Slowly evolving random graphs II: Adaptive geometry in finite-connectivity Hopfield models
arXiv:cond-mat/0404658 · doi:10.1088/0305-4470/37/32/002
Abstract
We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural network (Hopfield) models and we show that due to the minimisation of the frustration effects the retrieval region of the phase diagram can be significantly enlarged. Moreover, the fraction of misaligned spins is reduced by this effect, and is smaller than in the infinite connectivity regime. The main cause of this difference is found to be the non-zero fraction of sites with vanishing local field when the connectivity is finite.
17 pages, 8 figures
References in corpus (16)
- Statistical mechanics of complex networks
- Evolution of networks
- The Bethe lattice spin glass revisited
- Statistical mechanics of the random K-SAT model
- Typical Performance of Gallager-type Error-Correcting Codes
- Trajectories in phase diagrams, growth processes and computational complexity: how search algorithms solve the 3-Satisfiability problem
- Finite Connectivity Attractor Neural Networks
- Replicated Transfer Matrix Analysis of Ising Spin Models on `Small World' Lattices
- Coupled dynamics of fast spins and slow exchange interactions in the XY spin-glass
- Average and reliability error exponents in low-density parity-check codes
- Cluster derivation of Parisi's RSB solution for disordered systems
- Metastable configurations of spin models on random graphs
- The XY Spin-Glass with Slow Dynamic Couplings
- Hierarchical Self-Programming in Recurrent Neural Networks
- Analysis of common attacks in LDPCC-based public-key cryptosystems
- Diluted neural networks with adapting and correlated synapses