I currently understand and made a simple neural network which solves the XOR problem. I want to make a neural network for digit recognition. I know using MNIST data I would need 784 input neurons, 15 hidden neurons and 10 output neurons (0-9).
However, I don’t understand how the network would be trained and how feed forward would work with multiple output neurons.
For example, if the input was the pixels for the digit 3, how would the network determine which output neuron is picked and when training, how would the network know which neuron should be associated with the target value.
Any help would be appreciated.
So you have a classification problem with multiple outputs. I'm supposing that you are using a softmax activation function for the output layer.
How the network determines which output neuron is picked: simple, the output neuron with the greatest probability of being the target class.
The network would be trained with standard backpropagation, same algorithm that you would have with only one output.
There is only one difference: the activation function.
For binary classification you need only one output (for example with digits 0 and 1, if probability < 0.5 then class is 0, else 1).
For multi-class classification you need an output node for each class; then the network will pick the node with the greatest probability of being the target class.
Related
In a neural network, for an intermediate layer, I need to threshold the output. The output of each neuron in the layer is a real value, but I need to binarize it (to 0 or 1). But with hard thresholding, backpropagation won't work. Is there a way to achieve this?
Details:
I have a GAN kind of network i.e. there are 2 neural networks trained end-to-end. The output of first neural network is real values. I need them to be binary values. I read that Gumbel Softmax (Categorical Reparameterization) is used to handle discrete variables in a neural network. Is there a way to use that for my use-case? If yes, how? If not, is there any other way?
From what I could gather in internet is that Gumbel is a probability distribution. Using that we can generate a discrete distribution. But for use-case, I need a function that can take a real input and output a binary value. So, I need an activation function of that form. How can I achieve that?
Thanks!
Here is my scenario
I have used EMNIST database of capital letters of english language.
My neural network is as follows
Input layer has 784 neurons which are pixel values of image 28x28 grey scaled image divided by 255 so value will be in range[0,1]
Hidden layer has 49 neuron fully connected to previous 784.
Output layer has 9 neurons denoting class of image.
Loss function is defined as cross entropy of softmax of output layer.
Initialized all weights as random real number from [-1,+1].
Now I did training with 500 fixed samples for each class.
Simply, passed 500x9 images to train function which uses backpropagation and does 100 iterations changing weights by learning_rate*derivative_of_loss_wrt_corresponding_weight.
I found that when I use tanh activation on neuron then network learns faster than relu with learning rate 0.0001.
I concluded that because accuracy on fixed test dataset was higher for tanh than relu . Also , loss value after 100 epochs was slightly lower for tanh.
Isn't relu expected to perform better ?
Isn't relu expected to perform better ?
In general, no. RELU will perform better on many problems but not all problems.
Furthermore, if you use an architecture and set of parameters that is optimized to perform well with one activation function, you may get worse results after swapping in a different activation function.
Often you will need to adjust the architecture and parameters like learning rate to get comparable results. This may mean changing the number of hidden nodes and/or the learning rate in your example.
One final note: In the MNIST example architectures I have seen, hidden layers with RELU activations are typically followed by Dropout layers, whereas hidden layers with sigmoid or tanh activations are not. Try adding dropout after the hidden layer and see if that improves your results with RELU. See the Keras MNIST example here.
I have trained a feedforward neural network in Matlab. Now I have to implement this neural network in C language (or simulate the model in Matlab using mathematical equations, without using direct functions). How do I do that? I know that I have to take the weights and bias and activation function. What else is required?
There is no point in representing it as a mathematical function because it won't save you any computations.
Indeed all you need is the weights, biases, activation and your architecture. I'm assuming it is a simple feedforward network as you said, you need to implement some kind of matrix multiplication and addition in C. Also, you'll need to implement the activation function. After that, you're ready to go. Your feed forward NN is ready to be implemented. If the C code will not be used for training, it won't be necessary to implement the backpropagation algorithm in C.
A feedforward layer would be implemented as follows:
Output = Activation_function(Input * weights + bias)
Where,
Input: (1 x number_of_input_parameters_for_this_layer)
Weights: (number_of_input_parameters_for_this_layer x number_of_neurons_for_this_layer)
Bias: (1 x number_of_neurons_for_this_layer)
Output: (1 x number_of_neurons_for_this_layer)
The output of a layer is the input to the next layer.
