Keith Duggar: evaluation

Transcript context

…No. Very good. It does several things. So first of all, and this is gonna be an increasing order of importance, the syntax of einsum in this language, there's also this package called inops, is incredibly clunky. So at a very basic level, tensor logic is just a much pithier, more compact, easier to write and understand way to write einsums. And you know, physics and mathematicians famously like to say that a good notation is half the battle. So this might not seem like a big deal, but my experience is that you can just think better and faster once you have this notation that like this funky procedure call with these indices and these arrows and these arguments. It's a nightmare and you know, the syntax of tensor logic is like you write a ninth sum like you would write a rule. There's a tensor equation with a tensor on the left hand side and and and and this join of tensors on on on on the on the right on the right hand side. Right? So this is 1 aspect. Another very important aspect and 1 that I think could prove decisive is that people don't use ions so much because it's not very efficient. Under the hood, it's not as efficient as you tip, you know, sometime I you know, this could be done so much better. Right? But I've done some of programming of this and I wound up even I wound up not using Einstein because it's so slow and clunky. And all of that can be fixed. Once you have this 1 abstraction of the tensor equation and you implement it on CUDA, for example, you can optimize the heck out of it and you'll just be able to, you know, Einstein will finally be able to reach its potential. Right? But actually none of these things actually the most important part. The most important part is that the the Einstein as we know it is only good for for for tensor algebra. Tensor logic is a language where the same construct does all the symbolic and all the the numeric parts and and any mix and variation between them including learning the symbolic part and whatnot. These are all things that in world just didn't exist. Right? You talk about the people in Einstein whether in AI or mathematics or physics and they just had no idea that any of this had anything to do with reasoning. You look at all the ways that people are trying to do reasoning today and just wanna pull out your hair. Let me ask a very concrete, you know, in some sense, I'm a simple simple man. I need, like, a very concrete example because I completely agree with you, which is that the symbols we use, the language we use are just simplicity is so fundamental to our ability to, like, reason at higher and higher levels. So let's take 1 example, you know, from your paper, which is a logical or logical or of a bunch of values is equivalent to an EIN sum within a Heaviside, you know, function applied to it. Like you give this example. Right? The or just to so to be precise, what I did in in, you know, maybe this is an important piece of context. So if you look at so the simplest form of logic programming is data log, right, which is the foundation of databases. Right? You know, most SQL queries have variations on on data log rules. And data log rules are composed of 2 things, joints and projections. Alright, this is like databases 101. And what I have done is I have generalized join and projection to numeric values. There's this thing which I defined called the tensor join and the tensor projection, which when the tensors are boolean becomes the regular symbolic database 1. But now the the the numeric version has all these things as special cases. And by the way, it's also more general than the EIN sum, right? So another benefit of this is that it actually goes goes beyond the EIN sum. Now, an or, right, the way you get an or is is is by having more Is is it just as in So how do you get an or in prologue or data log? Is by having, you know, multiple rules with the same head. And then those rules, and then they implicitly being disjoint. Alright? So if I have AFBC and AFDE, then that means AFBC or DE. And the same thing happens here. And you could also of course just put them all in the same equation because like you know it might be more convenient just to say like well a b plus c d. Right? So so doing a NOR is a completely you know straightforward thing, but it's really not where the main action is. It's in the tensor joints and tensor projections.…

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