Gaussian function

He also addresses practical concerns, like false positives and fitting strategies.

Traditional fitting methods are slow and depend on Gaussian assumptions.

By mapping hits directly to parameters, Whiteson says the new approach can be far faster, more flexible, and better suited to both discovery and precision measurement.

It's a genuinely different way of looking at the problem.

If you want to abstract even one step up and be like, I just want to film people in it and direct, this is a great...

I don't know if Gaussian splats the word anymore.

Who knows? Being able to actually go in

there and direct it is great.

And then the different angles, stopping the time, all of this stuff is done because they used Atlas to...

To regenerate all of the different frames and angles.

One thing, it's not creating Gaussians, right? I think it's creating

points.

What's IID?

The short answer to your question is Gaussianity.

Sorry, can you clarify IID?

Oh, sorry.

Good.

So there's, there's a few ways.

Uh, typically, you, you ty- you stare at the theorem that tells you that at large N, this th- thing becomes Gaussian, which was known, um, years ago, even in, in Neel's PhD thesis, and you violate one of those assumptions that guarantees g- guarantees Gaussianity.

So there's essentially three ways that you can do this.

If that one does not hold, my next mark is going to be on the daily chart.

Huge order block down here around 916, around that daily Gaussian band.

I'm not convinced we get all the way down there, but that is the next big, big order block.

So do you see a flash crash on link in a bear trend? I would be scooping up a lot of link around that nine 15 mark.

It's a breaker block, which means it was an order block.

I think you're looking back.

between $2,100 to $2,000 back towards that 200-day moving average slash daily Gaussian band for your bigger pullback.

If we slash through this level, then you're looking for an oversold daily buy signal.

But when you have repeating stuff in time, pi comes in there too.

Now, why does the pi come into the Gaussian distribution? you know, the normal distribution for like, if I want to calculate the area under the Gaussian, to normalize it to have area one, I'm going to have some square roots of two pi in the formula.

Well, that's because to calculate that area, you use the symmetry properties of the Gaussian.

So the Gaussian is this bell, and it's very hard to calculate the area under the bell.

But if you rotate the bell in two dimensions to make something that really looks like a bell, a two-dimensional surface of a bell, then the math becomes much more beautiful because instead of just having bilateral symmetry of the bell curve, you have rotational symmetry of a bell surface.

And you can do that integral in polar coordinates.

Why is that happening? It's sort of because, it's interesting to think about.

I mean, the two pi is very much related to a trick about two dimensions.

But practically speaking, doesn't MPPI just collapse back down to a weighted average once you actually run it? Sample some sequences, score them, average them.

That sounds a lot like optimization again, just dressed up with a different vocabulary in a Gaussian instead of a gradient step.

At the moment of action, sure, you often collapse to the mean, but the derivation matters.

We'll build it next.

Short version.

The optimal control distribution is a Boltzmann term weighted by a temperature lambda, controlling how sharply it favors low-cost trajectories times a prior over controls.

Variational inference is what turns that into something computable by fitting a tractable distribution, like a Gaussian, to approximate it.

MPPI is Honda's representative example.

I can write down a law called Fick's law, which tells me how to relate flux to the gradient in the concentration.

I will get a partial differential equation called the diffusion equation, and when I solve it, I will get a Gaussian.

And so that's a deterministic, like there is no lack of determinism there.

You tell me an initial condition, I will tell you what happens all the way to infinity.

Now, what's amazing is if I average over those molecules that are hopping around, like let's say that I do it a thousand times, and you can do this in your class, and probably you do.

You know, like you flip coins, you get a bunch of random walkers.

You add up and average all their trajectories, and guess what? It's a Gaussian.

So I'm not super excited about the dichotomy between these things, and let me give you a second example, which is mRNA and its production.