I have a simple question. I know that the main purpose of activation function is to convert an input signal of a node to an output signal. And that output signal is gonna used as an input in the next layer. But I dont have any idea about the way that activation function such as sigmoid do this in classification problem.
All I know is about converting.
Could any one pleas clarify this to me?
Thanks!
In simple terms the function gets inputs and assigns some weights to the inputs.
Then the activation function calculates the value (eg :- Sigmoid).
Then it compares the value with the threshold value assigned . If its more than the threshold value then it backtracks (back propagation Algorithm). and adjusts the weights. You can find more details at https://en.wikipedia.org/wiki/Backpropagation
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Given a trained system, a network can be run backward with output values and partial inputs to find the value of a missing input value. Is there a name for this operation?
In example with a trained XOR network with 2 input neurons (with values 1 and X) and an output layer neuron (with value 1). If someone wanted to find what the value of the second input neuron was, they could feed the information backwards can calculate that it would be close to 0. What exactly is this operation called?
I think your issue is related to Feature Extraction and Feature selection is the process of selecting a subset of relevant features (variables, predictors) for use in model construction. Also This article is related to your issue.
The Backwards Pass:
The goal with back propagation is to update each of the weights in the network so that they cause the actual output to be closer the target output, thereby minimising the error for each output neuron and the network as a whole. This is the step you wanted to know i guess.
I am learning neural networks for the first time. I was trying to understand how using a single hidden layer function approximation can be performed. I saw this example on stackexchange but I had some questions after going through one of the answers.
Suppose I want to approximate a sine function between 0 and 3.14 radians. So will I have 1 input neuron? If so, then next if I assume K neurons in the hidden layer and each of which uses a sigmoid transfer function. Then in the output neuron(if say it just uses a linear sum of results from hidden layer) how can be output be something other than sigmoid shape? Shouldn't the linear sum be sigmoid as well? Or in short how can a sine function be approximated using this architecture in a Neural network.
It is possible and it is formally stated as the universal approximation theorem. It holds for any non-constant, bounded, and monotonically-increasing continuous activation function
I actually don't know the formal proof but to get an intuitive idea that it is possible I recommend the following chapter: A visual proof that neural nets can compute any function
It shows that with the enough hidden neurons and the right parameters you can create step functions as the summed output of the hidden layer. With step functions it is easy to argue how you can approximate any function at least coarsely. Now to get the final output correct the sum of the hidden layer has to be since the final neuron then outputs: . And as already said, we are be able to approximate this at least to some accuracy.
I'm sorry, I've just learned about the neural network and I have not yet understood in its implementation. Suppose I want to make a back propagation neural network that accepts multiple real numbers as input and produces two types of output, which is a real number, and the other is a choice that is between A, B, and C or only the choice between 0 and 1. What activation function should I use or how do I structure and compute it?
The activation function depends on the values of the input and output signals. Here http://www.mathworks.com/help/nnet/ug/multilayer-neural-network-architecture.html are some example of transfer functions. As I understood, all your input and output values are positive numbers, so pureline or logsig functions are maybe the most suitable for your problem. When you form your input and output matrix be careful with sorting input and output values (first row in input matrix correspond to the first row in output matrix).
Hope this help you.
It seems there is a bit of confusion between activation and transfer function. From Wikipedia ANN:
It seems that the transfer function calculates the net while the activation function the output of the neuron. But on Matlab documentation of an activation function I quote:
satlin(N, FP) is a neural transfer function. Transfer functions calculate a layer's output from its net input.
So who is right? And can you use the term activation function or transfer function interchangeably?
No, they are the same. I also quote from wikipedia: "Usually the sums of each node are weighted, and the sum is passed through a non-linear function known as an activation function or transfer function. Don't take the matlab documentation too literally, it's thousand of pages long so some words might not be used in their strict sense.
In machine learning at least, they are used interchangeably by all books I've read.
activation function is used almost exclusively nowadays.
transfer function is mostly used in older (80/90's) books, when machine learning was uncommon, and most readers had an electrical engineering/signal processing background.
