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Welcome back to another episode of decoded.
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Today, I'm back with Wa C visiting partner Francois Chopard to talk about one of the most interesting recent trends in AI research, recursion.
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Specifically, we're going to talk about how we can improve a model's reasoning performance by using recursion at inference time, [music] rather than by just making the model bigger and bigger.
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There were two papers that made the power of this approach really clear in 2025.
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One on hierarchical reasoning models or HRM, and another on tiny recursive models, TRM.
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>> [music] >> Francois, thanks for joining us.
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Um, can you tell us a little bit about these two models and what was so interesting about them? >> Sure.
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I guess, um, to set up a little bit of a foundation, uh, you already did an amazing lecture on RNNs and LMs in one of the previous videos, so I won't overdo it, but just to give the cliff notes, um, an RNN is just a model that you, uh, recursively call again and again and again, um, on itself.
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And we were very much in the belief that this was required to get to AGI.
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Um, peak RNN use was probably until 2016 with Alex Graves, um, NeurIPS keynote which is just fantastic, and all his his his his adaptive compute time work.
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>> So, this is about 10 years ago people were working on these models.
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This was in the era of LSTMs and LSTMs with attention.
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>> Yeah, and, uh, depending which professors you talked to, uh, before attention was invented. >> Yes. Yes, totally.
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>> [laughter] >> Um, and, uh, and I think what really was the the the limiting step on, uh, RNNs in general was a thing called backprop through time, where you have to you roll out the model, and then to update the weights you need to approximate the gradient and you step back back back and you keep rolling out.
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And as the the model, um, gets, uh, bigger and bigger, and as you roll out for more and more steps, then you have all these, uh, accumulation of errors and the gradient gets noisier and noisier, and then it could just kind of stop to work.
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>> you have these like vanishing or exploding gradient problems.
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And it's because if you have an input with 20 steps, you're like multiplying these matrices 20 times, and that causes >> And we're talking about getting context length of like a million or like a billion.
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And so like it's not even just 20, it's like a billion.
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And even worse, you have to retain the activations at every single step.
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And so like if this were happening in your brain, you would need like a million copies of your brain at every single activation so that I can backprop through it.
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>> There's tricks around this that you can you can do and you can do a gradient checkpointing and things like that to reduce that issue, but then you're just like trading off memory for wall clock time and and compute. Right.
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So now if you contrast that with LLMs, the ones that people are widely using, these while at face value they appear to be similar, at training time they're doing basically this one one-shot feedforward process for every input, right?
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The The LLM, the transformer block can take all of the inputs in parallel.
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It's not actually iteratively going over them one at a time at train time, so you don't have this needing to store tons of activations problem or this giant vanishing gradients problem. >> Yeah, exactly.
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Like it it's actually like all happening in time in one shot, magically.
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And that was like the the tril or lower triangle trick that kind of happens, this causal mask that occurs.
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And so you actually do all all time steps in one shot, and you forward pass a feedforward model on all time steps in one shot, and you backwards in one shot, and it's amazing for train time in terms of like wall clock.
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It requires a lot of flops, and it still requires a lot of the memory.
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You still need it there, but you don't have the vanishing gradient issue.
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And what you actually paid for that you have to give up is this latent reasoning thing and this compression [snorts] in the time direction.
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There is no compression in LLMs.
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Every single decode that I do, I still have to retain the entire, you know, Shakespeare novel just to like decode a little bit.
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And in RNNs, you don't have to do that.
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It's all compressed in this hidden state that you kind of roll out.
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>> Wait, so so let's talk about that in a little bit more detail.
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Like you you refer to this um inherent reasoning ability.
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You know, many people think about LLMs as doing reasoning, and we're going to talk about that a little bit later.
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But, help me understand where you see the biggest limitations in LLMs reasoning ability or is in terms of what the model does in an actual forward pass? >> Yeah.
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And so, um I guess we go back to chat GPT-2.
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GPT-2 was this uh landmark uh uh architecture and paper that um basically was just get next token next token next token, and it kind of worked.
