Contents

- 1 Does bias change in gradient descent?
- 2 Why does gradient descent fail?
- 3 What does high bias mean?
- 4 Do we need to update bias in backpropagation?
- 5 Is gradient descent the best?
- 6 Which model has highest bias?
- 7 How to calculate gradients for bias terms in backpropagation?
- 8 Do you sum gradients for biases in Layer 2?
- 9 Which is the upper gradient for bias terms?
- 10 Do you sum the gradient of the sigmoid function?

## Does bias change in gradient descent?

Basically, biases are updated in the same way that weights are updated: a change is determined based on the gradient of the cost function at a multi-dimensional point. Think of the problem your network is trying to solve as being a landscape of multi-dimensional hills and valleys (gradients).

## Why does gradient descent fail?

If the execution is not done properly while using gradient descent, it may lead to problems like vanishing gradient or exploding gradient problems. These problems occur when the gradient is too small or too large. And because of this problem the algorithms do not converge.

## What does high bias mean?

Bias is the accuracy of our predictions. A high bias means the prediction will be inaccurate. Intuitively, bias can be thought as having a ‘bias’ towards people. If you are highly biased, you are more likely to make wrong assumptions about them.

## Do we need to update bias in backpropagation?

In both cases, you only do backpropagation calculation from neuron activation deltas to the bias weight deltas, you don’t need to calculate the “activation” delta for bias, because it is not something that can change, it is always 1.0. Also the bias does not contribute deltas back further to anything else.

## Is gradient descent the best?

Gradient descent is best used when the parameters cannot be calculated analytically (e.g. using linear algebra) and must be searched for by an optimization algorithm.

## Which model has highest bias?

In a simple model, there tends to be a higher level of bias and less variance. To build an accurate model, a data scientist must find the balance between bias and variance so that the model minimizes total error.

## How to calculate gradients for bias terms in backpropagation?

In terms of the maths, if your loss is J, and you know ∂ J ∂ z i for a given neuron i which has bias term b i . . . because the network is designed to process examples in (mini-)batches, and you therefore have gradients calculated for more than one example at a time.

## Do you sum gradients for biases in Layer 2?

Thus, we must accumulate them to update the biases of layer 2. However, for the gradients come to layer 1, since they come from many nodes of layer 2, you have to sum all the gradient for updating the biases and weights in layer 1. This case is different from the sum of biases in layer 2.

## Which is the upper gradient for bias terms?

If i take partial derivative of loss with respect to bias it will give me upper gradient only which is dz2 because z2=h1.dot (theta2)+b2 h1 and theta will be 0 and b2 will be 1. So the upper term will be left. The bias term is very simple, which is why you often don’t see it calculated.

## Do you sum the gradient of the sigmoid function?

You must use the output of the sigmoid function for σ (x) not the gradient. You must sum the gradient for the bias as this gradient comes from many single inputs (the number of inputs = batch size). Thus, we must accumulate them to update the biases of layer 2.