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Effect of dilution in asymmetric recurrent neural networks

Viola Folli, Giorgio Gosti, Marco Leonetti, Giancarlo Ruocco
2018 Neural Networks  
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution  ...  The network dilution measures the fraction of neuron couples that are connected, and the network asymmetry measures to what extent the underlying connectivity matrix is asymmetric.  ...  Conflict of Interest Statement The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest  ... 
doi:10.1016/j.neunet.2018.04.003 pmid:29705670 fatcat:ddp3ohi5krgf5c4gk3c7iiemba

Network dilution and asymmetry in an efficient brain

Marco Leonetti, Viola Folli, Edoardo Milanetti, Giancarlo Ruocco, Giorgio Gosti
2020 Philosophical Magazine  
Here, we studied the effects of symmetry and dilution on a discrete-time recurrent neural network with McCulloch-Pitts neurons.  ...  Mammalian brains show large variations of dilution, and mostly asymmetric connectivity, unfortunately the advantages which drove evolution to these state of network dilution and asymmetry are still unknown  ...  Moreover, if we call Hopfield neural networks completely connected symmetric neural networks, diluted Hopfield networks diluted symmetric networks, then in the diluted asymmetric networks the number of  ... 
doi:10.1080/14786435.2020.1750726 fatcat:yb5w4beguzhnvcja5vcl55g4wu

An Evaluation of the Dynamics of Diluted Neural Network

Lijuan Wang, Jun Shen, Qingguo Zhou, Zhihao Shang, Huaming Chen, Hong Zhao
2016 International Journal of Computational Intelligence Systems  
In this paper, we use the annealed dilution method to design a diluted neural network with fixed degree of dilution.  ...  By analyzing the dynamics of the diluted neural network, it is verified that asymmetric fullconnected neural network do have significant advantages over the asymmetric diluted neural network.  ...  Section 2 describes the rule to design asymmetric neural network with binary weighted values, and the rule to design diluted neural network with fixed degree of dilution.  ... 
doi:10.1080/18756891.2016.1256578 fatcat:tfnuow6wprf3rbx3hy5gwhvqk4

The three-state layered neural network with finite dilution

W.K Theumann, R Erichsen
2004 Physica A: Statistical Mechanics and its Applications  
in extension of a recent work on a recurrent network.  ...  The dynamics and the stationary states of an exactly solvable three-state layered feed-forward neural network model with asymmetric synaptic connections, finite dilution and low pattern activity are studied  ...  of feature dependence in recurrent networks.  ... 
doi:10.1016/j.physa.2004.04.130 fatcat:bac5qo5vafello75nducm3jowq

An Evolutionary Approach to Associative Memory in Recurrent Neural Networks [article]

Sh. Fujita, H. Nishimura (Hyogo University of Education)
1994 arXiv   pre-print
In this paper, we investigate the associative memory in recurrent neural networks, based on the model of evolving neural networks proposed by Nolfi, Miglino and Parisi.  ...  Experimentally developed network has highly asymmetric synaptic weights and dilute connections, quite different from those of the Hopfield model.  ...  In this paper we apply a genetic evolutionary scheme to recurrent neural networks and investigate associative memory.  ... 
arXiv:adap-org/9411003v1 fatcat:ens3dykxxvg3bldvuvlp5rssuu

Artificial Neural Networks [chapter]

Hanspeter A Mallot
2013 Springer Series in Bio-/Neuroinformatics  
Kendall, TJ.Hall The Generalisation Ability of Dilute Attractor Neural Networks 187 C. Campbell Attractor Structure of Constrained Neural Networks at Finite Temperature 191 C.  ...  Klaassen Attractor Learning of Recurrent Neural Networks 371 K. Gouhara, H. Takase, Y. Uchikawa, K.  ...  Self-organizing Neural Network Apllication to Technical Process Parameters Estimation 579 E. Govekar, E. Susie, P. Muzic, I. Grabec High-precision Robot Control: The Nested Network 583 A.  ... 
doi:10.1007/978-3-319-00861-5_4 fatcat:l3v3etbv6zfxlcfkxnzml4v3xu

Setting the Activity Level in Sparse Random Networks

Ali A. Minai, William B. Levy
1994 Neural Computation  
Introduction to the Theory of Neural Computation. Addison-Wesley, Redwood City, CA. Kree, R., and Zippelius, A. 1991. Asymmetrically diluted neural networks. In Models of Neural Networks, E.  ...  The length of attractors in asymmetric random neural networks with deterministic dynamics. J. Phys. A: Math. Gen. 24, L151-157. Rolls, E. T. 1989.  ... 
doi:10.1162/neco.1994.6.1.85 fatcat:ltvtedx6anfurjiyqjeslzlpfi

TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State

Mattia Miotto, Lorenzo Monacelli
2021 Entropy  
the most likely positions of cells when data are missing; and (iii) an application to recurrent neural networks, in which we measure the information stored in different realizations of the Hopfield model  ...  We present ToloMEo (TOpoLogical netwOrk Maximum Entropy Optimization), a program implemented in C and Python that exploits a maximum entropy algorithm to evaluate network topological information.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/e23091138 pmid:34573763 fatcat:fmtpivpe7jhsxjsrfmaz27j3si

From statistical inference to a differential learning rule for stochastic neural networks [article]

Luca Saglietti, Federica Gerace, Alessandro Ingrosso, Carlo Baldassi, Riccardo Zecchina
2018 Interface Focus   accepted
Nevertheless, the DCM rule is capable of storing a large, extensive number of patterns as attractors in a stochastic recurrent neural network, under general scenarios without requiring any modification  ...  Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli.  ...  In [61] , in the context of diluted neural networks, the authors used as a learning criterion the matching of equaltime correlations, still comparing a system driven by a finite field with a freely evolving  ... 
doi:10.1098/rsfs.2018.0033 pmid:30443331 pmcid:PMC6227809 arXiv:1805.10714v2 fatcat:6zzypqmnuvftpmqpyabsexznim

Effects of refractory periods in the dynamics of a diluted neural network

F. A. Tamarit, D. A. Stariolo, S. A. Cannas, P. Serra
1996 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We propose a stochastic dynamics for a neural network which accounts for the effects of the refractory periods ͑absolute and relative͒ in the dynamics of a single neuron.  ...  The dynamics can be solved analytically in an extremely diluted network.  ...  CONCLUSIONS In this paper we have introduced a model for an attractor neural network which incorporates some realistic features observed in biological neurons, namely, asymmetric dilution of the synapses  ... 
doi:10.1103/physreve.53.5146 pmid:9964847 fatcat:rh3gpxkxnfgytox6bfy5fmglse

Asymmetrically extremely dilute neural networks with Langevin dynamics and unconventional results

J P L Hatchett, A C C Coolen
2004 Journal of Physics A: Mathematical and General  
We study graded response attractor neural networks with asymmetrically extremely dilute interactions and Langevin dynamics.  ...  non-persistent order parameters, atypically for recurrent neural network models.  ...  In this paper, we study the dynamics of asymmetrically extremely dilute graded response attractor neural networks with Langevin dynamics, near saturation.  ... 
doi:10.1088/0305-4470/37/29/003 fatcat:vq75v5rypbfzjjpq2blaan56uq

Mean-field dynamics of sequence processing neural networks with finite connectivity

W.K. Theumann
2003 Physica A: Statistical Mechanics and its Applications  
A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type (During, Coolen and Sherrington, 1998) is extended and analized here for a symmetrically diluted  ...  network with finite connectivity.  ...  Acknowledgments We thank Alba Theumann for discussions at an early stage of the work.  ... 
doi:10.1016/s0378-4371(03)00569-7 fatcat:h3bftgbhijcjdcx7xc32vyixyi

Fractal properties of percolation clusters in Euclidian neural networks

Igor Franović, Vladimir Miljković
2009 Chaos, Solitons & Fractals  
The process of spike packet propagation is observed in two-dimensional recurrent networks, consisting of locally coupled neuron pools.  ...  The formation of dynamic attractors in our model, synfire chains, exhibits critical behavior, corresponding to percolation phase transition, with probability for non-zero synaptic strength values representing  ...  Acknowledgement This research was performed as part of the work within Project No. 141020, funded by the Serbian Ministry of Science and Protection of Life Environment.  ... 
doi:10.1016/j.chaos.2007.06.026 fatcat:2lxzuuywpjd6plmv574brfuici

Chaotic Wandering and Search in a Cycle-Memory Neural Network

S. Nara, P. Davis
1992 Progress of theoretical physics  
845 Numerical investigation of a single layer recurrent neural network model in which the synaptic connection matrix is formed by summing direct products of succesive patterns in cyclic sequences shows  ...  Introduction In this paper we consider chaotic dynamics in a neural network in the context of a memory search task.  ...  Acknowledgements This work has been partially supported by the Grant-in-Aid for Scientific Researchfrom the Ministry of Education, Science and Culture of Japan.  ... 
doi:10.1143/ptp/88.5.845 fatcat:m622jjaw3bf5tako3e2ytsglfm

Chaotic Wandering and Search in a Cycle-Memory Neural Network

Shigetoshi Nara, Peter Davis
1992 Progress of theoretical physics  
845 Numerical investigation of a single layer recurrent neural network model in which the synaptic connection matrix is formed by summing direct products of succesive patterns in cyclic sequences shows  ...  Introduction In this paper we consider chaotic dynamics in a neural network in the context of a memory search task.  ...  Acknowledgements This work has been partially supported by the Grant-in-Aid for Scientific Researchfrom the Ministry of Education, Science and Culture of Japan.  ... 
doi:10.1143/ptp.88.845 fatcat:7kcvh7cxl5bptiiwgejogyeygu
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