arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2402.08010cs.LGcs.AIstat.ML

CNN需要哪些频率?特征学习中的涌现瓶颈结构

Which Frequencies do CNNs Need? Emergent Bottleneck Structure in Feature Learning

Courant Institute of Mathematical Sciences, New York University(纽约大学柯朗数学科学研究所)

Yuxiao Wen, Arthur Jacot

AI总结:

描述了CNN中卷积瓶颈(CBN)结构的涌现,定义了CBN秩并证明参数范数随深度与CBN秩缩放,揭示了该结构与下采样的关系,并用于解释CNN学到的函数。

摘要:

我们描述了CNN中卷积瓶颈(CBN)结构的涌现,网络利用前几层将输入表示转换为仅由少数频率和通道支持的表示,随后利用最后几层映射回输出。我们定义了CBN秩,用于描述瓶颈内保留的频率数量和类型,并部分证明表示函数$f$所需的参数范数随深度与CBN秩$f$的乘积而缩放。我们还表明参数范数在下一阶上依赖于$f$的正则性。我们证明任何具有近乎最优参数范数的网络都会在权重中表现出CBN结构,且在网络对大学习率稳定的假设下,其激活值也会表现出该结构,这为下采样的常见做法提供了动机;我们验证了在下采样情况下CBN结果依然成立。最后,我们利用CBN结构来解释CNN在多项任务中学习到的函数。

英文摘要:

We describe the emergence of a Convolution Bottleneck (CBN) structure in CNNs, where the network uses its first few layers to transform the input representation into a representation that is supported only along a few frequencies and channels, before using the last few layers to map back to the outputs. We define the CBN rank, which describes the number and type of frequencies that are kept inside the bottleneck, and partially prove that the parameter norm required to represent a function $f$ scales as depth times the CBN rank $f$. We also show that the parameter norm depends at next order on the regularity of $f$. We show that any network with almost optimal parameter norm will exhibit a CBN structure in both the weights and - under the assumption that the network is stable under large learning rate - the activations, which motivates the common practice of down-sampling; and we verify that the CBN results still hold with down-sampling. Finally we use the CBN structure to interpret the functions learned by CNNs on a number of tasks.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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