## Why are convolutional neural networks translation invariant?

There are multiple hypotheses regarding the source of translation invariance in CNNs. One idea is that translation invariance is due to the increasing receptive field size of neurons in successive convolution layers. Another possibility is that invariance is due to the pooling operation.

**What is invariant translation?**

Translation invariance means that the system produces exactly the same response, regardless of how its input is shifted.

### Is deep neural network translation invariant?

It is commonly believed that Convolutional Neural Networks (CNNs) are architecturally invariant to translation thanks to the convolution and/or pooling operations they are endowed with. In fact, several works have found that these networks systematically fail to recognise new objects on untrained locations.

**What is Equivariance and invariance?**

The equivariance allows the network to generalise edge, texture, shape detection in different locations. The invariance allows precise location of the detected features to matter less. These are two complementary types of generalisation for many image processing tasks.

## Why is CNN invariance?

Translational Invariance makes the CNN invariant to translation. Invariance to translation means that if we translate the inputs the CNN will still be able to detect the class to which the input belongs. Translational Invariance is a result of the pooling operation.

**Are CNN shifts invariant?**

Modern convolutional networks are not shift-invariant, as small input shifts or translations can cause drastic changes in the output.

### Is CNN invariant or equivariant?

The Convolution Operator is Translation Equivariant meaning it preserves Translations however the CNN processing allows for Translation Invariance which is achieved by means of a proper (i.e. related to spatial features) dimensionality reduction.

**Is CNN rotation invariant?**

Unless your training data includes digits that are rotated across the full 360-degree spectrum, your CNN is not truly rotation invariant.

## Why is CNN shift invariant?

We can achieve one of the most important features of CNNs, Shift Invariant, due to the parameter sharing of convolutional layers and a partial effect from pooling layers. It means that when the input shifts the output also shifts but stays otherwise unchanged.

**How do you know if a system is invariant shift?**

Shift-invariance: this means that if we shift the input in time (or shift the entries in a vector) then the output is shifted by the same amount. Mathematically, we can say that if f(x(t)) = y(t), shift invariance means that f(x(t + ⌧)) = y(t + ⌧).

### Is CNN invariant to translation?

**Why is CNN not scale invariant?**

Again, these filters themselves are not rotation invariant — it’s just that the CNN has learned what a “9” looks like under small rotations that exist in the training set. Unless your training data includes digits that are rotated across the full 360-degree spectrum, your CNN is not truly rotation invariant.