Optimal Weighted Convolution for Classification and Denosing

2025-05-30

AI Summary

Standard convolutional neural networks neglect the relative spatial positions between neighboring and central pixels, limiting their capacity for spatial modeling. To address this, we propose a novel weighted convolution operator that embeds a learnable spatial density function directly into the convolution kernel—enabling adaptive, position-aware weight assignment based on relative coordinates—without increasing model parameters or compromising architectural compatibility. The operator is dimension-agnostic, supporting arbitrary-dimensional regular grid signals, and is designed for plug-and-play integration. Implemented in PyTorch with precomputation for efficient inference, it achieves significant improvements: on CIFAR-100, VGG accuracy increases by 10.05 percentage points to 66.94%; on the DIV2K image denoising benchmark, PSNR improves by 2.46 dB to 22.63—substantially outperforming standard convolution baselines.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning on the Edge & Model Compression

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We introduce a novel weighted convolution operator that enhances traditional convolutional neural networks (CNNs) by integrating a spatial density function into the convolution operator. This extension enables the network to differentially weight neighbouring pixels based on their relative position to the reference pixel, improving spatial characterisation and feature extraction. The proposed operator maintains the same number of trainable parameters and is fully compatible with existing CNN architectures. Although developed for 2D image data, the framework is generalisable to signals on regular grids of arbitrary dimensions, such as 3D volumetric data or 1D time series. We propose an efficient implementation of the weighted convolution by pre-computing the density function and achieving execution times comparable to standard convolution layers. We evaluate our method on two deep learning tasks: image classification using the CIFAR-100 dataset [KH+09] and image denoising using the DIV2K dataset [AT17]. Experimental results with state-of-the-art classification (e.g., VGG [SZ15], ResNet [HZRS16]) and denoising (e.g., DnCNN [ZZC+17], NAFNet [CCZS22]) methods show that the weighted convolution improves performance with respect to standard convolution across different quantitative metrics. For example, VGG achieves an accuracy of 66.94% with weighted convolution versus 56.89% with standard convolution on the classification problem, while DnCNN improves the PSNR value from 20.17 to 22.63 on the denoising problem. All models were trained on the CINECA Leonardo cluster to reduce the execution time and improve the tuning of the density function values. The PyTorch implementation of the weighted convolution is publicly available at: https://github.com/cammarasana123/weightedConvolution2.0.

Problem

• Enhancing CNNs with weighted convolution for better feature extraction
• Improving image classification and denoising performance using spatial density
• Generalizing weighted convolution for multi-dimensional data processing

Innovation

• Weighted convolution with spatial density function
• Compatible with existing CNN architectures
• Efficient pre-computed density function implementation