Invariant Scattering Convolution Networks

By Joan Bruna, Stéphane Mallat. 2012

1,419 citations recorded by the source corpus.

A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear modulus and averaging operators. The first network layer outputs SIFT-type descriptors whereas the next layers provide complementary invariant information which improves classification. The mathematical analysis of wavelet scattering networks explain important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having same Fourier power spectrum. State of the art classification results are obtained for handwritten digits and texture discrimination, with a Gaussian kernel SVM and a generative PCA classifier.

Subfields: Computer Vision and Pattern Recognition, Model Architectures

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Citations in the corpus

Making Convolutional Networks Shift-Invariant Again (2019, background): “Recent work has strived to build in additional types of in-variances, such as rotation, reﬂection, and scaling (Sifre & Mallat, 2013; Bruna & Mallat, 2013; Esteves et al., 2018; Kanazawa et al., 2014; Worrall et al., 2017; Cohen & Welling, 2016).”
Spatial Transformer Networks (2015, background): “In this section we discuss the prior work related to the paper, covering the central ideas of modelling transformations with neural networks [12, 13, 27], learning and analysing transformation-invariant representations [3, 5, 8, 17, 19, 25], as well as attention and detection mechanisms for feature ”
A critical analysis of self-supervision, or what we can learn from a single image (2019, methodology): “The scatter transform of Bruna & Mallat (2013); Oyallon et al. (2017) is an handcrafted design that aims at replacing at least the ﬁrst few layers of a deep network.”
Scattering Networks for Hybrid Representation Learning (2018, methodology): “We recall the algorithm to compute a Scattering Transform and its implementation in [11], [1] for order 2 Scattering with a scale of J and L different orientations for the wavelets.”
Deformable Convolutional Networks (2017, background): “Some works learn invariant CNN representations with respect to different types of transformations such as [50], scattering networks [3], convolutional jungles [32], and TI-pooling [33].”
Differentially Private Learning Needs Better Features (or Much More Data) (2020, methodology): “We focus on computer vision, a canonical domain for private deep learning (Abadi et al., 2016; Yu et al., 2019b; Papernot et al., 2020b; Nasr et al., 2020)), with a rich literature on handcrafted features (Lowe, 1999; Dalal & Triggs, 2005; Bruna & Mallat, 2013).”
Robust Large Margin Deep Neural Networks (2016, background): “The authors in [13], [14] provide insight into convolutional DNNs by proposing the Scattering transform a convolutional DNN like transform, which is based on the wavelet transform and pointwise non-linearities.”
Invariant Risk Minimization (2019, background): “Unfortunately, spurious correlations and biases are often simpler to detect than the true phenomenon of interest [17, 9, 10, 11].”
General E(2)-Equivariant Steerable CNNs (2019, background): “…a wide range of equivariant models, covering regular GCNNs [6, 7, 8, 9, 10, 11], classical Steerable CNNs [1], Harmonic Networks [12], gated Harmonic Networks [2], Vector Field Networks [13], Scattering Transforms [14, 15, 16, 17, 18] and entirely new architectures, in one uniﬁed framework.”
Equivariance Through Parameter-Sharing (2017, methodology): “An alternative path to invariance via harmonic analysis and in particular cascade of wavelet transforms is investigated in Bruna & Mallat (2013); Oyallon & Mallat (2015); Sifre & Mallat (2013).”
Geometric Deep Learning: Going beyond Euclidean data (2016, background): “These statistical properties have been related to physics [16] and formalized in specific classes of convolutional neural networks (CNNs) [17], [18], [19].”
Unsupervised Feature Learning from Temporal Data (2015, background): “Invariances to such changes can be achieved us-ing appropriate pooling operators Bruna & Mallat (2013); LeCun et al. (1998).”
Excessive Invariance Causes Adversarial Vulnerability (2018, background): “The role of invariance has been studied extensively in the context of deep neural networks (Bruna & Mallat, 2013; Mallat, 2016; Achille & Soatto, 2018; Behrmann et al., 2018; Cadena et al., 2018).”
Sorting out Lipschitz function approximation (2018, methodology): “Motivated by the observations of Bruna & Mallat [7] we investigated the performance of Lipschitz networks on small amounts of training data, where learning robust features to avoid overﬁtting is critical.”
Variational Inference of Disentangled Latent Concepts from Unlabeled Observations (2017, background): “…assumes the knowledge about the nature of input transformations (e.g., rotations, translations, scaling for images, etc.) (Schmidt and Roth, 2012; Bruna and Mallat, 2013; Anselmi et al., 2014, 2016; Cohen and Welling, 2016; Dieleman et al., 2016; Haasdonk et al., 2005; Mroueh et al., 2015; Raj…”
Understanding Image Representations by Measuring Their Equivariance and Equivalence (2014, background): “By contrast, our aim is not to propose yet another mechanism to learn invariances (Anselmi et al. 2016; Bruna and Mallat 2013; Huang et al. 2007) or equivariance (Dieleman et al.”
Convolutional Kernel Networks (2014, background): “Only recently, the invariance of some related architectures has been characterized; this is the case for the wavelet scattering transform [8], or the hierarchical models of [7].”