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Updated: Oct 6, 2025
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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
Published on: June 27, 2013
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Eigenvalue spectrum of neural networks with arbitrary Hebbian length
Jianwen Zhou1, Zijian Jiang2, Tianqi Hou3
1PMI Lab, School of Physics, Sun Yat-sen University, Guangzhou 510275, People's Republic of China and CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
Physical Review. E
|January 15, 2022
Summary
This study introduces a generalized associative memory model with long-range Hebbian interactions. It connects arbitrary Hebbian lengths to the neural coupling matrix
Area of Science:
- Computational Neuroscience
- Statistical Physics
Background:
- Associative memory is a core brain function.
- Standard models often assume limited interaction ranges.
Purpose of the Study:
- To generalize associative memory models.
- To incorporate long-range Hebbian interactions.
- To analyze the impact of extended synaptic integration windows.
Main Methods:
- Developed a generalized associative memory model.
- Applied the replica method to derive spectral density.
- Utilized free probability methods for consistency checks.
- Derived maximal eigenvalue via an iterative equation.
Main Results:
- The spectral density of the coupling matrix was derived.
- Consistency was shown between replica and free probability methods.
- The maximal eigenvalue was linked to paramagnetic-spin glass transitions.
- Established a connection between Hebbian length and neural coupling spectrum.
Conclusions:
- The generalized model accommodates arbitrary Hebbian lengths.
- This work bridges associative memory dynamics with neural network spectral properties.
- Provides a theoretical framework for understanding memory with extended temporal integration.
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