Conceptually, people talk both are different. There has been a confusion still. Let me summarize what i understood, please educate me. There is a tiny differentiating factor between these two.
1) A tiny change in the weight/bias of a particular perceptron would drastically make other perceptrons behave differently, thought the changed perceptron is intented to perform correctly?
2) A Small change in perceptron can produce different output.
3) With said above, sigmoid neuron is one good example that makes tiny changes in the output with respect to tiny weight/bias changes.
4) Perceptron outputs either 0 or 1, whereas neuron ( ex: sigmoid neuron) can produce the values in between 0-1.
Is my understanding is correct?. Or, is it totally dump?
A perceptron is a neural network architecture type; a regular, layered, feed forward neural network.
A neural network consists of neurons - neurons have activation functions and a bias. Neurons are connected to each other with weights.
Thus, a perceptron contains neurons.
1) A tiny change in the weight/bias of a particular perceptron would drastically make other perceptrons behave differently, thought the changed perceptron is intented to perform correctly?
No. A perceptron is a neural network on its own, it has no effect on other neural networks.
2) A Small change in perceptron can produce different output.
Yes, that's possible. But it should be A Small change in perceptron input can produce different output.
4) Perceptron outputs either 0 or 1, whereas neuron ( ex: sigmoid neuron) can produce the values in between 0-1. Is my understanding is correct?. Or, is it totally dump?
Mothern perceptrons output values between 0 and 1 as well.
Related
I am try to write a neural network class but I don't fully understand some aspects of it. I have two questions on the folling design.
Am I doing this correctly? Does the bias neuron need to connect to all of neurons (except those in the input layer) or just those in the hidden layer?
My second question is about calculation the output value. I'm using the equation below to calculate the output value of the neurons.
HiddenLayerFirstNeuron.Value =
(input1.Value * weight) + (input2.Value * weight) + (Bias.Value * weight)
After this equation, I'm calculating the activation and the result send the output. And output neurons doing same.
I'm not sure what I am do and I want to clear up problems.
Take a look at: http://deeplearning.net/tutorial/contents.html in theano. This explains everything you need to know for multi layer perceptron using theano (symbolic mathematic library).
The bias is usually connected to all hidden and output units.
Yes, you compute the input of activation function like summation of weight*output of previous layer neuron.
Good luck with development ;)
There should be a separate bias neuron for each hidden and the output layer. Think of the layers as a function applied to a first order polynomials such as f(m*x+b)=y where y is your output and f(x) your activation function. If you look at the the linear term you will recognize the b. This represents the bias and it behaves similar with neural network as with this simplification: It shifts the hyperplane up and down the in the space. Keep in mind that you will have one bias per layer connected to all neurons of that layer f((wi*xi+b)+...+(wn*xn+b)) with an initial value of 1. When it comes to gradient descent, you will have to train this neuron like a normal weight.
In my opinion should you apply the activation function to the output layer as well. This is how it's usually done with multilayer perceptrons. But it actually depends of what you want. If you, for example, use the logistic function as activation function and you want an output in the interval (0,1), then you have to apply your activation function to the output as well. Since a basic linear combination, as it is in your example, can theoretically go above the boundaries of the previously mentioned Intervall.
I have inputs x_1, ..., x_n that have known 1-sigma uncertainties e_1, ..., e_n. I am using them to predict outputs y_1, ..., y_m on a trained neural network. How can I obtain 1-sigma uncertainties on my predictions?
My idea is to randomly perturb each input x_i with normal noise having mean 0 and standard deviation e_i a large number of times (say, 10000), and then take the median and standard deviation of each prediction y_i. Does this work?
I fear that this only takes into account the "random" error (from the measurements) and not the "systematic" error (from the network), i.e., each prediction inherently has some error to it that is not being considered in this approach. How can I properly obtain 1-sigma error bars on my predictions?
You can get a general analysis of what "jittering" (generation of random samples) brings to the neural network optimization here http://wojciechczarnecki.com/pdfs/preprint-ml-with-unc.pdf
In short - jittering is just a regularization on network's weights.
For errors bars as such you should refer to works of Will Penny
http://www.fil.ion.ucl.ac.uk/~wpenny/publications/error_bars.ps
http://www.fil.ion.ucl.ac.uk/~wpenny/publications/nnerrors.ps
u r right. That method only takes the data uncertainty into account (assuming u don't fit the neural net while applying the noise). As a side note, alternatively when fitting the data using a neural net u may also apply mixture density networks (see one of the many tutorials).
More importantly, in order to account for model uncertainty u should apply bayesian neural nets. U could could start e.g. with Monte-Carlo dropout. Also very interesting should be this work on performing sampling-free inference when using Monte-Carlo dropout
https://arxiv.org/abs/1908.00598
This work explicitly uses error propagation through neural networks and should be very interesting for u!
Best
I have implemented Q-Learning as described in,
http://web.cs.swarthmore.edu/~meeden/cs81/s12/papers/MarkStevePaper.pdf
In order to approx. Q(S,A) I use a neural network structure like the following,
Activation sigmoid
Inputs, number of inputs + 1 for Action neurons (All Inputs Scaled 0-1)
Outputs, single output. Q-Value
N number of M Hidden Layers.
Exploration method random 0 < rand() < propExplore
At each learning iteration using the following formula,
I calculate a Q-Target value then calculate an error using,
error = QTarget - LastQValueReturnedFromNN
and back propagate the error through the neural network.
Q1, Am I on the right track? I have seen some papers that implement a NN with one output neuron for each action.
Q2, My reward function returns a number between -1 and 1. Is it ok to return a number between -1 and 1 when the activation function is sigmoid (0 1)
Q3, From my understanding of this method given enough training instances it should be quarantined to find an optimal policy wight? When training for XOR sometimes it learns it after 2k iterations sometimes it won't learn even after 40k 50k iterations.
Q1. It is more efficient if you put all action neurons in the output. A single forward pass will give you all the q-values for that state. In addition, the neural network will be able to generalize in a much better way.
Q2. Sigmoid is typically used for classification. While you can use sigmoid in other layers, I would not use it in the last one.
Q3. Well.. Q-learning with neural networks is famous for not always converging. Have a look at DQN (deepmind). What they do is solving two important issues. They decorrelate the training data by using memory replay. Stochastic gradient descent doesn't like when training data is given in order. Second, they bootstrap using old weights. That way they reduce non-stationary.
Given a target function f: R^4 -> R^2, can you draw me(give me an example) an Artificial Neural Network , lets say with two layers, and 3 nodes in the hidden layer.
Now, I think I understand how an ANN works when a function is like [0,1]^5 ->[0,1], but I am not quite sure how to do an example from R4 to R2.
I am new to machine learning, and it's a little bit diffult to catch up with all this concepts.
Thanks in advance.
First, you need two neurons in the output layer. Each neuron would correspond to one dimension of your output space.
Neurons in the output layer don't need an activation function that limits their values in the [0,1] interval (e.g. the logistic function). And even if you scale your output space in the interval [0,1], don't use a sigmoid function for activation.
Although your original data is not in [0,1]^4, you should do some preprocessing to scale and shift them to have mean zero and variance 1. You must apply same preprocessing to all your examples (training and test).
This should give you something to build up on.
I understand the role of the bias node in neural nets, and why it is important for shifting the activation function in small networks. My question is this: is the bias still important in very large networks (more specifically, a convolutional neural network for image recognition using the ReLu activation function, 3 convolutional layers, 2 hidden layers, and over 100,000 connections), or does its affect get lost by the sheer number of activations occurring?
The reason I ask is because in the past I have built networks in which I have forgotten to implement a bias node, however upon adding one have seen a negligible difference in performance. Could this have been down to chance, in that the specifit data-set did not require a bias? Do I need to initialise the bias with a larger value in large networks? Any other advice would be much appreciated.
The bias node/term is there only to ensure the predicted output will be unbiased. If your input has a dynamic (range) that goes from -1 to +1 and your output is simply a translation of the input by +3, a neural net with a bias term will simply have the bias neuron with a non-zero weight while the others will be zero. If you do not have a bias neuron in that situation, all the activation functions and weigh will be optimized so as to mimic at best a simple addition, using sigmoids/tangents and multiplication.
If both your inputs and outputs have the same range, say from -1 to +1, then the bias term will probably not be useful.
You could have a look at the weigh of the bias node in the experiment you mention. Either it is very low, and it probably means the inputs and outputs are centered already. Or it is significant, and I would bet that the variance of the other weighs is reduced, leading to a more stable (and less prone to overfitting) neural net.
Bias is equivalent to adding a constant like 1 to the input of every layer. Then the weight to that constant is equivalent to your bias. It's really simple to add.
Theoretically it isn't necessary since the network can "learn" to create it's own bias node on every layer. One of the neurons can set it's weight very high so it's always 1, or at 0 so it always outputs a constant 0.5 (for sigmoid units.) This requires at least 2 layers though.