2014/07/18 by Elena Agliari, Adriano Barra, Andrea Galluzzi +3 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Computer science #Consistency (knowledge bases) #Content-addressable memory #Hopfield network #Limit (mathematics) #Machine learning #Markov chain #Mathematics #Mean field theory #Neural Networks and Applications #Neural dynamics and brain function #Physics #Quantum mechanics #Simple (philosophy) #Statistical mechanics #Statistical physics #Theoretical and Computational Physics #Theoretical computer science #Thermodynamic limit #cond-mat.dis-nn #physics.soc-ph #q-bio.NC
paper · pdf · doi:10.1103/physrevlett.114.028103
published as Physical Review Letters 114, 028103, (2015)
arxiv created 2014/07/18 · openalex publication_date 2015/01/16 · arxiv updated 2016/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider statistical-mechanics models for spin systems built on hierarchical structures, which provide a simple example of non-mean-field framework. We show that the coupling decay with spin distance can give rise to peculiar features and phase diagrams much richer than their mean-field counterpart. In particular, we consider the Dyson model, mimicking ferromagnetism in lattices, and we prove the existence of a number of metastabilities, beyond the ordered state, which become stable in the thermodynamic limit. Such a feature is retained when the hierarchical structure is coupled with the Hebb rule for learning, hence mimicking the modular architecture of neurons, and gives rise to an associative network able to perform single pattern retrieval as well as multiple-pattern retrieval, depending crucially on the external stimuli and on the rate of interaction decay with distance; however, those emergent multitasking features reduce the network capacity with respect to the mean-field counterpart. The analysis is accomplished through statistical mechanics, Markov chain theory, signal-to-noise ratio technique, and numerical simulations in full consistency. Our results shed light on the biological complexity shown by real networks, and suggest future directions for understanding more realistic models.