PreprintCC BY 4.0HAL
Understanding Group Delay in Random Convnets
Abstract
A core tenet of filterbank design is to minimize discrepancies in group delay, defined as the negative derivative of each filter's phase response with respect to frequency. Yet, in a convolutional neural network (convnet) layer, finite impulse responses (FIRs) are initialized with i.i.d. random Gaussian weights, thereby making group delay a random function of frequency. In the context of machine learning for signal processing, our article conducts a probabilistic analysis of group delay in convnets. We find that a zero-mean initialization causes heavy tails in the distribution of group delay. To reduce the probability of large deviations, a simple workaround is to introduce residual connections, as in residual neural networks (ResNets).
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BibTeX
@misc{lostanlen2026understanding,
title = {{Understanding Group Delay in Random Convnets}},
author = {Vincent Lostanlen and Daniel Haider and Peter Balazs},
howpublished = {HAL},
year = {2026},
month = nov,
url = {https://hal.science/hal-05847165v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Understanding Group Delay in Random Convnets
AU - Vincent Lostanlen
AU - Daniel Haider
AU - Peter Balazs
PY - 2026
DA - 2026/11/02
PB - HAL
UR - https://hal.science/hal-05847165v2
AB - A core tenet of filterbank design is to minimize discrepancies in group delay, defined as the negative derivative of each filter's phase response with respect to frequency. Yet, in a convolutional neural network (convnet) layer, finite impulse responses (FIRs) are initialized with i.i.d. random Gaussian weights, thereby making group delay a random function of frequency. In the context of machine learning for signal processing, our article conducts a probabilistic analysis of group delay in convnets. We find that a zero-mean initialization causes heavy tails in the distribution of group delay. To reduce the probability of large deviations, a simple workaround is to introduce residual connections, as in residual neural networks (ResNets).
ER -