Attractor Network Models For Fractal And Weighted Patterns

The Hopfield attractor network model uses the Hebbian rule to adjust the strength of the coupling matrix between the network units,and stores the pattern as the attractor of the network,thus realizing the memory of the pattern.When the initial state of the network is in the basin of attraction,with the energy reduction,the network state enters the attractor or the nearest attractor.This process realizes the recognition of the pattern.The units and coupling in the Hopfield model are similar to the Ising model in statistical physics,so it has attracted the attention of physicists.The author studies the Hopfield network based on the following two ideas:(1)The Diffusion-limited Aggregation(DLA)model is a special pattern with fractal characteristics,which has been studied by many scholars.With the fractal pattern generated by the DLA model as the attractor of the network,it is interesting to research content to study the Hopfield network's memory of fractal pattern.(2)The brain often remembers some repeated events.If the connection weight is set as a quantity proportional to the frequency of attractor appearing in the network,the process of remembering repeated events can be simulated through the attractor network.Based on the above two ideas,this thesis mainly studies the Hopfield network's memory of fractal pattern and the influence of connection weight on the stability and retrieval time of the network in two chapters through numerical simulation and theoretical analysis.In the first part,the author studies the Hopfield attractor network's memory of fractal patterns.The state of the network node is +1,indicating that the neuron is in the firing state.The simulation results show that the stability of fractal patterns is higher than that of random patterns when the ratio of excited states of network nodes is equal to 0.25.If both fractal patterns and random patterns are stored in the network,the stability of fractal patterns is higher than that of random patterns,and with the increase of the number of fractal patterns in the network,the stability advantage of fractal patterns will become more and more obvious.Then,the stability of the pattern and the output state of the network is studied by changing the proportion of the excited states.The simulation results show that the stability of fractal patterns is higher than that of random patterns when the proportion of excited states of network nodes is low.The proportion of excited states in the input state of the fractal pattern is very little different from that in the output state of the network.The proportion of excited states in the input state of the random pattern is greatly different from that in the output state of the network.When the proportion of excited states is high,the stability of random patterns is higher than that of fractal patterns.The proportion of excited states in the input state of the fractal pattern is still not significantly different from that in the output state of the network.The proportion of excitation state in the input state of the random pattern is consistent with that in the output state of the network.Finally,the stability of network nodes in different excited state ratios is theoretically deduced by using signal-to-noise ratio analysis.The author found that once the excited state of the network deviates from 0.50,the noise items of the excited state and the unexcited state nodes in the network presents different distribution,which is consistent with the simulation results obtained by us.By the probability formula of node instability,it is proved that the stability of fractal patterns is higher than that of random patterns when the proportion of excited states is 0.25.In the second part,the author mainly studies the influence of attractor weight on the stability of weighted pattern and network retrieval time.The simulation results show that the greater the weight of the attractor is,the stronger the stability.The stability of the weighted pattern is also related to the randomness of the network,the stronger the randomness of the network,the stronger the stability of the weighted pattern.The relationship between retrieving time and attractor weight does not change monotone.Besides,the author also studies the influence of the randomness of the network on the stability and retrieval time of weighted patterns.The simulation results show that the stronger the randomness of the network,the stronger the stability of the weighted pattern,and the longer the retrieval time of the network.