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Related Experiment Video

Updated: Aug 27, 2025

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
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Data-driven emergence of convolutional structure in neural networks.

Alessandro Ingrosso1, Sebastian Goldt2

  • 1Quantitative Life Sciences, The Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy.

Proceedings of the National Academy of Sciences of the United States of America
|September 26, 2022
PubMed
Summary

Fully connected neural networks can learn convolutional structures from translation-invariant data. This learning is driven by the higher-order structure of natural images, revealing insights into feature detection.

Keywords:
convolutioninvarianceneural networksreceptive fields

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Area of Science:

  • Machine Learning
  • Computational Neuroscience
  • Artificial Intelligence

Background:

  • Exploiting data invariances is key for efficient learning in artificial and biological neural circuits.
  • Understanding how neural networks discover representations that harness input symmetries is crucial for both machine learning and neuroscience.
  • Convolutional neural networks (CNNs) leverage translation symmetry, driving early deep learning successes, but learning convolutions directly from translation-invariant data remains challenging.

Purpose of the Study:

  • To investigate how initially fully connected neural networks can autonomously learn convolutional structures from translation-invariant data.
  • To understand the role of input data's higher-order statistics in the emergence of learned convolutional patterns.
  • To characterize the mechanism behind receptive field formation and its link to tensor decomposition.

Main Methods:

  • Training initially fully connected neural networks on a discrimination task with translation-invariant data.
  • Analyzing the emergent receptive field structures within the trained networks.
  • Designing data models that capture the non-Gaussian, higher-order local structure characteristic of natural images.
  • Employing analytical and numerical methods to characterize the pattern formation mechanism and its relation to tensor decomposition.

Main Results:

  • Initially fully connected networks learned localized, space-tiling receptive fields, mimicking CNN filters.
  • The emergence of these convolutional structures was triggered by the non-Gaussian, higher-order local structure of the input data.
  • A link was established between receptive field formation and the tensor decomposition of higher-order input correlations.

Conclusions:

  • Fully connected networks can learn convolutional representations directly from data exhibiting specific higher-order statistics.
  • The non-Gaussian structure of natural images plays a critical role in the development of feature detectors.
  • Findings offer insights into low-level feature detection in sensory systems and the impact of higher-order statistics on neural network learning.