How is shift Invariance achieved in ConvNets?

The convolutional layers are shift equivariant. If an input image is shifted a little bit, the convolutional filters will produce the same response at the shifted location. The pooling layers are approximately shift invariant. For example, if an input image is shifted a little bit under a max pooling layer, the maximum value will still be the same. Overall, given an input image x, a shift S, a shift equivariant convolutional layer f, and a shift invariant pooling layer g, the ConvNet g(f(x)) is shift invariant because g(f(Sx)) = g(Sf(x)) = g(f(x)). (see Note02)

Why do we include dropout in the network architecture ?

Dropout randomly removes connections between neurons in neural networks. It offers regularization through preventing the model from relying on all features, often termed co-adaption, helping reduce overfitting. In addition, Monte Carlo dropout can be used as a Bayesian approximation to estimate uncertainties in neural networks (see https://arxiv.org/abs/1506.02142).

Model Ensembling is:

Which of the following activation functions helps with the vanishing gradients problem?

Hyperbolic activation functions have gradients in the range of 0-1 with significant proportions of the activation function space yielding very low gradients. As backpropagtion involves the chain role, repeatedly calculating the product of partial derivatives, the gradients passed back become vanishingly small. This does not occur in ReLUs for example as the gradient is either 0 or 1.

True or False. Two 3x3 convolutional layers have the same receptive field as one 5x5 convolutional layer, results in more non linearities and requires less weights.

What causes vanishing gradients?

Vanishing gradients occur when the derivative of a function becomes very close to zero, meaning large changes in input (X) cause only small changes in output (Y). This is a problem as backpropagation is done by calculating the derivatives of the error with respect to the weights, so if the derivatives are very small, the parameters will barely change, and the error will remain.