# DCFNet: Deep Neural Network with Decomposed Convolutional Filters

arXiv: https://arxiv.org/abs/1802.04145 · HTML: https://mlsanity.com/paper/1802.04145/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2018.

## Built on by (most cited first, 23 of 23)

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- [ME-D2N: Multi-Expert Domain Decompositional Network for Cross-Domain Few-Shot Learning](https://mlsanity.com/paper/2210.05280/) (2022)
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- [Phase Collapse in Neural Networks](https://mlsanity.com/paper/2110.05283/) (2021)
- [unzipFPGA: Enhancing FPGA-based CNN Engines with On-the-Fly Weights Generation](https://mlsanity.com/paper/2103.05600/) (2021)
- [The Power of Linear Combinations: Learning with Random Convolutions](https://mlsanity.com/paper/2301.11360/) (2023)
- [Learning Kernel-Modulated Neural Representation for Efficient Light Field Compression](https://mlsanity.com/paper/2307.06143/) (2023)
- [Coeff-Tuning: A Graph Filter Subspace View for Tuning Attention-Based Large Models](https://mlsanity.com/paper/2503.18337/) (2025)
- [CoShNet: A Hybrid Complex Valued Neural Network using Shearlets](https://mlsanity.com/paper/2208.06882/) (2022)
- [Adaptive aggregation of Monte Carlo augmented decomposed filters for efficient group-equivariant convolutional neural network](https://mlsanity.com/paper/2305.10110/) (2023)
- [Mitigating Memory Wall Effects in CNN Engines with On-the-Fly Weights Generation](https://mlsanity.com/paper/2307.13412/) (2023)
- [Generative Quanta Color Imaging](https://mlsanity.com/paper/2403.19066/) (2024)
- [Sparse Fine-Tuning of Transformers for Generative Tasks](https://mlsanity.com/paper/2507.10855/) (2025)
- [AdjointBackMapV2: Precise Reconstruction of Arbitrary CNN Unit's Activation via Adjoint Operators](https://mlsanity.com/paper/2110.01736/) (2021)
- [Learning-based Spatial and Angular Information Separation for Light Field Compression](https://mlsanity.com/paper/2304.06322/) (2023)
- [Efficient 3D affinely equivariant CNNs with adaptive fusion of augmented spherical Fourier-Bessel bases](https://mlsanity.com/paper/2402.16825/) (2024)
- [Boosting Medical Image Segmentation Performance with Adaptive Convolution Layer](https://mlsanity.com/paper/2404.11361/) (2024)
- [Stability Analysis of Equivariant Convolutional Representations Through The Lens of Equivariant Multi-layered CKNs](https://mlsanity.com/paper/2408.04277/) (2024)
- [Extra Clients at No Extra Cost: Overcome Data Heterogeneity in Federated Learning with Filter Decomposition](https://mlsanity.com/paper/2503.08652/) (2025)

## Abstract (arXiv)

Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the Decomposed Convolutional Filters network (DCFNet), where the expansion coefficients remain learned from data. Such a structure not only reduces the number of trainable parameters and computation, but also imposes filter regularity by bases truncation. Through extensive experiments, we consistently observe that DCFNet maintains accuracy for image classification tasks with a significant reduction of model parameters, particularly with Fourier-Bessel (FB) bases, and even with random bases. Theoretically, we analyze the representation stability of DCFNet with respect to input variations, and prove representation stability under generic assumptions on the expansion coefficients. The analysis is consistent with the empirical observations.