I'm new to Neual Networks and I suppose I don't fully understand what 'bias' param does in Matlab's NN.
It simply means an additive term in the neuron computation. Typically you have the input vector to a neuron x, and you perform a dot product with the weights, w. Then you add on the bias term, b and apply a non-linear mapping.
The b number (per neuron) is part of the training and will change during training (unless you specifically disable it in training, but I know no reason to do this.)
The term bias is probably simply because it's an additive value in addition to the neuron's activation (that comes from the weighted inputs). Once trained, the bias is a fixed term that does not depend on the neuron inputs.
A neuron's bias is basically an extra input value that doesn't change. It is added to the normal inputs to get the total input to the neuron.
Related
I was reading some literature about ANN and got a bit confused with how the biases are updated. I understand that the process is done through backpropagation, however I am confused to which part of the biases are actually adjusted since I read that their value is always one.
So my question is if the biases values are adjusted because their connection channel weights are update therefore causing the adjustment or if is the actual value one that is updated.
Thanks in advance!
Bias is just another parameter that is trained by computing derivatives, as every other part of the neural network. One can simulate a bias by concatenating extra 1 to activations on the previous layer, since
w x + b = <[w b], [x 1]>
where [ ] is concatenation. Consequently it is not the bias that is 1, bias is just a trainable parameter, but one can think about a bias as if it was regular neuron-neuron connection, where the input neuron is equal to 1.
I'm student in a graduate computer science program. Yesterday we had a lecture about neural networks.
I think I understood the specific parts of a perceptron in neural networks with one exception. I already made my research about the bias in an perceptron- but still I didn't got it.
So far I know that, with the bias I can manipulate the sum over the inputs with there weights in a perception to evaluate that the sum minus a specific bias is bigger than the activation function threshold - if the function should fire (Sigmoid).
But on the presentation slides from my professor he mentioned something like this:
The bias is added to the perceptron to avoid issues where all inputs
could be equal to zero - no multiplicative weight would have an effect
I can't figure out whats the meaning behind this sentence and why is it important, that sum over all weighted inputs can't be equal to zero ?. If all inputs are equal to zero, there should be no impact on the next perceptions in the next hidden layer, right? Furthermore this perception is a static value for backpropagation and has no influence on changing this weights at the perception.
Or am I wrong?
Has anyone a solution for that?
thanks in advance
Bias
A bias is essentially an offset.
Imagine the simple case of a single perceptron, with a relationship between the input and the output, say:
y = 2x + 3
Without the bias term, the perceptron could match the slope (often called the weight) of "2", meaning it could learn:
y = 2x
but it could not match the "+ 3" part.
Although this is a simple example, this logic scales to neural networks in general. The neural network can capture nonlinear functions, but often it needs an offset to do so.
What you asked
What your professor said is another good example of why an offset would be needed. Imagine all the inputs to a perceptron are 0. A perceptron's output is the sum of each of the inputs multiplied by a weight. This means that each weight is being multiplied by 0, then added together. Therefore, the result will always be 0.
With a bias, however, the output could still retain a value.
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 know a Gaussian Process Regression model is mainly specified by its covariance matrix and the free hyper-parameters act as the 'weights'of the model. But could anyone explain what do the 2 hyper-parameters (length-scale & amplitude) in the covariance matrix represent (since they are not 'real' parameters)? I'm a little confused on the 'actual' meaning of these 2 parameters.
Thank you for your help in advance. :)
First off I would like to point out that there are infinite number of kernels that could be used in a gaussian process. One of the most common however is the RBF (also referred to as squared exponential, the expodentiated quadratic, etc). This kernel is of the following form:
The above equation is of course for the simple 1D case. Here l is the length scale and sigma is the variance parameter (note they go under different names depending on the source). Effectively the length scale controls how two points appear to be similar as it simply magnifies the distance between x and x'. The variance parameter controls how smooth the function is. These are related but not the same.
The Kernel Cookbook give a nice little description and compares RBF kernels to other commonly used kernels.
I was wondering, MATLAB has a removeconstantrows function that should be applied to feedforward neural network input and target output data. This function removes constant rows from the data. For example if one input vector for a 5-input neural network is [1 1 1 1 1] then it is removed.
Googling, the best explanation I could find is that (paraphrasing) "constant rows are not needed and can be replaced by appropriate adjustments to the biases of the output layer".
Can someone elaborate?
Who does this adjustment?
From my book, the weight adjustment for simple gradient descent is:
Δ weight_i = learning_rate * local_gradient * input_i
Which means that all weights of a neuron at the first hidden layer are adjusted the same amount. But they ARE adjusted.
I think there is a misundertanding. The "row" is not an input pattern, but a feature, that is i-th component in all patterns. It's obvious that if some feature does not have big variance on all data set, it does not provide valuable information and does not play a noticable role for network training.
The comparison to a bias is feasible (though I don't agree, that this applies to output layer (only), bacause it depends on where the constant row is found - if it's in input data, then it is right as well for the first hidden layer, imho). If you remeber, it's recommended for each neuron in backpropagation network to have a special bias weight, connected to 1 constant signal. If, for example, a training set contains a row with all 1-th, then this is the same as additional bias. If the constant row has a different value, then the bias will have different effect, but in any case you can simply eliminate this row, and add the constant value of the row into the existing bias.
Disclaimer: I'm not a Matlab user. My background in neural networks comes solely from programming area.