Four words to keep separate

Four operations share one kernel and get confused constantly:

• Correlation — slide the kernel as written.
• Convolution — flip the kernel, then slide it.
• Transposed convolution — spread each input value through the kernel and add the overlaps.
• Deconvolution — try to recover an unknown original from a blurred observation.

The first two are forward filtering. Transposed convolution is an adjoint-style operator that changes shape. Deconvolution is an inverse problem. The notebook’s sentence to remember:

Convolution applies a structured forward operator; transposed convolution applies its shape-changing partner; deconvolution tries to solve the inverse problem.

And its shortest form: changing shape is not the same as recovering lost information.