Dan Fu: prediction

Transcript context

…st time compute and you want to spend a bunch of tokens thinking about what comes next, the longer that that goes the, the, the more tokens you spend on that, that compute grows quadratically in that. One of the questions that we're interested in is, can we take that basic sequence model, that basic sequence primitive at the bottom, and get it to scale better? Can we scale in, let's say, n to the 3 halves or n log n? So in, in the first part of the talk, so we just went over the introduction. What I'm gonna do over the next few slides is just talk about some of the key advances and ideas that have shown over the past few years since maybe early 2020 to, to now that shown promise that this might actually be possible. That you can actually get potentially the same quality that we want while scale, while scaling better. So to do that, we're and, and basically the, the story that we're gonna look is we're gonna start to see [00:06:00] how. So this is a basic graph of just the past couple years of progress of perplexity where that blue line, that dotted blue line, is attention. It's your basic transformer, full dense attention. And then the dots coming down are some of the methods that you'll see in this presentation today. We're going to turn the clock back all the way to 2020. So this, this, this question of can we make attention subquadratic? Basically, as soon as we said attention is all you need, People started asking this question. So we have this quadratic attention operator. Can we do better? I'll briefly talk about why attention is quadratic. And the basic thing that happens, if you're not familiar, is that you have these inputs, these keys and queries. And what you do in this attention matrix, this S matrix over here, is that you're using, you're comparing every token in your input to every other token. So when I try to do something like upload a whole book to Gemini, what happens beyond the Maybe not Gemini, because we don't necessarily know what architecture is. But let's say we upload it to LLAMA, what happens beyond [00:07:00] the scenes, behind the scenes, is that it's going to take every single word in that book and compare it to every other word. And this has been a really, it's, it's led to some pretty impressive things. But it's kind of a brute forcing of the way that you would try to interpret a interpret something. And what attention does in particular is the, and then what attention, sorry, don't want to. Okay, no, no laser pointer. What, what attention does afterwards is that instead of always operating in this quadratic thing, it takes a row wise softmax over this matrix, and then multiplies it by this values matrix. So, one of the key points to notice is that the output size is always going to be the same as the inputs, at least in standard self attention. So one of the first things that folks tried to do around 2020 is this thing called linear attention, which is just, just noticing that if we take out this softmax from here, if we take out this non linearity in the middle of the attention operation, and then if you compute the keys and the values operation first, you actually never hit this quadratic bottleneck. rom here, if we take out this non linearity in the middle of the attention operation, and then if you compute the keys and the values operation first, you actually never hit this quadratic bottleneck. So that, that's potentially a way [00:08:00] to get a lot more computationally efficient. And there are various ways to do this by basically using feature maps or try to approximate this overall attention computation. But some of this work sort of started to hit a wall in 2020. And the basic challenges were, were two. So one was quality. It was back then, it was kind of hard to, to get good quality with these linear attention operators. The other one was actually hardware efficiency. So these, this feature map that was just shown by a simplify simplify here. Actually ends up being quite computationally expensive if you just implement it naively. So you started having these operators that not only were you sure, you're not really sure if they have the same quality, but also they're actually just wall clock slower. So you kind of end up getting the worst of both worlds. So this was the the stage. So that kind of sets the stage for four years ago. Keep this in mind because linear attention is actually going to come back in a few years once we have a better understanding. But one of the works that started kicking off this, this [00:09:00] mini revolution in post transformer architectures was this idea called states based model. So here the seminal work is, is one about our work queue in 2022. And this, this piece of work really brought together a few ideas from, from some long running research research lines of work. The first one was, and this is really one of the keys to, to closing the gap in quality was just using things that, that if you talk to a, a, an electrical engineer off the street, they might know off, off the, like the back of their hand. But taking some of those properties with how we model dynamical systems in signal processing and then using those ideas to model the inputs, the, the text tokens in, for example a transformer like Next Token Prediction Architecture. So some of those early states-based model papers were looking at this relatively, relatively simple recurrent update model that comes from maybe chapter one of a signal processing class. But then using [00:10:00] some principle theory about how you should do that recurrent update in order to really get the most that you can out of your hidden state, out of your out of your sequence. So that, that was one key idea for quality and. When this was eventually realized, you started to see a bunch of benchmarks that were pretty sticky for a few years. Things like long range arena, some long sequence evaluation benchmarks, There was stuff in time series, time series analysis. They started to, you started to see the quality tick up in meaningful ways. But the other key thing that What's so influential about these states based models is that they also had a key idea about how you can compute these things efficiently. lity tick up in meaningful ways. But the other key thing that What's so influential about these states based models is that they also had a key idea about how you can compute these things efficiently. So if you go back to your machine learning 101 class where you learned about RNNs, one thing that you may have learned is that they don't paralyze as well as detention, because if you just run them naively, you have to do this kind of sequential update to process new tokens, [00:11:00] whereas in attention, you can process all the tokens in parallel at one time. One of the key insights behind the S4 paper was that these recurrent models, you could take them and you could also formulate them as a convolution. And in particular, with a convolution, you could, instead of using a PyTorch conv1d operation, you can compute that with the FFT. And that would give you n log n compute in the in the sequence length n with an operator that was relatively well optimized for modern hardware. So those are really, I'd say, the two key ideas in 2022 that started allowing these breakthroughs to happen in these non transformer architectures. So, these ideas about how to principally model sorry, how to model the recurrent updates of a mo of, of a sequence in a principled way, and also these key ideas in how you can compute it efficiently by turning it into a convolution and then scaling it up with the FFT. Along those same lines, so afterwards we started putting out some work on specialized kernels, so just [00:12:00] like we have flash attention for transformers, we also have works like flash fft conf, and if you look at these lines of work oftentimes when, whenever you see a new architecture, you see a new primitive one of the, one of the table stakes now is, do you have an efficient kernel so that you can actually get wall clock speed up? So by 2022, We are starting to have these models that had promising quality primitives, but and, and also promising wall clocks. So you could actually see regimes where they were better than transformers in meaningful ways. That being said, there were, there's still sometimes a quality gap, particularly for language modeling. And because languages, It's so core to what we do in sequence modeling these days the, the next, the next key idea that I'm going to talk about is this idea of selection mechanisms. And this is basically an idea of, so you have this recurrent state that you're keeping around that just summarizes everything that, that came before. And to get a good sequence model, one of the things that you really need to be able to do is have the model learn what's the best way to pick out pieces from that recurrent [00:13:00] state. So one of the, one of the major ideas here in a line of work called H3, Hungry Hungry Hippos, and also these hyena models were One way you can do this is by just adding some simple element wise gates.…

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