I'm trying to understand an answer to a question on simple model.
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On input we have 2 signals applied on 2 neurons x1 and x2 (look at the image, provided above please). The question is - what will be the output value on y? The answer is y=max(x1,x2). Could you please explain this?
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My neural network looks like this
but I'm a bit confused by this diagram.
Clearly we have 10 input values and 2 output values.
There are also 10 hidden neurons. So I assume each of the 10 inputs are connected to each of the 10 hidden neurons?
Also what do the Ws and Bs mean?
I have yet to find a description of this diagram in Matlab's documentation, but it is a simplification of the diagram shown here. You have one hidden layer with neurons which are each connected to all the inputs. Note that the number of neurons won't always be the same as the number of inputs, which are both 10 here. W=weights, b=biases. There is a nice intro here.
I'm building a Neural Network from scratch that categorizes values of x into 21 possible estimates for sin(x). I plan to use MSE as my loss function.
MSE of each minibatch = ||y(x) - a||^2, where y(x) is the vector of network outputs for x-
values in the minibatch. a is the vector of expected outputs that correspond to each x.
After finding the loss, the column vector of all weights in the network is recalculated. Column vector of delta w's ~= column vector of partial derivatives of C with respect to each weight.
∇C≡(∂C/∂w1,∂C/∂w2...).T and Δw =−η∇C where η is the (positive) learn rate.
The problem is, to find the gradient of C, you have to differentiate with respect to each weight. What does that function even look like? It's not just the previously stated MSE right?
Any help is appreciated. Also, apologies in advance if this question is misplaced, I wasn't sure if it belonged here or in a math forum.
Thank you.
(I might add that I have tried to find an answer to this online, but few examples exist that either don't use libraries to do the dirty work or present the information clearly.)
http://neuralnetworksanddeeplearning.com/chap2.html
I had found this a while ago but only now realized it's significance. The link describes δ(j,l) as an intermediary value to arrive at the partial derivative of C with respect to weights. I will post back here with a full answer if the link above answers my question, as I've seen a few posts similar to mine that have yet to be answered.
This question already has answers here:
How does a back-propagation training algorithm work?
(4 answers)
Closed 6 years ago.
I've recently completed Professor Ng's Machine Learning course on Coursera, but I have some problem with understanding backpropagation algorithm. so I try to read Bishop codes for backpropagation using sigmoid function. I searched and found clean codes which try to explain what backpropagation does, but still have problem with understanding codes
can any one explain me what does really backpropagation do? and also explain codes for me?
here is the code that I found in the github and I mentioned it before
You have an error of the network. And first step of backpropagation is to compute a portion of guilt for each neuron in network. Your goal is to describe an error as dependence of weights(parameter which you can change). So backprop equation is partial derivation error/weights.
First step: error signal = (desired result - output of output neuron) x derivationactivation(x)
where x is input of output neuron. That is portion of guilt for output neuron.
Next step is compute a portion of guilt for hidden units. First part of this step is summation of error signals of next layer x weights which connect hidden unit with next layer unit. And rest is partial derivation of activation function. error signal = sum(nextlayererror x weight)x derivationactivation(x).
Final step is adaptation of weights.
wij = errorsignal_i x learning_rate x output_of_neuron_j
My implementation of BP in Matlab
NN
I have 3 neurons x1, x2, x3. Now I know my value is being overflowed by the actual result value at output (as it is wrong answer) and my weights need new value, but how much value to be set for each neuron ? How to calculate that ?
One way is to divide the (desired value - output value) / 3 and assign the answer to each neuron ... but it won't work for new input, as no proper learning is made.
From your question it seems you do not understand yet how really neural networks work.
First of all, neural networks are a class of algorithms that fall under machine learning techniques. Therefore, they learn, either unsupervised, supervised or in a reinforcement type of training. This of course require a learning paradigm. In neural networks the most well studied supervised training is the backpropagation method. However, to understand how this work you first need to understand how a network is developed.
A description of what is a neural network and its foundations can be seen here: http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html
One practical explanation how you can implement a functional network through backpropagation can be seen here: http://galaxy.agh.edu.pl/~vlsi/AI/backp_t_en/backprop.html
If you read these you will probably know enough to answer your question.
I have a data set with three input variables and one output. I want to fit the target column to the input data using an artificial neural network with one layer, for example. My concern is, can I obtain a closed form or analytical formula that links the modeled target to the three input variable? Please let me know whether the software can process that.
Technically, you can always translate a one-layer neural net into a closed form solution. Let's call your input variables x, y, and z, your bias node b, and the connections between them and your output cx, cy, cz, and cb respectively. Once you've trained the neural network so that the connection weights are adjusted, the output value should equal xcx + ycy + zcz + cb. (technically the bias term is bcb, but b = 1).
If you were using a more complicated neural network, this equation would get a lot more complicated, particularly as you add hidden layers, but theoretically you can always write it out analytically. It just won't always be tractable to evaluate the analytic form.
For a more detailed answer, see: Deriving equation by weights and biases from a neural network