The Activation Function

The node uses the total input to calculate its output signal or activation, yf. This is the signal that the node sends onwards to other nodes or to the outside world. To calculate its output, the node feeds netf into an activation function or squashing function  

The curious name squashing function reflects the action of the function. Activation functions can take as input any real number between - and + that value is then squashed down for output into a narrow range, such as (0, +1) or [-1, +1). 

Using Artificial Intelligence in Chemistry and Biology A Practical Guide 

Nodes that employ a step activation function are sometimes known as threshold logic units (TLUs). 

The binary threshold activation function was used in early attempts to create ANNs because of a perceived parallel between this function and the way that neurons operate in the brain. Neurons require a certain level of activation before they will fire, otherwise they are quiescent. A TLU functions in the same way. 

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The activation function/(.v) (where. v is the weighted sum) can take many forms, some of which are shown in Figure 10.21. From Figure 10.21 it can be seen that the bias bj in equations (10.54) and (10.55) will move the curve along the. v axis, i.e. effectively... 

If the activation function is the sigmoid function given in equation (10.56), then its derivative is... 

P is a vector of inputs and T a vector of target (desired) values. The command newff creates the feed-forward network, defines the activation functions and the training method. The default is Fevenberg-Marquardt back-propagation training since it is fast, but it does require a lot of memory. The train command trains the network, and in this case, the network is trained for 50 epochs. The results before and after training are plotted. 

Passive—Minimizing the hazard by process and equipment design features which reduce either the frequency or consequence of the hazard without the active functioning of any device e.g., the use of equipment rated for higher pressure. 

In case of MLP, the activation function has to be monotonous and differentiable (because of Eq. 6.122). Frequently used is the sigmoid function... 

Although for each neuron a specific activation function can be defined, the most applications use the same function for the neurons of a given layer. When the activation function has a limited range, then X and Y must be scaled correspondingly. 

Equation (2.27) reveals why some activation functions are more convenient computationally than others. In order to apply BP, the derivative of the activation function must be determined. If no closed form expression for this derivative exists, it must be calculated numerically, which will slow the algorithm. Since training is in any case a slow process because of the number of samples that must be inspected, the advantage of using an activation function whose derivative is quick to calculate is considerable. 

Is the activation function the only criterion to select an enantioselective catalyst ... 

The fewer the active functions are available to serve as haptenic determination, the lesser will be the specificity of the reaction in radioimmunoassay in other words, the greater the number of antigenic determinants in a hapten molecule the more specific shall be its reaction with its antibody. 

The partial hydrolysis of the metal organic compound (e.g. a metal alkoxide) introduces the active functional OH groups, attached to metal atoms. 

The activation function of the biochemical neuron is defined by the reaction mechanism and the pertinent rate equations. This function is actually a set of differential equations derived from mass balances for the components taking part in the enzymic reactions in each biochemical neuron (see Section 4.1.3). 

As the laws of dilute solution are limiting laws, they may not provide an adequate approximation at finite concentrations. For a more satisfactory treatment of solutions of finite concentrations, for which deviations from the limiting laws become appreciable, the use of new functions, the activity function and excess thermodynamic functions, is described in the following chapters. 

With the definition of the activity function, we could derive a general expression that relates AG of a reaction to the equilibrium constant and hence to eliminate the restrictions imposed on previous relationships. 

Having established the definitions and conventions for the activity function and for the excess Gibbs function in Chapter 16, we are in a position to understand the experimental methods that have been used to determine numeric values of these quantities. 

Another reason for copolymerization is to insert functional grouping in the polymer. A functional group is one that is easily reacted. For example, copolymerization of styrene with acrylonitrile, CH2=CH-CN, involves only the double bond, leaving the newly formed copolymer with the active functional group -CN, available for subsequent reaction. The copolymer might be reacted later with itself or another monomer to give a cross-linked thermoset. 

Certain expressions describing a solvent acidity function, where S is a base that is protonated by an aqueous mineral acid solution. The equations describe a linear free-energy relationship between log([SH+]/[S]) + Ho and Ho + log[H ], where Ho is Hammett s acidity function and where Ho + log[H+] represents the activity function log(7s7H+/ysH ) for the nitroaniline reference bases to build Ho. Thus, log([SH+]/[S]) log[H+] = ( 1)... 

A modification of the Bunnett-Olsen equation concerned with solvent acidity in which log([SH+]/[S]) - log[H+] = m X -h p/ sH where [S] and [SH+] are the solvent and protonated solvent concentrations, and X is the activity function log[(7s7H+/ysH+)] for an arbitrary reference base. In practice, X = - (Ho + log[H+]), called the excess acidity (where Ho is the Hammett acidity function, m = 1- (f), and 4> represents the response of the S + H+ SH+ equilibrium to changes in the acid concentration). See Acidity Function Bunnett-Olsen Equation... 

From the structure of the Cys2 element with bound phorbol ester (Fig. 7.9), it was concluded that the activating function of the phorbol ester is based, in particular, in promotion of membrane association of protein kinase C. The binding site of the phor-... 

Lactams are produced from amino acids, where the amino and the carboxylic acid groups of the same molecule react to form an amide linkage. (3-lactams are the active functionality in modem antibiotics, e.g. penicillin V. 

The numerical value of aj determines whether the neuron is active or not. The bias, 0j, should also be optimised during training [8]. The activation function, ranges currently from 0 to 1 or from — 1 to +1 (depending on the mathematical transfer function, /). When a, is 0 or — 1 the neuron is totally inactive,... 

Table 5.1 Activation functions currently employed in artificial neurons, where n represents the overall net input to the neuron and a denotes the result of the activation function...

Going back to the main issue of this book, multivariate calibration, the most common situation is to accept the value of the activation function without further processing. In this case, the output function has no effect and it just transfers the value to the output (this can be considered as an identity function). Recall that the final response of the ANN has to be scaled back to obtain concentration units. 

As was explained above, each neuron of the hidden layer has one response (a°), calculated with the activation function (f )-. 

As in our example here there is only a neuron at the exit layer (we are considering only calibration), the activation function yields a value that is the final response of the net to our input spectrum (recall that the output function of the neuron at the output layer for calibration purposes is just the identity function) ... 

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