Tim Scarfe: disagreement

Transcript context

…going to take a list and delete half of its elements for no reason. Let's start with pathfinding. So we talk a lot about algorithms like Dijkstra or Bellman Ford inside a computer science curriculum. In short, those are algorithms that, starting with a directed weighted graph, predict what are the shortest paths lengths inside that graph. Right? Now, the thing is there are many, many different graphs with different weights that are going to have exactly the same shortest paths and potentially even the same shortest path lengths. However, those graphs are different. And once you've applied the transformations of Dijkstra's algorithm or Bellman Ford algorithm, you'll have lost the information that is contained about the graph in the final output of that algorithm, right? Because many different graphs will be compressed to exactly the same output, right? So this is not an operation I can describe using asymmetry. And then this journey gradually like, took me a while to realize how we can be formal about this, how can we try to put some theory on this, and even now down the line, how can we build some practical models using this. And I was fortunate enough to to start chatting with Andrew, who is my colleague at DeepMind, who has a category theory background. And he's been thinking himself about some of these problems in the past. So it was a great match because together with him, it was a long way. But we managed to gradually relax the constraints of what a group is giving us. We first looked at removing the invertibility part, which led us to monoids. And then we derived some interesting theory and asynchrony invariance in models using monoids. And now we're also looking into removing the second constraint of groups, which is the requirement that every single computation must compose with every other piece of computation. As you might also know in computer science, you cannot always do that. You must make the output of your first function match the input type of the second 1. Otherwise, they can't compose. So this now leads us to categories. And well, that's what led us now to categorical deep learning. Things like intentionality and planning and system 2 and reasoning and stuff like that, I think you're placing the assumption that there's something standard about that. Yeah. Exactly. I mean and to some extent, there is. Because for a lot of these algorithms, we have even proofs that they will arrive at optimal solutions if you give them enough time and put them in the right context. And I actually think it's going to it should be a synergy, right? Because as you said, with modern large scale deep learning systems, we actually stand the chance to map really complicated, noisy, real world scenarios into a space where those algorithms might become applicable. Right? Now, the main argument that maybe we are trying to make in some part here is that asking the model to both do that translation and robustly invoke the algorithm is likely a bit too much to ask because, among other things, you've said fixed computational budget. That's already 1 recipe for failure as inputs get larger because, as you know, for example, multiplication, as I mentioned, is an algorithm which is a is a problem for which we don't really have a super efficient algorithm yet. The best known 1 is n log n, and that 1 relies on, like, complicated number theoretic constructions, let's say. So most people know just the n squared quadratic algorithm for multiplication. So the amount of resources that you need to reliably multiply 2 numbers will grow, and sometimes super linearly, based on the size of those 2 numbers. And currently, our systems can cope with that implicitly if you add things like chain of thought, which gives the model more thinking time and so on. But fundamentally, all of those things are patches that might help for a particular class of problems but then fail somewhere else just because of the nature of how complicated the entire space of computational problems is. Right? So basically, I believe in a future where the neural network will deal with the understanding of the world, with the translation of what's happening in the world into some abstract space which might just be high dimensional embeddings, by the way. That's also plausible. And then there will be some component that we have baked into the system, either through priors or through very careful losses or even through combining systems with tools, which has already proved really, really useful, that will actually then execute execute that that computation in a way that we can reason about it. And I should stress, by the way, what I mean by reasoning is not 100% accuracy on every single input. Find that humans can reason, and humans are not 100% accurate on every single input you give to them. As you can see, if you ask me to multiply 2 numbers that are, like, 50 digits long, I will definitely make some failures if you ask me to do that. But, you know, the point is that, like, what I would like is that, a system understands the amount of effort that needs to go into doing some kind of computation and maybe at least to give me some either an estimate of how likely it is to make mistakes or some notion even some notion of, I'm sorry.…

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