This seems a bit cryptic. The way I understand hyperparamters, they define how a model learns, i.e. you can set an alpha in gradient descent. Now when you compare them to "ordinary" parameters, hyperparamters do not define relationship between data and output.
And you misunderstood my suggestion for the article as a request for your help. But thanks. I don’t doubt what you wrote is accurate and helpful in the same way that saying “a transom is a part of a building” is accurate and helpful.
Yes, both data and hyper-parameters are inputs to the algorithm.
I wasn't trying to offer anything more than a sketch of the terms for someone already semi-informed.
To "define" terms in a way that a person without any experience of the area could understand would require quite a long article.
My goal wasn't to answer you specifically but to take your observation as establishing a plausible interest in others for something like my comment.
Parameter: an aspect of the model, a dial which is fixed by data (eg., a)
Kernel (as used here): a subset of such parameters
Algorithm: procedure which accepts data and produces a model
Hyperparameter: an aspect of the algorithm, a dial which changes model production
Convolution: A convolution of image A and Filter B describes to what degree A is "like" B. Here "Filter B" is a kernel, ie., a parameter set learnt by the network.
The goal of a CNN is to produce a model whose parameters are image filters that describe the degree to which an images expresses various shapes. By learning the filters from an image set, the network is specialized to distinguish images in that set.