Example Of Argumentative Essay On Hopfield Network And Mind-Brain

Introduction

A Hopfield network refers to a form of recurrent artificial neural network that was invented by John Hopfield (1982). These Hopfield nets are designed to function as content-addressable memory systems conjoined with binary threshold nodes. They usually converge at a local minimum. Hopfield networks are essentially designed to present a model that can be used in understanding of human memory. Being a physicist that he is, Hopfield illustrated that models of physical systems can be applied in solving computational problems.

Learning rules

Various different learning rules can be applied in storing of information in a human memory that has been named as a Hopfield Network. It is always desirable for every learning rule to contain each of these two properties:
Incremental: The learning of newer patterns can be done without necessarily using of information drawn from old patterns that have been adopted for training. This implies that whenever a new pattern is implemented for training, the new values designed for weights will only rely on the new pattern as well as the old values.
Local: By ‘local’, it means that every weight gets updated by using the information available to neurons on each side of the connection being associated within the same weight.
According to Polyn & Kahana (2008), such properties are very desirable because the learning rule meant to satisfy them is more biologically plausible. For instance, because the human brain is all the time learning new concepts, it is prudential for one to note that human learning is incremental. Of key to note is that a learning system cannot be said to be incremental if it has once been trained, with the help of a big bunch of training data.

The Concept of Hopfield Network

Like any other computer, a brain is a dynamical system mandated with the function of performing its computations, and in the process, relying on the change of its ‘condition’ with time.  Storkey, Amos & Romain (1999) records that, most simple dynamics composed of neural circuits have collective dynamic features, which could be explored in identifying of sensory patterns. Integrating of these collective features in information processing is effectual because it exploits the simultaneous characteristics of circuits and nerve cells for the sake of producing multiple computations. It is in this regard that Hopfield’s research focuses much on understanding how the brain and human circuits produce complex and powerful computations.
Though it is arguably true that there is a big distinction between the brain and modern computers, the large share of what is performed by the brain can be elaborated well with the conception of computation. Some of the best examples of computational activity processes include: generating of proper sequences of locomotor muscle directions; splitting the world into smaller objects; identifying an odor/chess positions; inference and logic; and associative memory.

Olfaction

The simplest and easiest problem in olfaction is recognizing a known odor. The significance of olfaction is that it basically allows for remote sensing, further, that majority of complex computations encompassing fluctuating mixtures of odors and wind direction do account for the capability of homing pigeons to navigate in the usage of odors. In addition, Hopfield has been engaged in exploring how all these computations are done by mammals as well as the analogous circuits of many simpler animals.

Capacity

The network capability under the Hopfield network model is dictated by neuron amounts as connections within a particular network. Moreover, it was established that the recall accuracy occurring between nodes and accuracy was recorded as 0.138 (this figure approximates to 138 vectors that can be possibly recalled from storage in each group of 1000 nodes) (Rizzuto & Kahana, 2001). It is clearly evident that in the process, majority of mistakes are bound to happen when a person endeavors to store large figure of vectors. Whenever the Hopfield model fails to recall the right pattern, the forthcoming point is that there could be a possibility of intrusion. This happens because semantically-related points may confuse a person, leading to the occurrence of the collection of the wrong pattern. Consequently, the Hopfield network model starts confusing, starting with one stored thing with that of another during the retrieval process. At this stage, the Hebbian learning method comes into effect, especially when perfect calls as well as high capacity (or around >0.14) are loaded within the network.

Dynamical Systems

Every programmed computer performs its computation systems comprising of differential equations by relying solely on its changes in the internal state. In the same way, Hopfield relates the same concept of neurology to shed light on some of the facets of the potential transformation of neurons.

Capacity of the Hopfield Memory

In the process of training the net (through the outside-product rule), the brain normally stores patterns by forcing different attractors into the system’s state-space. This enables the brain to use the net for searching for the closest attractor. The finding of the suitable choice enables the outputting of the corresponding pattern of activation. The modification of the Hopfield network was based on his desire to work with the continuous activation as well as adopting of a dynamical-systems approach. The outcome proved that the resulting systems is defined by a Lyaponov-function who named it ‘Computational-Energy’, meant to cater for the net for specified optimizations. In practical areas, the significance of Hopfield nets is majorly limited by theoretical drawbacks of the structure.

Human memory

The model developed by Hopfield so far accounts for associative memory by the integration of memory vectors. This implies that memory vectors can be relatively used in initiating the retrieval of the various similar sectors in the network. Intrusions are the most desirable outcomes out of this process. The associative memory attached to the Hopfield network is composed of two major types of operations: hetero assisiantion and hetero-association. The former refers to when there is a direct association between the vector and itself, while the latter exists between different vectors associated in storage, notably, both of these operations can be possibly be stored within a singular memory matrix. Rizzuto & Kahana (2001) notes that Hopfield’s network model has a basic application and utilization as the learning rule (developed by Hebb), a model that illustrated that learning happens due to the strengthening of the weights during when there is an occurrence any activity. If Hopfield chose to use non-linear activation function, which creates Hopfield dynamical rule. According to Hopfield, some of the basic non-linear activation functions are responsible for modifying the state vectors values possible in the direction of the one of the values stored in the region space.

References

Polyn, S.M., & Kahana, M.J. (2008). Memory search and the neural representation of context. Trends in Cognitive Sciences, 12, 24-30.
Rizzuto, D.S., & Kahana, M.J. (2001). An autoassociative neural network model of paired- associate learning. Neural Computation, 13, 2075-2092.
 Storkey, Amos J., and Romain Valabregue. (1999). The basins of attraction of a new Hopfield learning rule. Neural Networks 12(6), 869-876.