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And like, we just watched val loss go down, perplexity goes down, like the model just is more performant, looks better, starts to make some Shakespeare that actually sounds somewhat plausible. >> Right.
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>> And then we have to get these things to reason and to actually solve some really hard problems.
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And um and I've done extensive experiments on this, but like if you take uh for example, sort.
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You get you have infinite amounts of unsorted lists, and you give it sorted lists.
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You keep feeding it to the model. It should work, right?
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Um it's actually impossible for the model to map from unsorted list to sorted list.
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If I have >> In a one-shot, basically >> In a one-shot basis.
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It's like it's like literally that we know a theoretical lower bound that um for uh comparison sort, you can't do better than n log n uh steps.
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And if I have a list that's 31 uh uh uh uh characters or elements long, and my transformer is 30, I run out of steps to do comparisons.
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It's not possible for me to like do all the steps that is needed to be done.
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Um in HRM and TRM, they use uh Sudoku as an incompressible problem.
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Similarly, and so are mazes, those are incompressible problems.
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Rolling sum, incompressible problem.
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>> So, when you mentioned the sorting algorithm, when I think back to my algorithms class from college, the one way you could get faster than n log n in a sorting algorithm is if you had some access to an external memory cache.
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If you had some tape you could write to, then you can actually do faster than n log n by basically selectively putting things onto this memory.
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And I suspect that's, you know, a key limitation of these LLMs in that because there's no external memory tape inbuilt into the model, you lose certain performance possibilities in terms of how fast you can go. >> That's right.
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And so, I guess like it it radix sort would be like the most common one.
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You had like you you depending on on this the number of buckets that you have, you can kind of get from n log n to order n.
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You can't get less than n.
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You have to touch all the the elements.
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You're Sorry, you have to do that.
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And if you run out of uh um layers in in transformer layers in your uh neural network, then you ran out of chances to do that.
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>> Yeah, so this is just like a turn This is like going back to like Al- Alan Turing now and like a Turing machine, right?
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Like what's So, what's the analogy there exactly that we should think about in terms of LLMs I guess not quite satisfying how you think about a Turing machine.
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>> Yeah, so if we let's just talk about like chat GPT-2 GPT-2 the the original like no bells and whistles.
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Um it's just a feedforward model.
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And so, it's just forward passing one step.
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And to Taking an input, creating a bunch of outputs. >> Mhm.
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And the Sudoku case, um if I have uh 50 different uh sequential steps.
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And it's provable that I can only do one given this information, then and I have this many layers, then that's all I can do.
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And the cheat this the cheat is that the chain of thought.
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And so, it's completely true that at test time, they are uh Turing complete and you can simulate all Turing computable functions at test time.
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But how do you get it to learn it? You need to train it.
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And that's where uh unless you're training it on human labeled uh uh traces, uh for which there's a lot of problems like the millennial prize problem.
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We don't have the trace for it. >> Right.
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>> [laughter] >> So, we'd love to have the trace for it. Does it exist? >> Totally. Makes sense.
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Okay, so with that context in mind now, let's talk about these two papers cuz I think that sets up a lot of the the the contrast we're going to draw between these papers and the models that people are maybe more used to.
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So, let's talk about HRMs first.
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Um walk me through a little bit about how this model works and some of the intuition behind it. >> Sure.
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So, um the the the This is directly in the lineage of RNNs.
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There's not that much novel from like the RNN standpoint, uh at least in my opinion.
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They do have this idea of uh you know, from a inspired by the brain where I have like um there's different parts of of the brain that operate on different frequencies.
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There's some that that operate at really high frequency, which is then the low level of the hierarchy, some that operate in a really uh a low frequency, which is the higher level of the hierarchy, and the interplay between those things is really interesting.
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>> So, this is like literally in the human brain there's some like bio inspiration here, which is that like you have like different waves running at different frequencies at different parts of the brain or something like that. Cool.
