January 19, 2004
Similar papers 4
May 16, 2005
There is growing interest in a phenomenon called the ``synfire chain'', in which firings of neurons propagate from pool to pool in the chain. The mechanism of the synfire chain has been analyzed by many resarchers. Keeping the synfire chain phenomenon in mind, we investigate a layered associative memory neural network model, in which patterns are embedded in connections between neurons. In this model, we also include uniform noise in connections, which induces common input in...
October 10, 2002
The thermodynamic and retrieval properties of fully connected Blume-Emery-Griffiths networks, storing ternary patterns, are studied using replica mean-field theory. Capacity-temperature phase diagrams are derived for several values of the pattern activity. It is found that the retrieval phase is the largest in comparison with other three-state neuron models. Furthermore, the meaning and stability of the so-called quadrupolar phase is discussed as a function of both the temper...
August 22, 1994
We propose a network of oscillators to retrieve given patterns in which the oscillators keep a fixed phase relationship with one another. In this description, the phase and the amplitude of the oscillators can be regarded as the timing and the strength of the neuronal spikes, respectively. Using the amplitudes for encoding, we enable the network to realize not only oscillatory states but also non-firing states. In addition, it is shown that under suitable conditions the syste...
April 19, 2007
The effects of dominant sequential interactions are investigated in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation in which the interaction consists of a Hebbian part and a symmetric sequential term. Phase diagrams of stationary states are obtained and a new phase of cyclic correlated states of period two is found for a weak Hebbian term, independently of the number of condensed patterns $c$.
March 23, 2004
For the retrieval dynamics of sparsely coded attractor associative memory models with synaptic noise the inclusion of a macroscopic time-dependent threshold is studied. It is shown that if the threshold is chosen appropriately as a function of the cross-talk noise and of the activity of the memorized patterns, adapting itself automatically in the course of the time evolution, an autonomous functioning of the model is guaranteed. This self-control mechanism considerably improv...
September 30, 2002
We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive...
April 11, 1996
We investigate the retrieval phase diagrams of an asynchronous fully-connected attractor network with non-monotonic transfer function by means of a mean-field approximation. We find for the noiseless zero-temperature case that this non-monotonic Hopfield network can store more patterns than a network with monotonic transfer function investigated by Amit et al. Properties of retrieval phase diagrams of non-monotonic networks agree with the results obtained by Nishimori and Opr...
January 27, 1998
An Ashkin-Teller neural network, allowing for two types of neurons is considered in the case of low loading as a function of the strength of the respective couplings between these neurons. The storage and retrieval of embedded patterns built from the two types of neurons, with different degrees of (in)dependence is studied. In particular, thermodynamic properties including the existence and stability of Mattis states are discussed. Furthermore, the dynamic behaviour is examin...
April 1, 2004
We study the influence of network topology on retrieval properties of recurrent neural networks, using replica techniques for diluted systems. The theory is presented for a network with an arbitrary degree distribution $p(k)$ and applied to power law distributions $p(k) \sim k^{-\gamma}$, i.e. to neural networks on scale-free graphs. A bifurcation analysis identifies phase boundaries between the paramagnetic phase and either a retrieval phase or a spin glass phase. Using a po...
May 6, 1998
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium statistical mechanical analysis. Using generating functional methods we derive exact closed equations for dynamical order parameters, viz. the sequence overlap and correlation- and response functions, in the thermodynamic limit. We calculate the ti...