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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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Related Experiment Videos

Training convolutional neural networks with the Forward-Forward Algorithm.

Riccardo Scodellaro1, Ajinkya Kulkarni2, Frauke Alves2,3,4

  • 1Translational Molecular Imaging, Max Planck Institute for Multidisciplinary Sciences, Hermann-Rein Straße 3, 37075, Göttingen, Germany. riccardo.scodellaro@mpinat.mpg.de.

Scientific Reports
|November 4, 2025
PubMed
Summary
This summary is machine-generated.

Researchers adapted the Forward-Forward (FF) algorithm for Convolutional Neural Networks (CNNs), showing it can successfully train deeper networks. This biologically inspired approach offers a promising alternative to backpropagation for image analysis and neuromorphic computing.

Keywords:
CNNClass activation mapsExplainable AIForward–forward

Related Experiment Videos

Area of Science:

  • Artificial Intelligence
  • Computer Vision
  • Computational Neuroscience

Background:

  • Deep neural networks, particularly Convolutional Neural Networks (CNNs), dominate image analysis, primarily trained with backpropagation (BP).
  • Geoffrey Hinton proposed the Forward-Forward (FF) algorithm as a biologically plausible alternative, utilizing local goodness functions and joint presentation of positive/negative data.
  • Extending FF to CNNs requires novel methods for label information propagation across spatial locations.

Purpose of the Study:

  • To adapt the Forward-Forward (FF) algorithm for use with Convolutional Neural Networks (CNNs).
  • To develop and evaluate spatially extended labeling strategies for FF-trained CNNs.
  • To investigate the learning dynamics, stability, and feature learning capabilities of FF-trained CNNs.

Main Methods:

  • Introduced two spatially extended labeling strategies: Fourier patterns and morphological transformations.
  • Applied these strategies to train deeper CNNs on CIFAR10 and CIFAR100 datasets using the FF algorithm.
  • Utilized Class Activation Maps (CAMs) to analyze learned features.

Main Results:

  • Demonstrated successful optimization of deeper FF-trained CNNs on image datasets.
  • Showcased that morphology-based labels effectively prevent shortcut solutions on complex datasets.
  • Confirmed that FF training scales effectively to 100 classes (CIFAR100) and that FF-CNNs learn meaningful, complementary features across layers.

Conclusions:

  • FF training is feasible and effective for Convolutional Neural Networks, extending beyond fully connected architectures.
  • Spatially extended labeling strategies enable FF CNNs to learn effectively and avoid shortcut solutions.
  • FF-trained CNNs exhibit biologically plausible learning dynamics and hold potential for neuromorphic computing.