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>> And um and I guess that interpret That's one interpretation of it uh of the way that they they're talking about um you know, classifying these these hierarchies uh of frequencies, and the way the most interesting part, at least for me, is the way that they train the neural network.
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You take in some X, some input, um whether it's a incomplete Sudoku puzzle, uh a maze, or an Arc Prize challenge, um you uh do TL steps with the L the the lower level uh module, then you do go to go to H, you do that um TH times, and then you have uh N sub outer refinement steps. >> Yeah.
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So, you basically are like running through the input with a given uh matrix with with a given transformation repeatedly on it, and you're doing that through two levels of refinement, and then basically running that process several times. >> Yes.
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So, there's exactly three levels of recursion occurring here.
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There's the low level, there's the high level, and then there's the outer refinement steps.
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>> And we're calling it recursion cuz it's the same weights that are being applied repeatedly.
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We're not changing the weights in between these steps. >> Exactly right.
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You get to recurse on on the L net uh L TL times, you recurse on the TH and the TL this looped recursion TH times, and then you do n sub you do this whole outer refinement step n sub times. >> Cool.
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And so, what's the basic intuition for why that works?
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Like why does that produce an effective paper result?
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And what even were the results that this paper showed? >> Yeah.
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And so, I mean this got state of the art on art prize one and two.
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This is a only a 27 million million parameter model that was only trained on art prize.
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>> So, it's like a thousand puzzles or something like that. Like puzzles basically.
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>> a thousand tasks which is extremely small.
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There is no pre-training at all.
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This is starts from like literally tabular rasa weights and it can outperform at that time.
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If we go back, you know, we had 03 if you remember back way back when.
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[laughter] And it and it 03 gets zero.
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Literally zero and this got like something like 70% on art prize one at least.
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At the time which was just a huge breakthrough.
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And so, kind of the the way you can kind of think this is like variable scoping.
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And so, like if I have like you know, three nested functions, I guess the first the lowest level function has like scoped variables which they'll call zl which is the carry that inits to zero.
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>> A latent variable basically.
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>> and and like traditional RNN literature they would call this the hidden state.
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The low level hidden state.
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And I get to recurse recurse recurse and then I pass back that zl back to the the outer scoped function, the higher level one.
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I let that one do one iter.
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It goes back and calls the lower level again.
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It does this whole thing in a third outer loop which is called the outer refinement step.
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>> Okay, but when you describe it like that, it seems like it would have the same backprop through time problem that you would have with RNNs.
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And I think they came up with clever trick to basically get around that.
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So, like what was that trick that they figured out?
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>> And this is really the the crux of the paper that like differentiates it in my opinion in the literature is they instead of doing what Alex Graves did in all of his papers from Neural Turing Machines to adaptive compute time to a differential neural computers is he always back propped through all of the recursion steps.
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And he was limited by back prop through time so he could only make the model so big.
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You have all these issues, vanishing gradients, etc. etc.
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And what they do is they they kind of have this DEQ method of doing fixed point iteration.
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It feels like deep equilibrium.
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>> Yeah, deep equilibrium.
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>> equilibrium learning where if I take a batch and this is this is completely counterintuitive as a computer vision person cuz you'd never do this, but it actually does make sense and I'll explain why.
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If I take a batch of like ImageNet or CIFAR-10 and I forward pass through the model and I get some loss and I back prop and I update the weights.
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I would go get a different batch for the next one.
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But what they do instead is they actually do that 16 times.
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And so and as you do that you actually can see the change in your residuals get less and less and less.
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And why it actually makes sense is because when in the RNN case the ZL and the ZH which are the carry the task carry >> The hidden states.
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>> The hidden states start out at zeros.
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Those are zeros, then we go through this whole loopy recursion three the the the at least the two loops the two lower loops T the the TL and TH steps and then I back prop just through the two modules just once and I don't recurse all the way back. I do a stop grad. I stop right there.
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And then there's a huge residual and then I don't reset ZL and ZH.
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I do it again at a different point in the carry or hidden variable space space.
