Parametric Scattering Networks

The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to outperform learned representations in certain tasks, particularly on limited labeled data and highly structured signals. The wavelet filters used in the scattering transform are typically selected to create a tight frame via a parameterized mother wavelet. In this work, we investigate whether this standard wavelet filterbank construction is optimal. Focusing on Morlet wavelets, we propose to learn the scales, orientations, and aspect ratios of the filters to produce problem-specific parameterizations of the scattering transform. We show that our learned versions of the scattering transform yield significant performance gains in small-sample classification settings over the standard scattering transform. Moreover, our empirical results suggest that traditional filterbank constructions may not always be necessary for scattering transforms to extract effective representations.

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Small Data Image Classification CIFAR-10, 1000 Labels LearnableScatteringNetwork+WRN Accuracy (%) 70.14 # 2
Small Data Image Classification CIFAR-10, 1000 Labels FixedScatteringNetwork+WRN Accuracy (%) 68.16 # 3
Small Data Image Classification CIFAR-10, 1000 Labels WRN Accuracy (%) 71.37 # 1
Small Data Image Classification CIFAR-10, 100 Labels FixedScatteringNetwork+WRN Accuracy (%) 43.16 # 2
Small Data Image Classification CIFAR-10, 100 Labels WRN Accuracy (%) 38.78 # 3
Small Data Image Classification CIFAR-10, 100 Labels LearnableScatteringNetwork+WRN Accuracy (%) 43.6 # 1
Small Data Image Classification CIFAR-10, 500 Labels WRN Accuracy (%) 62.97 # 2
Small Data Image Classification CIFAR-10, 500 Labels FixedScatteringNetwork+WRN Accuracy (%) 61.66 # 3
Small Data Image Classification CIFAR-10, 500 Labels LearnableScatteringNetwork+WRN Accuracy (%) 63.13 # 1

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