This doesn't strike directly at the sampling question, but it is related to several of your ideas about incorporating the differentiable function: Neural Ordinary Differential Equations.
This is being exploited most heavily in the Julia community. The broader pitch is that they have formalized the relationship between differential equations and neural networks. This allows things like:
The last one is the most intriguing to me, mostly because it solves the problem of machine learning models having to start from scratch even in environments where information about the environment's structure is known. For example, you can provide it with Maxwell's Equations and then it "knows" electromagnetism.
There is a blog post about the paper and using it with the DifferentialEquations.jl and Flux.jl libraries. There is also a good talk by Christopher Rackauckas about the approach.
It is mostly about using ML in the physical sciences, which seems to be going by the name Scientific ML now.
Strong upvote, this is amazing to me. On the post:
Some thoughts on the results:
I claim that 1939 Germany would not be able to conquer western Europe. There are two reasons for this: first, 1939 Germany did not have reserves in fuel, munitions, or other key industrial inputs to complete the conquest when they began (even allowing for the technical disparities); second, the industrial base of 1910 Europe wasn't able to provide the volume or quality of inputs (particularly fuel and steel) needed to keep the warmachine running. Europe would fall as fast as 1939 German tanks arrived - but I expect those tanks to literally run out of gas. Of course if I am wrong about either of those two core arguments I would have to update.
I am not sure what lessons to draw about the AGI scenario in particular either; mostly I am making the case for extreme caution in the assumptions we make for modelling the problem. The Afghanistan example shows that capability and goals can't be disentangled the way we usually assume. Another particularly common one is the perfect information assumption. As an example, my current expectation in a slow takeoff scenario is multiple AGIs which each have Decisive Strategic Advantage windows at different times but do not execute it for uncertainty reasons. Strictly speaking, I don't see any reason why two different entities could not have Decisive Strategic Advantage simultaneously, in the same way the United States and Soviet Union both had extinction-grade nuclear arsenals.
I broadly agree that Decisive Strategic Advantage is still plausible under a slow takeoff scenario. That being said:
Objection to Claim 1A: transporting 1939 Germany back in time to 1910 is likely to cause a sudden and near-total collapse of their warmaking ability because 1910 lacked the international trade and logistical infrastructure upon which 1939 Germany relied. Consider the Blockade of Germany, and that Czarist Russia would not be able to provide the same trade goods as the Soviet Union did until 1941 (nor could they be invaded for them, like 1941-1945). In general I expect this objection to hold for any industrialized country or other entity.
The intuition I am pointing to with this objection is that strategic advantage, including Decisive Strategic Advantage, is fully contextual; what appear to be reasonable simplifying assumptions are really deep changes to the nature of the thing being discussed.
To reinforce this, consider that the US invasion of Afghanistan is a very close approximation of the 30 year gap you propose. At the time the invasion began, the major source of serious weapons in the country was the Soviet-Afghan War which ended in 1989, being either provided by the US covert alliance or captured from the Soviets. You would expect at least local strategic advantage vis-a-vis Afghanistan. Despite this, and despite the otherwise overwhelming disparities between the US and Afghanistan, the invasion was a political defeat for the US.
It was not until reading this that I really understood that I am in the habit of reasoning about myself as just a part of the environment.