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And so you one can actually look at it as like a different batch every time even though it's the same exact X's.
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>> Yeah, like the way I kind of think about it is like the the 16 or whatever that you're re- recursing over it's like constructing a mini batch not from different inputs but from like different memory states basically.
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It's like across this um hidden or carry memory access basically.
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>> And and that math holds and it works.
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It follows DEQ directly in the event that the ZL and the the delta and ZL and the delta and ZH go to zero. >> Mhm.
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>> Which it actually does doesn't do.
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And so we'll get to TRM but Alexia basically shows that it's just not the case and you can't actually apply this math.
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Um and that's ex- it it it why it's working that's not sufficient support for why it's working.
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We actually don't know why it's really working.
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Um and she figures out that you actually uh can uh backprop through all the way to the deep recursion which we're going to get into TRM in a second.
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Um and that actually improves performance much much more. >> Interesting.
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Okay, so before we get into TRM yeah on you know on this paper, you know, I think there's a bunch of different ways people have looked at this, right?
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In terms of how they came up with it and then why this may or may not be working.
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One is the sort of bioplausibility argument.
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Now as you know, I'm usually not super keen on these.
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You know, I think uh machine learning tends to have a long history of people starting with bioplausible arguments and then realizing that there's some variant of them that seems highly bio implausible that actually works better.
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I think you have example of lots of that sort of thing.
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>> classic the first deep deep learning paper that started this whole um craziness is AlexNet and and in AlexNet there's actually this funny little thing called like local receptive activation or depression or something like that where like once this uh activation fires then like I have this like, you know, a refractory thing region or something like that.
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It actually doesn't work at all.
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And like it didn't work and you didn't need that and then VGG came out and said get rid of all that, just go deeper and 3 by 3 conv and it actually just like outperforms dramatically. >> Right.
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>> And so like this is like always the Maybe you need to do it to get accepted into NeurIPS and stuff like >> Yeah, sure. Totally. Totally, yeah.
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>> You're definitely the expert here but what do you consider to be bio plausible and what's not?
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>> Well, I think that a lot of machine learning literature has overlapped a lot with people working in neuroscience.
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And I think it is very natural for us to ask questions about how does our brain work cuz our brain is like an incredible instrument that does a ton of computing, obviously, and does it in a very shockingly efficient manner, it seems like.
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And so, a lot of machine learning research has for a long time sought analogue from how we think to understand our brain to work and try to encode that in various machine learning systems.
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So, from the very basic concept of what a neural network is, it's called a neural network cuz we think it's some basic model for what a neuron is, how certain activation functions work are meant to be inspired by certain biological premises. >> theme?
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>> The thing about them is that often we use bio plausibility to inspire us to come up with ideas, but we end up veering away from the bio plausible to something adjacent to them that is likely bio implausible, but that seems to work better.
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>> So, it runs better on a GPU. >> Exactly.
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It runs better on a GPU, it's more efficient in some capacity that is relevant to how we actually encode it in a computational system.
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So, I find thinking about bio plausibility fun and interesting and it's definitely a great way to inspire us to think about new things, but I tend to not be bounded by bio plausibility as when I think about what machine learning systems we should prioritize working on or think are particularly exciting other than as, you know, an interesting scientific launching point for a deeper exploration.
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I think the the version of this that I find more compelling is actually that original discussion we were having around automata theory, basically.
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And and honestly, just actually like fundamental data structures and algorithms theory, which is that if you're running a complex algorithm, having access to sort of a memory cache is actually very useful for being able to run that algorithm efficiently.
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And I kind of think of this set of hidden states or carry as akin to a Turing machine tape or akin to the radix sort memory bank, where you can basically train a model to use this memory cache in an intelligent way in a single forward pass so that you can get a more efficient time operation that would otherwise require some sort of more complicated reasoning.
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>> Yeah, I think that a point I wanted to make earlier is that like we did this COT stuff and this tool use thing as ways to get beyond the the the the the in limitations of of GPT-2.
