2003/07/21 by D. Bolle, D. Bollé, J. Busquets Blanco +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · Physics and Astronomy · #Gene Regulatory Network Analysis #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/37/6/001
26 pages, 3 figures
arxiv created 2003/07/21 · openalex publication_date 2004/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Using the generating functional analysis an exact recursion relation is derived for the time evolution of the effective local field of the fully connected Little–Hopfield model. It is shown that, by leaving out the feedback correlations arising from earlier times in this effective dynamics, one precisely finds the recursion relations usually employed in the signal-to-noise approach. The consequences of this approximation as well as the physics behind it are discussed. In particular, it is pointed out why it is hard to notice the effects, especially for model parameters corresponding to retrieval. Numerical simulations confirm these findings. The signal-to-noise analysis is then extended to include all correlations, making it a full theory for dynamics at the level of the generating functional analysis. The results are applied to the frequently employed extremely diluted (a)symmetric architectures and to sequence processing networks.