用最优密度函数加权卷积，提升图像任务精度。
Optimal Density Functions for Weighted Convolution in Learning Models
- 基于距离设计密度函数，动态调节邻域像素贡献。
- 图像去噪任务中损失降低53%，测试准确率显著提升。
- 适合对精度要求高、可接受小幅提速的图像学习场景。
本文提出加权卷积，通过引入最优密度函数，根据邻近像素与中心像素的距离动态调整其在卷积中的贡献，区别于传统均匀卷积。该方法可应用于卷积神经网络以提高逼近精度。针对给定网络，构建最小化模型框架，分别使用随机梯度下降优化卷积核权重，采用DIRECT-L算法优化密度函数。在图像到图像任务（如图像去噪）上的实验表明，加权卷积可使损失减少高达53%，同时提升测试准确率。尽管执行时间增加11%，但对多种超参数具有鲁棒性。未来工作将拓展至真实场景的2D和3D图像卷积学习问题。
原文摘要 · Abstract (English)
The paper introduces the weighted convolution, a novel approach to the convolution for signals defined on regular grids (e.g., 2D images) through the application of an optimal density function to scale the contribution of neighbouring pixels based on their distance from the central pixel. This choice differs from the traditional uniform convolution, which treats all neighbouring pixels equally. Our weighted convolution can be applied to convolutional neural network problems to improve the approximation accuracy. Given a convolutional network, we define a framework to compute the optimal density function through a minimisation model. The framework separates the optimisation of the convolutional kernel weights (using stochastic gradient descent) from the optimisation of the density function (using DIRECT-L). Experimental results on a learning model for an image-to-image task (e.g., image denoising) show that the weighted convolution significantly reduces the loss (up to 53% improvement) and increases the test accuracy compared to standard convolution. While this method increases execution time by 11%, it is robust across several hyperparameters of the learning model. Future work will apply the weighted convolution to real-case 2D and 3D image convolutional learning problems.
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