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And so the way that we get you can actually have done this experiment you can actually if you give me infinite amounts of unsorted list and sorted list if I have can do chain of thought and I can do every single step and teach it to do every single step then I can actually get it to do to do sort and become a Turing machine at test time.
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And similarly and even cheaper one that is much easier to do is you teach it and you say hey there's this Python function called sort.
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>> Just call the function. >> the function.
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Like that's the easiest thing to do and you don't need backprop at all.
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And so those are the two hacks.
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Now well Francois this is solved. Like we're done, right?
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No, because I needed to know what sort was.
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What happens if we didn't know what merge sort >> The chain of thought is not going to inherently discover sorting from first principles.
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It's it's finding it from our historical knowledge of everything it's trained on.
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>> Yeah, I mean this is like the the demos had this whole thing about like the ultimate test is the Einstein test.
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Like go back to 1911 and then like have it rebuild all the physics up until now.
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Similarly, let's just pretend that we only had bubble sort.
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We knew other no other sort system.
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If you chain of thought it on all the bubble sort input and output it will only do bubble sort.
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In fact, it won't even do bubble sort that well.
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>> [laughter] >> So this is the best situation and then the tool use of course it can only know bubble sort.
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I want to get to merge sort.
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How do I discover merge sort?
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>> And I think the the interesting thing just to emphasize here cuz it may not have been extremely clear is there already exists some type of recursion that people are used to in LLMs which is chain of thought we mentioned earlier.
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But that is a recursion that's happening in the token space of the models' outputs, not inherent to the model itself.
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And that's sort of the fundamental limitation, is that the model can only do a feed-forward one-shot output, and then we basically just have this hack that if you keep letting it output things, then it can read its outputs and do somewhat intelligent-seeming things with it.
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But it seems sort of be upper bounded by the data that we feed it, that, you know, the labs are very hungrily buying right now, and not the sort of like inherent underlying recursive reasoning.
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>> Yeah, so both in both cases, both hacks to solve this in COT and tool use, um you're bounded by the bounds of human knowledge.
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In the event it's outside the set of human knowledge, then like you're kind of SOL.
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And so that's that's one.
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The other you make a great point about discrete versus latent space.
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Um reasoning in uh a discrete it can only output the carry in the case of LLMs has to be snapped back to some discrete token space.
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And in the case of RNNs in general, they remain in this uh continuous latent space, which is much higher-dimensional.
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If you give me like a tape that's this long and you cut it up into 10 buckets, like versus all the possible values >> Right, exactly, yeah.
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>> it's much more expressive to be in continuous space.
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But we can't train it that way cuz we actually, you know, cuz you're inhibited by backprop through time largely.
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Um and this is why this paper is so exciting.
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>> Okay, so before we then go over to the TRM paper, um let's just summarize here.
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What matters most from the HRM paper that we should take away before we transition and contrast it with the TRM paper?
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>> Yeah, I think that the the number one piece uh to take away is this outer refinement loop.
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The outer refinement loop scales.
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And there's a a great uh breakdown.
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Um basically the the Sapient uh authors, which huge kudos for this paper cuz there's so many innovations in this paper, didn't really do like a scaling ablations on every single one of the inputs, but this guy Constantine at Francois Chollet's company India actually did.
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And it's this amazing breakdown that he put on posted on YouTube that you can go check out.
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But basically the main takeaway is that the outer final loops is the main beneficiary is the is the is the main reason why these things work so well, which Alexia basically takes the she found I think in parallel and and scales up and and shows that you can get rid of a lot of all this other stuff.
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>> Okay, so like a lot of machine learning, the follow-on paper is basically delete 75% of the first paper as we've often done in videos here and keep the magic basically.
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So okay, so so what's the magic then?
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Like what's the part that actually matters in terms of what stays in the TRM paper?
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And let's now contrast the core architectural differences between these two papers.
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>> Yeah, so I think that I guess if I break it down into two major things is this outer refinement loop thing is really great and works really well and that this like truncated backprop through time, which is backprop through time except I truncate at some time earlier point called T T back T equals 1 is actually is completely sufficient.
