Synaptic weights

Theorem 5 [goles87a] If the synaptic-weight matrix A is symmetric, and the number of sites in the lattice is finite, then the orbits of the generalized threshold rule (equation 5.121) are either fixed points or cycles of period two. 

Now, to be sure, McCulloch-Pitts neurons are unrealistically rendered versions of the real thing. For example, the assumption that neuronal firing occurs synchronously throughout the net at well defined discrete points in time is simply wrong. The tacit assumption that the structure of a neural net (i.e. its connectivity, as defined by the set of synaptic weights) remains constant over time is known be false as well. Moreover, while the input-output relationship for real neurons is nonlinear, real neurons are not the simple threshold devices the McCulloch-Pitts model assumes them to be. In fact, the output of a real neuron depends on its weighted input in a nonlinear but continuous manner. Despite their conceptual drawbacks, however, McCulloch-Pitts neurons are nontrivial devices. McCulloch-Pitts were able to show that for a suitably chosen set of synaptic weights wij, a synchronous net of their model neurons is capable of universal computation. This means that, in principle, McCulloch-Pitts nets possess the same raw computational power as a conventional computer (see section 6.4). 

Step 4 Adjust the synaptic weights according to either of the two learning rules given in equations 10.3 and 10.4. 

It is important to have a symmetric synaptic weight matrix, since even a small deviation away from this symmetry can often make the net unstable and therefore unable to settle into a required set of patterns. While it is true that a symmetric weight set w,... 

Having shown that the energy function (equation 10.9) is a Lyapunov function, let us go back to the main problem with which we started this section, namely to find an appropriate set of synaptic weights. Using the results of the above discussion, we know that we need to have the desired set of patterns occupy the minimum points on the energy surface. We also need to be careful not to destroy any previously stored patterns when we add new ones to our net. Our task is therefore to find a... 

Step 1 For a given set of patterns Pi,P2,..., Vn, where the pattern is encoded by the neuronal values, .., define the synaptic-weight matrix... 

As we mentioned above, however, linearly inseparable problems such as the XOR-problem can be solved by adding one or more hidden layers to the perceptron. Figure 10.9, for example, shows a solution to the XOR-problem using a perceptron that has one hidden layer added to it. The numbers appearing by the links are the values of the synaptic weights. The numbers inside the circles (which represent the hidden and output neurons) are the required thresholds r. Notice that the hidden neuron takes no direct input but acts as just another input to the output neuron. Notice also that since the hidden neuron s threshold is set at r = 1.5, it does not fire unless both inputs are equal to 1. Table 10.3 summarizes the perceptron s output. 

Boolean OR operation will be performed if the synaptic weights between the second hidden layer and the output layer are equal to one and the output neuron s thresholds are set to 0.5 [lipp87]. 

The problem was first addressed by Cover ([cover64], [cover65]), who found a lower bound on the minimum number of synaptic weights needed for an ADALINE network (see section 10.5.1) to realize any Boolean function. More recently. Cover s early work has been extended by Baum ([baumSSa], [baum89]). who has found a... 

Interneuron connechon strengths known as synaptic weights are used to store the knowledge. ... 

The network stores information as the synaptic weights and makes them available for further use. 

The network function is determined by the network structure (i.e., the particular mode by which the individual neurons are connected to one another), the connection strengths (synaptic weights) (i.e., the quantitative rules defining the information transfer), and the processing performed at the individual neuron. 

The networks can adapt themselves to produce a desired output. This adaptation is usually achieved by changing the synaptic weights, and this process is defined as learning. Some networks carry out the learning process by relying on task examples. 

In this study we showed that the biochemical networks function according to the mode of connection between the basic systems (e.g., network A, B, or C), and also according to the processing performed at each neuron (i.e., reaction mechanism or kinetic constants). For the biochemical systems, the strengths of connection between basic elements (i.e., synaptic weights) is represented by the concentration of the component that is shared between the neurons. 

The synaptic-weight model probably owes its status computer science, the enormous number of talented scientists momentum of opinion which may... 

Storage site for the information which they manipulate seems merely a default position (the synaptic-weight model). There is more logic to the idea that the information that is manipulated via the synaptic connections has been accessed in structures or locations independent from the synapses, otherwise the duty of the synapse in one function would seem to necessarily limit its capacity for the second function. 

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