning