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.
Related
From what I understand about DNN's dropout regularization is that:
Dropout:
First we randomly delete neurons from the DNN and leave only the input and output the same. Then we perform forward propagation and backward propagation based on a mini-batch; learn the gradient for this mini-batch and then update the weights and biases – Here I denote these updated weights and biases as Updated_Set_1.
Then, we restore the DNN to default state and randomly delete the neurons. Now we perform the forward and backward propagation and find a new set of weights and biases called Updated_Set_2. This process continues until Updated_Set_N ~ N represents the number of mini batches.
Lastly, we calculate the average of all weights and biases based on the total Updated_Set_N; example, from Updated_Set_1 ~ Updated_Set_N. These new average weights and biases will be used to predict the new input.
I would just want to confirm whether my understanding is correct or wrong. If wrong, please do share me your thoughts and teach me. thank you in advance.
Well, actually there is no averaging. During training, for every feed forward/back forward pass, we randomly "mute"/deactivate some neurons, so that their outputs and related weights are not considered during computation of the output neither during back propagation.
That means we are forcing the other activated neurons to give good prediction without the help of the deactivated neurons.
So this increase their independency to the other neurons(features) and in the same way increase the model generalization.
Other than this the forward and back propagation phase are the same without dropout.
Im trying to wrap my head around understanding neural networks and from everything I've seen, I understand that they are made up of layers created by nodes. These nodes are attached to each other with "weighted" connections, and by passing values through the input layer, the values travel through the nodes, changing their values dependent on the "weight" of the connections (right?). Eventually they reach the output layer with a value. I understand the process but I don't see how this leads to the network being trained. Does the network remember a pattern between weighted connections? How does it remember that pattern?
Each weight and bias on each node is like a stored variable. As new data causes its weights and biases to change, these variables change. Eventually a trained algorithm is done and the weights and biases don't need to change anymore. You can then store the information about the all the nodes, weights, biases and connections however you like. This information is your model. So the "remembering" is just the values of the weights and biases.
Neural network remembers what its learned through its weights and biases. Lets explain it with a binary classification example. During forward propagation, the value computed is the
probability(say p) and actual value is y. Now, loss is calculated using the formula:->
-(ylog(p) + (1-y)log(1-p)). Once the loss is calculated, this info is propagated backwards and corresponding derivatives of weights and biases are calculated using this loss. Now weights and biases are adjusted according to these derivatives. In one epoch, all the examples present are propagated and weights and biases are adjusted. Then, same examples are propagated forward and backward and correspondingly in each step, weights and biases are adjusted. Finally, after minimizing the loss to a good extent or, achieving a high accuracy (make sure not to overfit), we can store the value of weights and biases and this is what neural network has learned.
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 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.
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.