Comment by megaloblasto
8 hours ago
I disagree. It's absolutely possible to develop an intuition about extremely complex mathematical ideas, including llms or high dimensional systems. Learning to build an llm is a great way to start building that intuition.
Developing an intuition about high dimensional systems is pretty different from understanding the character of some specific point on a 1e9+ dimensional manifold of parameters, in my professional opinion (setting aside all the degrees of freedom that come from the structure of the thing). Sure one can understand generic principles like the curse of dimensionality, but truly groking how an LLM works is basically an open problem as far as I'm aware. I'm not saying there's no benefit for amateurs to study how LLMs work, but let's be realistic about how far mere intuition can truly take anyone in this space.
Seems like a silly goalpost.
As you say, there's a lot of value to unlock with understanding the generic principles, and I would add specific application.
Lots of people are building fantastic Tools or pulling down million dollar salaries without groking the precise representation of a single weight.
What provable conclusions have you intuited around how LLMs work? Give me some examples to prove your point? I'm absolutely happy to change my view with enough data.
I think provable conclusions and building an intuition are different things to be fair. In my opinion it is entirely possible to build intuition about seemingly impossible to understand topics like infinitesimal areas, infinite limits, function mappings, and high dimensional spaces. For example, 3D spaces are easy to intuit if you can visualize vectors in your head. Some people claim it is impossible to understand dimensions higher than 3 but that's obviously not true because you could assign a color to each vector to visualize the next dimension. You could then assign a width to visualize a 5th dimension, and an arrow shape to signify the next, and so on and so on. That's more of a creative act that can start to build at least a visual understanding in you head of these higher dimension spaces. That's a way to start to intuit about those things.
Now with llms we need way more that 6 dimensions so we can start thinking of assigning matrices to each 3d point for example. That allows us to increase the dimension from 3 to 3 + whatever the matrix dimension is.
We can visualize the matrices instead of having numbers as having colors for each entry, so they can be a sort of cube with each vowel being a different color.
Now you can start to visually intuit about how these massively high dimensional spaces can be formed of these colored matrices that can react to some input training data.
That's a start of an idea for intuiting things that might seem impossible to have an intuition about. I think visualization is a great way to start.
i read all that i still dont see what your intuition is about how llm work.
visualizign 100 dim matrix will not tell you how llm work. so what you even talking about.
1 reply →
I'm not looking to change your view. But for other readers who are curious, here is a link to an interesting task to gain intuition. Ahmad is a good data point for someone who tinkered, built intuition, then started his own ai company. https://twitter.com/TheAhmadOsman/status/2087742080793620593...
I think we are talking about different things to be honest. Understanding LLMs is a fine thing to do but to say you understand what the network is actually doing, even in toy examples like MNIST is extremely tricky. Figuring out what a ~3 trillion parameter network is doing in thousands of dimensions seems intractable to me.
Linking to a Twitter thread about training a small LLM to be good at Wordle is not an example of what I'm talking about. It might well be a useful task but it doesn't allow us to understand deeply what's happening.