# Harmonic Convolutional Networks based on Discrete Cosine Transform

arXiv: https://arxiv.org/abs/2001.06570 · HTML: https://mlsanity.com/paper/2001.06570/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2020.

## Built on by (most cited first, 14 of 14)

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- [A Hybrid Quantum-Classical Approach based on the Hadamard Transform for the Convolutional Layer](https://mlsanity.com/paper/2305.17510/) (2023)
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- [DCT Perceptron Layer: A Transform Domain Approach for Convolution Layer](https://mlsanity.com/paper/2211.08577/) (2022)
- [Performance of Gaussian Mixture Model Classifiers on Embedded Feature Spaces](https://mlsanity.com/paper/2410.13421/) (2024)
- [Multichannel Orthogonal Transform-Based Perceptron Layers for Efficient ResNets](https://mlsanity.com/paper/2303.06797/) (2023)
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- [Quaternion-Hadamard Network: A Novel Defense Against Adversarial Attacks with a New Dataset](https://mlsanity.com/paper/2502.10452/) (2025)
- [SL-FAC: A Communication-Efficient Split Learning Framework with Frequency-Aware Compression](https://mlsanity.com/paper/2604.07316/) (2026)
- [DCT-Mamba3D: Spectral Decorrelation and Spatial-Spectral Feature Extraction for Hyperspectral Image Classification](https://mlsanity.com/paper/2502.01986/) (2025)
- [PRISM: Lightweight Multivariate Time-Series Classification through Symmetric Multi-Resolution Convolutional Layers](https://mlsanity.com/paper/2508.04503/) (2025)
- [Breaking the Scale Barrier: One-Shot Knowledge Transfer via Frequency Transform](https://mlsanity.com/paper/2603.07523/) (2026)
- [Bit-Identical Medical Deep Learning via Structured Orthogonal Initialization](https://mlsanity.com/paper/2603.28040/) (2026)
- [Training Transformers in Cosine Coefficient Space](https://mlsanity.com/paper/2604.04440/) (2026)

## Abstract (arXiv)

Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. We propose to learn these filters as combinations of preset spectral filters defined by the Discrete Cosine Transform (DCT). Our proposed DCT-based harmonic blocks replace conventional convolutional layers to produce partially or fully harmonic versions of new or existing CNN architectures. Using DCT energy compaction properties, we demonstrate how the harmonic networks can be efficiently compressed by truncating high-frequency information in harmonic blocks thanks to the redundancies in the spectral domain. We report extensive experimental validation demonstrating benefits of the introduction of harmonic blocks into state-of-the-art CNN models in image classification, object detection and semantic segmentation applications.