One is data driven based on evidence.
The other is logic driven based on axioms and the logical implications of said axioms.
My statement is derived from the later. Therefore evidence is unnecessary. It is niave to blindly faith in all truth in the hands of data without understanding nuances between the relationship of data and logic.
If you have a pure function that takes the input, the output of that function has 3 possible outcomes.
1. The output of that function is some transformation of the input.
2. The output of the function has nothing to do with the input and is thus generated randomly generated.
3. The output of the function is a combination of both random generation and input transformation.
In this case your brain is the function. Input parameters are 100 percent of your existing knowledge. That includes genetic knowledge such as instinctual/rational processing behaviors evolved into the structure of your brain through evolution and learned knowledge such as what you gain when you read a book.
The result of the "innovation" operation performed by the brain includes novel output by definition. Thus by logic it must be must include components that are from a certain perspective randomly generated.
I guess at first glance it doesn't appear randomly generated because we vet the output and verify it and iterate over several pieces of randomly generated information. Additionally it's not completely random as we only try and test ideas within the realm of possibility. For example I'm not going to account for the possibility that my car will transform into a rock tomorrow that's just too random.
But make no mistake. Innovation must be partly randomly generated. Even the idea itself of composing two existing components of knowledge together is itself randomly generated.
That being said if we want to be pedantic, there's no real known way to randomly generate stuff via an algorithm. So I use the term "randomly generate" very loosely. Think of it in a similar way to random number generation on your computer: Random from a practical perspective but not technically random.