If it's trivially false then you should be able to present a counter-example but so far no one has done that but there has been a lot of hand-waving about "trivialities" of one sort or another.

Neural networks are stateless, the output only depends on the current input so the Markov property is trivially/vacuously true. The reason for the uniform random number for sampling from the CDF¹ is b/c if you have the cumulative distribution function of a probability density then you can sample from the distribution by using a uniformly distributed RNG.

¹https://stackoverflow.com/questions/60559616/how-to-sample-f...

You want me to show that it is trivially false that all Neural Networks are not Markov Chains? I mean we could point to a RNN which doesn't have the Markov Property. I mean another trivial case is when the rows do not sum to 1. I mean the internal states of neural networks are not required to be probability distributions. In fact, this isn't a requirement anywhere in a neural network. So whatever you want to call the transition matrix you're going to have issues.

Or the inverse of this? That all Markov Chains are Neural Networks? Sure. Well sure, here's my transition matrix [1].

I'm quite positive an LLM would be able to give you more examples.

  > the output only depends on the current input so the Markov property is trivially/vacuously true.

  > The reason for the uniform random number