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And so truncated backprop through time T equals 1 completely sufficient and that's very counterintuitive.
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>> Which is what HRM found.
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>> HRM found and TRM does a little bit further rather than going through just one call to the H net and the L net, it actually goes through one full recursion loop.
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So if I do it 16 times, I just go back through one time and that is is is kind of sufficient.
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And if you do it with this like fixed point iteration thing, pseudo fixed point iteration thing where you keep hitting it with a at every single step, it like weirdly works and this batch size across the carry space like actually works.
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>> that part is also kept between these two models, yeah.
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It seemed like another thing that changed was having these this sort of double layer of like, you know, higher order thinking and lower order thinking.
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It seems like it collapsed it down into just a single one.
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What's the intuition there and how does that actually work in the TRM paper?
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>> Yeah, so it's interesting.
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She actually ablates having two separate networks versus just having one.
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I guess the more important space is the variable scope is that you should have low-level features and high-level features but the same network.
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And so the the best performing >> The same network can extract both basically.
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>> Yeah, you weight share between the L-net and the H-net and it's just called net.
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And and you do just one transformer layer versus the four like they do in in Sapien and just whittle it down to one and do more of a recursion and that but you keep ZL and ZH to be distinct and separate.
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And she she calls it X and Y which I found very confusing. >> Yeah.
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>> XYZ it was very confusing and it's just like ZH and ZL is just cleaner.
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>> So, if you read the paper, Y is actually like latent space.
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It's like it's like Z basically. >> is not a label. >> Yeah, okay.
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>> Which [laughter] really threw me off the paper. >> Whatever, yeah.
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>> Uh but anyway, so I I we'll go through some code here and I'll walk you through it.
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So, I replaced all of her nomenclature and used the the Sapien notation which is much cleaner and and more straightforward to me at least. >> Okay, cool.
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Now, before we, you know, dive into the code for a sec, like in terms of how these two arms actually work, you know, it's it's pretty interesting because these this recursion advantage now gives you a bunch of advantages over transformers.
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So, rather than having you know, 500 or 1,000 or a million or whatever transformer layers and having tons and tons of parameters, you get compute depth basically without this parameter depth.
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Um and the optimization process process looks like more of like an iterative kind of like expectation maximization algorithm.
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Do you want to talk about how that worked in the TRM paper cuz I thought that was also pretty interesting.
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>> Um so both of them kind of had the same kind of uh um EM E feeling thing where like we update ZL condition upon the input X and ZH. >> Yep. >> Z the last ZH. ZH T minus 1, let's say.
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Um, and then we keep updating ZL ZL ZL ZL ZL and we keep updating it and then we go holding we update ZH condition upon ZL and actually just ZL, it's not even X.
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>> And then we just update >> update ZH and and the way to think about ZL and ZH is ZL is like your local scoped variables that are just being overwritten and updating updating updating and then ZH and Azelia makes this point sorry Azelia Alexia makes this point that is that is a candidate uh answer a proposed latent answer that is just an embedding space away one MLP look up away from the true answer.
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>> you're kind of like >> EMing just to like zoom out a little bit.
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>> You're you're kind of maximizing the probability of the correct, you know, information stored in your memory conditioned on a given output and maximizing the right output conditioned on the information stored in your memory {quote} {unquote} in parallel and like that optimization algorithm leads to you ultimately learning a recursive method that stores the right information to this local memory basically and then outputs it I think.
26:25
>> It really like if we actually think of Sudoku is actually a really natural way to think about what's actually happening under the hood where Sudoku is an incomplete puzzle you can't guess every cell at any one time.
26:35
You can actually it's designed where you can only guess one or two cells based on the available information.
26:41
So it's not it's an incompressible problem.
26:42
You actually can't do it unless you just randomly guessing and guessing and guessing which is very high combinatorial space.
