Understanding Generalization and Optimization Performance of Deep CNNs
Authors: Pan Zhou, Jiashi Feng
ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based training algorithms. Specifically, for a CNN model consisting of l convolutional layers and one fully connected layer, we prove that its generalization error is bounded by O( p θeϱ/n) where θ denotes freedom degree of the network parameters and eϱ = O(log(Ql i=1 bi(ki si + 1)/p) + log(bl+1)) encapsulates architecture parameters including the kernel size ki, stride si, pooling size p and parameter magnitude bi. To our best knowledge, this is the first generalization bound that only depends on O(log(Ql+1 i=1 bi)), tighter than existing ones that all involve an exponential term like O(Ql+1 i=1 bi). Besides, we prove that for an arbitrary gradient descent algorithm, the computed approximate stationary point by minimizing empirical risk is also an approximate stationary point to the population risk. This well explains why gradient descent training algorithms usually perform sufficiently well in practice. Furthermore, we prove the one-to-one correspondence and convergence guarantees for the non-degenerate stationary points between the empirical and population risks. It implies that the computed local minimum for the empirical risk is also close to a local minimum for the population risk, thus ensuring the good generalization performance of CNNs. |
| Researcher Affiliation | Academia | 1Department of Electrical & Computer Engineering (ECE), National University of Singapore, Singapore. Correspondence to: Pan Zhou <pzhou@u.nus.edu>. |
| Pseudocode | No | No, the paper does not contain any structured pseudocode or algorithm blocks. It focuses on theoretical proofs and mathematical derivations. |
| Open Source Code | No | No, the paper does not provide any concrete access to source code. It is a theoretical paper and does not mention any code release. |
| Open Datasets | No | No, the paper does not provide concrete access information for a publicly available or open dataset. The paper is theoretical and does not use or reference datasets for experimental purposes. |
| Dataset Splits | No | No, the paper does not provide specific dataset split information. This is a theoretical paper and does not involve experimental dataset partitioning. |
| Hardware Specification | No | No, the paper does not provide specific hardware details. This is a theoretical paper and does not describe computational experiments requiring hardware. |
| Software Dependencies | No | No, the paper does not provide specific ancillary software details with version numbers. This is a theoretical paper and does not describe software dependencies for experimental replication. |
| Experiment Setup | No | No, the paper does not contain specific experimental setup details such as hyperparameters or training configurations. This is a theoretical paper focused on mathematical analysis rather than empirical experiments. |