Reproduce “Aliasing in Convnets: A Frame-Theoretic Perspective” on OpenResearch
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About this paper
Daniel Haider, Vincent Lostanlen, Martin Ehler, Nicki Holighaus, Peter Balazs
This research provides a frame-theoretic approach using the Walnut representation to explicitly quantify aliasing in strided convolutional layers and its direct impact on numerical stability. The study introduces computationally efficient optimization objectives that effectively promote Parseval stability, demonstrating significantly faster computation than existing methods.
Key insights
- Aliasing terms, represented by off-diagonal components in the Fourier-transformed frame operator, are direct determinants of the numerical stability and tightness of strided convolutional layers.
- Parseval stability can be characterized by conditions (flat direct response and zero aliasing terms) that are independent of total signal length but depend on kernel size, making them practical for ConvNets.
- Optimization objectives directly targeting aliasing terms offer substantial computational efficiency over traditional stability regularizers, enabling broader adoption in deep learning.
Summary by alphaXiv.
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