Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models on the other hand have gained popularity due to their interpretability but their application to complex machine learning tasks remains limited. In this work, we present a diffusion model-inspired deep random feature model that is interpretable and gives comparable numerical results to a fully connected neural network having the same number of trainable parameters. Specifically, we extend existing results for random features and derive generalization bounds between the distribution of sampled data and the true distribution using properties of score matching. We validate our findings by generating samples on the fashion MNIST dataset and instrumental audio data.

翻译：扩散概率模型已成功用于从噪声生成数据，然而大多数扩散模型计算成本高昂且缺乏理论解释性。相比之下，随机特征模型因其可解释性而受到关注，但在复杂机器学习任务中的应用仍有限。本文提出一种受扩散模型启发的深度随机特征模型，该模型具有可解释性，且在与具有相同可训练参数数量的全连接神经网络相比时，能产生可比较的数值结果。具体而言，我们扩展了现有随机特征的理论结果，并利用分数匹配的性质推导了采样数据分布与真实分布之间的泛化界限。我们通过在Fashion MNIST数据集和乐器音频数据上生成样本来验证我们的发现。