# Aliasing in Convnets: A Frame-Theoretic Perspective

arXiv: https://arxiv.org/abs/2507.06152 · HTML: https://mlsanity.com/paper/2507.06152/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 8 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [WavLM: Large-Scale Self-Supervised Pre-Training for Full Stack Speech Processing](https://mlsanity.com/paper/2110.13900/) (2021)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [Speaker Recognition from Raw Waveform with SincNet](https://mlsanity.com/paper/1808.00158/) (2018)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Orthogonal Convolutional Neural Networks](https://mlsanity.com/paper/1911.12207/) (2019)
- [Neural Photo Editing with Introspective Adversarial Networks](https://mlsanity.com/paper/1609.07093/) (2016)
- [Orthogonalizing Convolutional Layers with the Cayley Transform](https://mlsanity.com/paper/2104.07167/) (2021)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [LEAF: A Learnable Frontend for Audio Classification](https://mlsanity.com/paper/2101.08596/) (2021)
- [Avoiding Overfitting: A Survey on Regularization Methods for Convolutional Neural Networks](https://mlsanity.com/paper/2201.03299/) (2022)
- [Scaling-up Diverse Orthogonal Convolutional Networks with a Paraunitary Framework](https://mlsanity.com/paper/2106.09121/) (2021)
- [(Almost) Smooth Sailing: Towards Numerical Stability of Neural Networks Through Differentiable Regularization of the Condition Number](https://mlsanity.com/paper/2410.00169/) (2024)
- [Fitting Auditory Filterbanks with Multiresolution Neural Networks](https://mlsanity.com/paper/2307.13821/) (2023)
- [Frame Theory for Signal Processing in Psychoacoustics](https://mlsanity.com/paper/1611.00966/) (2016)
- [Parseval Convolution Operators and Neural Networks](https://mlsanity.com/paper/2408.09981/) (2024)
- [Hold Me Tight: Stable Encoder-Decoder Design for Speech Enhancement](https://mlsanity.com/paper/2408.17358/) (2024)

## Abstract (arXiv)

Using a stride in a convolutional layer inherently introduces aliasing, which has implications for numerical stability and statistical generalization. While techniques such as the parametrizations via paraunitary systems have been used to promote orthogonal convolution and thus ensure Parseval stability, a general analysis of aliasing and its effects on the stability has not been done in this context. In this article, we adapt a frame-theoretic approach to describe aliasing in convolutional layers with 1D kernels, leading to practical estimates for stability bounds and characterizations of Parseval stability, that are tailored to take short kernel sizes into account. From this, we derive two computationally very efficient optimization objectives that promote Parseval stability via systematically suppressing aliasing. Finally, for layers with random kernels, we derive closed-form expressions for the expected value and variance of the terms that describe the aliasing effects, revealing fundamental insights into the aliasing behavior at initialization.