Does Max-pooling translate Equivariant?

What the max-pooling layers do is provide some translation invariance as @Matt points out. That is to say, the equivariance in the feature maps combined with max-pooling layer function leads to translation invariance in the output layer (softmax) of the network.

Are convolutions Equivariant?

How about translation invariance? While convolutions are translation equivariant and not invariant, an approximative translation invariance can be achieved in neural networks by combining convolutions with spatial pooling operators.

Are convolutional layers rotation invariant?

Deep Convolutional Neural Networks (CNNs) are empirically known to be invariant to moderate translation but not to rotation in image classification. This paper proposes a deep CNN model, called CyCNN, which exploits polar mapping of input images to convert rotation to translation.

What is translation Equivariant?

Equivariant translation means that a translation of input features results in an equivalent translation of outputs. This is desirable when we need to find the pattern rectangle. Invariant translation means that a translation of input does not change the outputs at all.

What is rotation equivariant?

At a high level a rotation equivariant neural network produces features that undergo a rotation in feature space given a rotation of the input. The key point is that this trans- form only depends on the rotation applied to the input.

What is equivariant representation?

In mathematics, equivariance is a form of symmetry for functions from one space with symmetry to another (such as symmetric spaces). A function is said to be an equivariant map when its domain and codomain are acted on by the same symmetry group, and when the function commutes with the action of the group.

What are pooling layers?

Pooling layers are used to reduce the dimensions of the feature maps. Thus, it reduces the number of parameters to learn and the amount of computation performed in the network. The pooling layer summarises the features present in a region of the feature map generated by a convolution layer.