Occam's razor as a thinking experiment, or model.

"A new Oxford University study reveals that deep neural networks (DNNs) naturally favor simpler solutions when learning, acting as an inbuilt form of Occam’s razor that balances the exponential growth of complex solutions. This simplicity bias allows DNNs to generalize well on real-world data but limits their performance on more complex patterns, hinting at deeper parallels between AI learning and natural evolutionary processes. Credit: SciTechDaily.com. (ScitechDaily, Scientists Discover AI’s Hidden “Occam’s Razor” for Simplified Solutions)

A couple of formulations of the Occam's razor. 

"This principle is sometimes phrased as Pluralitas non est ponenda sine necessitate ("Plurality should not be posited without necessity").In his Summa Totius Logicae,"

"To quote Isaac Newton, "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. " 

"Therefore, to the same natural effects we must, as far as possible, assign the same causes." In the sentence hypotheses non fingo, Newton affirms the success of this approach."

"Bertrand Russell offers a particular version of Occam's razor: "Whenever possible, substitute constructions out of known entities for inferences to unknown entities".

Quotes are from Wikipedia. (Wikipedia Occam's razor)

The origin of the Occam's razor is unknown. But Ptolemy once said: "We consider it a good principle to explain the phenomena by the simplest hypothesis possible." So here I don't write about the history of Occam's razor. I will write about principle that the Occam's razor represents. 

There are a couple of formulations about Occam's razor. There is an idea that the simplest solutions are the most common because complex solutions form through the simple solutions. Or the simple solution becomes before the complex solution. 

A simple solution must exist. So that it can intertwine with other simple solutions. So the complex solution requires more than one simple solution. And we can call solutions as models. So the complex model is the sum of simple models. That means there must be more than one simple model (or solution). That can form a complex model. (Or complex solution is the sum of simple solutions)

The Occam's razor is the thinking model. Where the thinker should select the simplest models if there are multiple offenders. The most usual models are the simplest models. And that means the AI should select the simplest model. Complicated models require more time and more structures to form. So everything begins from the simplest possible models. When we talk about Occam's razor and the principle that the simplest things are the most usual things we can make a model that if we choose the simplest model the probability that we hit the right point is more usual than if we choose complex models. 

That is one way to handle complex problems. And problems are systems. In the beginning is the simple model. Then that model collects layers on them. And those layers form complexity in the model. That is an important point in the thinking. The fact is that Occam's razor does not always give the right solution. That means sometimes the complex structure can be the right. But then we can think so simple things as the line. We can make lines that seem very complex. But if we look at those curves and loops we can see that even if that thing looks very complex. 

There is only one line that involves those things. If that line is woolen yarn that thing can form very complicated-looking structures. But if we have time we can clean up that mess and then use that woolen yarn. So everything that seems complex can turn simple if we think and try to fix that thing hard. Knots and curls don't make the woolen yarn useless. If we use little time and brains we can remove those knots and make the woolen yarn usable. Sometimes there is only one knot that holds very complicated curls. 

If we want to solve the problem we must know everything about that. If we lose pieces of the problem we cannot fix it in its entirety there we can solve it. When we think of woolen yarn and a razor. A thinker that we can call Occam can use the razor as a wire coil. This person uses a razor as the rack around which he wraps a woolen thread. So that means Occam's razor can be used as an example that there is always more than one possible use of the tools or subjects. 

And if we follow the woolen yarn from the end to begin, we can find the shape of that thing. Checking the answer for the calculations happens by calculating those things backward. So that means the mathematicians calculate all calculations using mirror calculations. When they check simple calculations for example 7+2=9 they can check that calculation by calculating 7=9-2 (or normally 9-2=7). That thing gives the second meaning for the Occam's razor. 

That means people must not use violence or destroy structures to find the key. If Occam uses a razor and cuts the woolen yarn in pieces, that means they turn carbage. There is no use for things that are cut into pieces. For making the woolen yarn people must have every part of it. And that things must be sorted into the right order if Occam wants to put possible colors in the woolen yarn into the original order. 

https://scitechdaily.com/scientists-discover-ais-hidden-occams-razor-for-simplified-solutions/

https://en.wikipedia.org/wiki/Occam%27s_razor