# Defects of Convolutional Decoder Networks in Frequency Representation

arXiv: https://arxiv.org/abs/2210.09020 · HTML: https://mlsanity.com/paper/2210.09020/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Builds on (most cited first, 20 of 20)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [L2 Regularization versus Batch and Weight Normalization](https://mlsanity.com/paper/1706.05350/) (2017)
- [Learning Representations for Neural Network-Based Classification Using the Information Bottleneck Principle](https://mlsanity.com/paper/1802.09766/) (2018)
- [Machine Learning from a Continuous Viewpoint](https://mlsanity.com/paper/1912.12777/) (2019)
- [Theory of the Frequency Principle for General Deep Neural Networks](https://mlsanity.com/paper/1906.09235/) (2019)
- [Discovering and Explaining the Representation Bottleneck of DNNs](https://mlsanity.com/paper/2111.06236/) (2021)
- [Early Stopping in Deep Networks: Double Descent and How to Eliminate it](https://mlsanity.com/paper/2007.10099/) (2020)
- [Bandlimiting Neural Networks Against Adversarial Attacks](https://mlsanity.com/paper/1905.12797/) (2019)

## Built on by (most cited first, 10 of 10)

- [Frequency-Adaptive Dilated Convolution for Semantic Segmentation](https://mlsanity.com/paper/2403.05369/) (2024)
- [Neuron Structure Modeling for Generalizable Remote Physiological Measurement](https://mlsanity.com/paper/2303.05955/) (2023)
- [Spectral Norm of Convolutional Layers with Circular and Zero Paddings](https://mlsanity.com/paper/2402.00240/) (2024)
- [Beyond Semantic Features: Pixel-level Mapping for Generalized AI-Generated Image Detection](https://mlsanity.com/paper/2512.17350/) (2025)
- [TLNets: Transformation Learning Networks for long-range time-series prediction](https://mlsanity.com/paper/2305.15770/) (2023)
- [Towards the Resistance of Neural Network Watermarking to Fine-tuning](https://mlsanity.com/paper/2505.01007/) (2025)
- [Frequency-Domain Regularized Adversarial Alignment for Transferable Attacks against Closed-Source MLLMs](https://mlsanity.com/paper/2605.21541/) (2026)
- [Frequency Disentangled Learning for Segmentation of Midbrain Structures from Quantitative Susceptibility Mapping Data](https://mlsanity.com/paper/2302.12980/) (2023)
- [Adaptive High-Pass Kernel Prediction for Efficient Video Deblurring](https://mlsanity.com/paper/2412.01559/) (2024)
- [GmNet: Revisiting Gating Mechanisms From A Frequency View](https://mlsanity.com/paper/2503.22841/) (2025)

## Abstract (arXiv)

In this paper, we prove the representation defects of a cascaded convolutional decoder network, considering the capacity of representing different frequency components of an input sample. We conduct the discrete Fourier transform on each channel of the feature map in an intermediate layer of the decoder network. Then, we extend the 2D circular convolution theorem to represent the forward and backward propagations through convolutional layers in the frequency domain. Based on this, we prove three defects in representing feature spectrums. First, we prove that the convolution operation, the zero-padding operation, and a set of other settings all make a convolutional decoder network more likely to weaken high-frequency components. Second, we prove that the upsampling operation generates a feature spectrum, in which strong signals repetitively appear at certain frequencies. Third, we prove that if the frequency components in the input sample and frequency components in the target output for regression have a small shift, then the decoder usually cannot be effectively learned.