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Updated: Jul 3, 2026
07:17
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Published on: June 23, 2022
Energy minimization in the nonlinear dynamic recurrent associative memory
1Rensselaer Polytechnic Institute, Cognitive Science Department, 110 Eighth Street, Carnegie 108, Troy, NY 12180-3590, USA. helies@rpi.edu
Summary
This study proves the global stability of Nonlinear Dynamic Recurrent Associative Memory (NDRAM) using energy function analysis. The findings confirm NDRAM
Area of Science:
- Computational neuroscience
- Artificial neural networks
- Nonlinear dynamics
Background:
- Nonlinear Dynamic Recurrent Associative Memory (NDRAM) is a nonlinear synchronous attractor neural network.
- Previous research showed NDRAM learning converges to real-valued attractors in neural networks.
- The global stability of NDRAM's nonlinear transmission has not been analytically proven.
Purpose of the Study:
- To analytically prove the global stability of NDRAM.
- To demonstrate NDRAM as an instance of Cohen-Grossberg models.
- To define and analyze NDRAM's energy function.
Main Methods:
- Classifying NDRAM within the Cohen-Grossberg class of models.
- Defining and analyzing the energy function of NDRAM.
- Conducting numerical simulations to validate analytical findings.
Main Results:
- NDRAM is shown to be an instance of the Cohen-Grossberg models.
- An energy function for NDRAM was defined and analyzed.
- Analysis confirms the stability of NDRAM's transmission across its entire domain.
Conclusions:
- The global stability of NDRAM's nonlinear transmission is analytically proven.
- The study establishes NDRAM as a stable associative memory model.
- Numerical simulations corroborate the theoretical stability analysis.
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