After some days of searching, I have found the following webpage to be very useful http://ufldl.stanford.edu/tutorial/supervised/MultiLayerNeuralNetworks/
The picture below shows a simple feedforward neural network. Picture taken from the above website.
In this figure, the circles denote the inputs to the network. The circles labeled “+1” are called bias units, and correspond to the intercept term. The leftmost layer of the network is called the input layer, and the rightmost layer the output layer (which, in this example, has only one node). The middle layer of nodes is called the hidden layer, because its values are not observed in the training set. In this example, the neural network has 3 input units (not counting the bias unit), 3 hidden units, and 1 output unit.
The mathematical equations representing this feedforward network are
This neural network has parameters (W,b)=(W(l),b(l),W(2),b(2)), where we write Wij(l) to denote the parameter (or weight) associated with the connection between unit j in layer l, and unit i in layer l+1. (Note the order of the indices.) Also, bi(l) is the bias associated with unit i in layer l+1.
So, from the trained model, as Mido mentioned in his answer, we have to take the input weight matrix which is W(1), the layer weight matrix which is W(2), biases, hidden layer transfer function and output layer transfer function. After this, use the above equations to estimate the output hW,b(x). A popular transfer function used for a regression problem is tan-sigmoid transfer function in the hidden layer and linear transfer function in the output layer.
Those who use Matlab, these links are highly useful
try to simulate neural network in Matlab by myself
Neural network in MATLAB
Programming a Basic Neural Network from scratch in MATLAB
I have come up with a solution for a classification problem using neural networks. I have got the weight vectors for the same too. The data is 5 dimensional and there are 5 neurons in the hidden layer.
Suppose neuron 1 has input weights w11, w12, ...w15
I have to explain the physical interpretation of these weights...like a combination of these weights, what does it represent in the problem.Does any such interpretation exist or is that the neuron has no specific interpretation as such?
A single neuron will not give you any interpretation, but looking at a combination of couple of neuron can tell you which pattern in your data is captured by that set of neurons (assuming your data is complicated enough to have multiple patterns and yet not too complicated that there is too many connections in the network).
The weights corresponding to neuron 1, in your case w11...w15, are the weights that map the 5 input features to that neuron. The weights quantify the extent to which each feature will effect its respective neuron (which is representing some higher dimensional feature, in turn). Each neuron is a matrix representation of these weights, usually after having an activation function applied.
The mathematical formula that determines the value of the neuron matrix is matrix multiplication of the feature matrix and the weight matrix, and using the loss function, which is most basically the sum of the square of the difference between the output from the matrix multiplication and the actual label.Stochastic Gradient Descent is then used to adjust the weight matrix's values to minimize the loss function.
I have trained a 3-layer (input, hidden and output) feedforward neural network in Matlab. After training, I would like to simulate the trained network with an input test vector and obtain the response of the neurons of the hidden layer (not the final output layer). How can I go about doing this?
Additionally, after training a neural network, is it possible to "cut away" the final output layer and make the current hidden layer as the new output layer (for any future use)?
Extra-info: I'm building an autoencoder network.
The trained weights for a trained network are available in the net.LW property. You can use these weights to get the hidden layer outputs
From Matlab Documentation
nnproperty.net_LW
Neural network LW property.
NET.LW
This property defines the weight matrices of weights going to layers
from other layers. It is always an Nl x Nl cell array, where Nl is the
number of network layers (net.numLayers).
The weight matrix for the weight going to the ith layer from the jth
layer (or a null matrix []) is located at net.LW{i,j} if
net.layerConnect(i,j) is 1 (or 0).
The weight matrix has as many rows as the size of the layer it goes to
(net.layers{i}.size). It has as many columns as the product of the size
of the layer it comes from with the number of delays associated with the
weight:
net.layers{j}.size * length(net.layerWeights{i,j}.delays)
Addition to using input and layer weights and biases, you may add a output connect from desired layer (after training the network). I found it possible and easy but I didn't exam the correctness of it.