Efficiently capturing the long-range patterns in sequential data sources salient to a given task -- such as classification and generative modeling -- poses a fundamental challenge. Popular approaches in the space tradeoff between the memory burden of brute-force enumeration and comparison, as in transformers, the computational burden of complicated sequential dependencies, as in recurrent neural networks, or the parameter burden of convolutional networks with many or large filters. We instead take inspiration from wavelet-based multiresolution analysis to define a new building block for sequence modeling, which we call a MultiresLayer. The key component of our model is the multiresolution convolution, capturing multiscale trends in the input sequence. Our MultiresConv can be implemented with shared filters across a dilated causal convolution tree. Thus it garners the computational advantages of convolutional networks and the principled theoretical motivation of wavelet decompositions. Our MultiresLayer is straightforward to implement, requires significantly fewer parameters, and maintains at most a (NlogN) memory footprint for a length N sequence. Yet, by stacking such layers, our model yields state-of-the-art performance on a number of sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets.
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Implementation of a physiographic complexity-based multiresolution snow modeling scheme: MULTIRESOLUTION SNOW MODELING
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Abstract We extend a stochastic aerosol‐snow albedo model to explicitly simulate dust internally/externally mixed with snow grains of different shapes and for the first time quantify the combined effects of dust‐snow internal mixing and snow nonsphericity on snow optical properties and albedo. Dust‐snow internal/external mixing significantly enhances snow single‐scattering coalbedo and absorption at wavelengths of <1.0 μm, with stronger enhancements for internal mixing (relative to external mixing) and higher dust concentrations but very weak dependence on snow size and shape variabilities. Compared with pure snow, dust‐snow internal mixing reduces snow albedo substantially at wavelengths of <1.0 μm, with stronger reductions for higher dust concentrations, larger snow sizes, and spherical (relative to nonspherical) snow shapes. Compared to internal mixing, dust‐snow external mixing generally shows similar spectral patterns of albedo reductions and effects of snow size and shape. However, relative to external mixing, dust‐snow internal mixing enhances the magnitude of albedo reductions by 10%–30% (10%–230%) at the visible (near‐infrared) band. This relative enhancement is stronger as snow grains become larger or nonspherical, with comparable influences from snow size and shape. Moreover, for dust‐snow external and internal mixing, nonspherical snow grains have up to ~45% weaker albedo reductions than spherical grains, depending on snow size, dust concentration, and wavelength. The interactive effect of dust‐snow mixing state and snow shape highlights the importance of accounting for these two factors concurrently in snow modeling. For application to land/climate models, we develop parameterizations for dust effects on snow optical properties and albedo with high accuracy.
