Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve competitive results both for supervised and unsupervised learning tasks, while making progress towards constructing more interpretable CNNs. For supervised learning, we demonstrate that the early layers of CNNs do not necessarily need to be learned, and can be replaced with a scattering network instead. Indeed, using hybrid architectures, we achieve the best results with predefined representations to-date, while being competitive with end-to-end learned CNNs. Specifically, even applying a shallow cascade of small-windowed scattering coefficients followed by 1 × 1-convolutions results in AlexNet accuracy on the ILSVRC2012 classification task. Moreover, by combining scattering networks with deep residual networks, we achieve a single-crop top-5 error of 11.4 percent on ILSVRC2012. Also, we show they can yield excellent performance in the small sample regime on CIFAR-10 and STL-10 datasets, exceeding their end-to-end counterparts, through their ability to incorporate geometrical priors. For unsupervised learning, scattering coefficients can be a competitive representation that permits image recovery. We use this fact to train hybrid GANs to generate images. Finally, we empirically analyze several properties related to stability and reconstruction of images from scattering coefficients.

中文翻译：

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用于混合表示学习的散射网络


散射网络是一类具有固定权重的设计卷积神经网络 (CNN)。我们认为它们可以作为图像建模的通用表示。特别是，通过在散射空间中工作，我们在监督和无监督学习任务上都取得了有竞争力的结果，同时在构建更具可解释性的 CNN 方面取得了进展。对于监督学习，我们证明了 CNN 的早期层不一定需要学习，可以用散射网络代替。事实上，通过使用混合架构，我们通过迄今为止的预定义表示实现了最佳结果，同时与端到端学习的 CNN 具有竞争力。具体来说，即使应用小窗口散射系数的浅级联，然后进行 1 × 1 卷积，也能提高 AlexNet 在 ILSVRC2012 分类任务上的准确率。此外，通过将散射网络与深度残差网络相结合，我们在 ILSVRC2012 上实现了 11.4% 的单作物 top-5 误差。此外，我们还表明，通过合并几何先验的能力，它们可以在 CIFAR-10 和 STL-10 数据集的小样本范围内产生出色的性能，超过其端到端的同行。对于无监督学习，散射系数可以是允许图像恢复的竞争性表示。我们利用这一事实来训练混合 GAN 来生成图像。最后，我们根据散射系数实证分析了与图像稳定性和重建相关的几个属性。