So, to sum up
prefer the term activation function. It's more common, and more appropriate, both from a biological point of view (neuron fires when you surpass a threshold) and an engineering point of view (an actual transfer function should describe the whole system)
if anyone else makes a distinction between them, ask them to clear up what they mean
After some research I've found in "Survey of Neural Transfer Functions", from Duch and Jankowski (1999) that:
transfer_function = activation function + output function
And IMO the terminology makes sense now since we need to have a value (signal strength) to verify it the neuron will be activated and then compute an output from it. And what the whole process do is to transfer a signal from one layer to another.
Two functions determine the way signals are processed by neurons. The
activation function determines the total signal a neuron receives. The value of the activation function is usually scalar and the
arguments are vectors. The second function determining neuron’s
signal processing is the output function o(I), operating on scalar
activations and returning scalar values. Typically a squashing
function is used to keep the output values within specified bounds.
These two functions together determine the values of the neuron
outgoing signals. The composition of the activation and the output
function is called the transfer function o(I(x)).
I think the diagram is correct but not terminologically accurate.
The transfer function includes both the activation and transfer functions in your diagram. What is called transfer function in your diagram is usually referred to as the net input function. The net input function only adds weights to the inputs and calculates the net input, which is usually equal to the sum of the inputs multiplied by given weights. The activation function, which can be a sigmoid, step, etc. function, is applied to the net input to generate the output.
Transfer function come from the name transformation and are used for transformation purposes. On the other hand, activation function checks for the output if it meets a certain threshold and either outputs zero or one. Some examples of non-linear transfer functions are softmax and sigmoid.
For example, suppose we have continuous input signal x(t). This input signal is transformed into an output signal y(t) through a transfer function H(s).
Y(s) = H(s)X(s)
Transfer function H(s) as can be seen above changes the state of the input X(s) into a new output state Y(s) through transformation.
A closer look at H(s) shows that it can represents a weight in a neural network. Therefore, H(s)X(s) is simply the multiplication of the input signal and its weight. Several of these input-weight pairs in a given layer are then summed up to form the input of another layer. This means that input to any layer to a neural network is simply the transfer function of its input and the weight, i.e a linear transformation because the input is now transformed by the weights. But in the real world, problems are non-linear in nature. Therefore, to make the incoming data non-linear, we use a non-linear mapping called activation function. An activation function is a decision making function that determines the presence of particular neural feature. It is mapped between 0 and 1, where zero mean the feature is not there, while one means the feature is present. Unfortunately, the small changes occurring in the weights cannot be reflected in the activation value because it can only take either 0 or 1. Therefore, nonlinear finctions must be continuous and differentiable between this range.
In really sense before outputting an activation, you calculate the sigmoid first since it is continuous and differential and then use it as an input to an activation function which checks whether the output of the sigmoid is higher than its activation threshhold. A neural network must be able to take any input from -infinity to +positive infinite, but it should be able to map it to an output that ranges between {0,1} or between {-1,1} in some cases - thus the need for activation function.
I am also a newbie in machine learning field. From what I understand...
Transfer function:
Transfer function calculates the net weight, so you need to modify your code or calculation it need to be done before Transfer function. You can use various transfer function as suitable with you task.
Activation function: This is used for calculating threshold value i.e. when your network will give the output. If your calculated result is greater then threshold value it will show output otherwise not.
Hope this helps.
I am interested in trying NN in a perhaps unusual setting.
The input to the NN is a vector. The output is also a vector. However, the training data and error is not computed directly on this output vector, but is a (nonlinear) function of this output vector. So at each epoch, I need to activate the NN, find an output vector, apply this to my (external) nonlinear function to compute a new output vector. However, this new output vector is of length 1 and the error is computed based on just this single output.
Some questions:
Is this something that NN might usefully do?
Is this a structure that is well-known already?
Any ideas how to approach this?
In principle, yes.
Yes, this is what a softmax unit does. It takes the activations at the output layer and computes a single value from them, which is then used to compute the error.
You need to know the partial derivative of your multivariate function (let's call it f). From there, you can use the chain rule to compute the derivative of the error in the parameters of f and backpropagate the error derivative.