What is the importance of the translational invariance of the CWT?

1. Why is convolution translation invariant?
2. What does the term translational invariance imply?
3. What is the purpose of continuous wavelet transform?
4. What is translational invariance convolution with learned kernels?

Why is convolution 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 does the term translational invariance imply?

Translational invariance implies that, at least in one direction, the object is infinite: for any given point p, the set of points with the same properties due to the translational symmetry form the infinite discrete set p + na | n ∈ Z = p + Z a.

What is the purpose of continuous wavelet transform?

The continuous wavelet transform (CWT) has played a key role in the analysis of time-frequency information in many different fields of science and engineering. It builds on the classical short-time Fourier transform but allows for variable time-frequency resolution.

What is translational invariance convolution with learned kernels?

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.