26:48
And so what the ZL is doing is is some type of let me try this, try that, do some computation, think about little things, and then and then it proposes and then we go to condition upon like something that it may have found, it sends it to ZH, ZH fills it in, and now we have a little bit more of of a filled-in Sudoku puzzle.
27:07
>> And the training process is training the algorithm to know to do that, right?
27:12
It's like it's maximizing that.
27:12
It's like, "Oh, this strategy for what you save tends to lead to correct output."
27:17
>> Without chain of thought.
27:19
>> Without chain of thought.
27:20
>> That's the most important part.
27:20
Is that if we had Sudoku and we knew how to solve Sudoku cuz like we were just, you know, dumb Homo sapiens that didn't know how to solve Sudoku, like it would just have solved it.
27:29
And that's why it's cool cuz it actually is able to discover things without being teacher forced via chain of thought. >> Yeah.
27:37
Should we look at some code? >> Let's do it.
27:39
>> Okay, let's dive in and I would love to see what these papers or bottles look like just distilled down to their core essence.
27:46
I know there's lots of details in how you train them, but kind of the core training algorithm.
27:49
It'd be great to contrast the two methods. >> Yeah.
27:52
So, I mean, they're remarkably similar.
27:54
Um and so, largely one is and learning one is learning the other, but basically you start out with some ZH and ZL that are just zeros. >> Yep.
28:03
>> Um you have some input embedding space.
28:06
We go from X raw to X, which is the maze state or whatever it is, uh initial maze state.
28:11
And then with no grad, uh you don't pass any gradients back through this.
28:15
You >> So, this is the trick, basically, to not backprop backprop through time.
28:20
>> Here are two of the three recursion levels.
28:22
So, you have this is like the the the they do this just for for for simplicity, but I hit ZL uh T low times, and then uh once for modulo T T low, then I hit the ZH and I do it again and again.
28:37
And like you said, I'm updating ZL condition upon ZH and X, and then I update ZH condition upon ZL. >> Right.
28:45
So, this is the like expectation-maximization style >> Exactly.
28:48
And then, you don't really need this.
28:50
This is like just for clean cleanliness to show clearly that there's no gradients occurring above this line.
28:56
>> freezing the weights past that. >> Exactly.
28:58
And then, I hit LNet and HNet one more time.
29:01
>> Which is the same thing as up above.
29:01
So, this is just okay, it's literally just the no grad thing running one more time. Cool. >> Yeah.
29:06
And just make it really clear. And then, there you go.
29:08
And that's your HRM model. >> Cool.
29:11
>> And they use two two two and two is completely sufficient.
29:17
If you actually go much higher, Constantine showed very clearly that it doesn't actually help.
29:23
>> So, that's two of the three recursions you said.
29:24
The third happens in the actual training loop.
29:26
>> in the train loop and at the test loop.
29:28
They both have this MTest or N supervision, which Alexia calls deep supervision.
29:33
They call it outer refinement steps.
29:35
It's just whatever you want to call it, call it N sub.
29:40
>> And so, you do this N sub times during training.
29:42
And then during test time, there's a different hyperparameter for how many times it recurses over each model, which is MTest basically. >> actually the same.
29:50
And so, the these this and this, we can probably just call this the same.
29:55
And but, it's it's it's the same.
29:55
And if you actually Constantine does a good job of this.
30:00
If you actually train on 16 and you test on only one, you get like 7/8 of the performance or like almost all the performance.
30:10
So, it's actually quite interesting that this is just redundant too much compute and it doesn't actually help you all that much.
30:18
So, setting this to one is actually like >> But presumably for like more complicated problems, having more test time compute is still useful is like the reason you would start them up that way. >> For sure.
30:28
And so, we call our HRM, we get some loss, we backprop through just the those two little parts here, and then we step.
30:36
We zero out the gradient, but we do not update ZH and ZL.
30:42
These are still the same in it.
30:44
So that's the really important detail there.
30:47
And then so we go back, we pass in the ZH and the ZL from the previous one.
30:49
So now this is actually not the same batch. >> Right.
30:54
>> Because we have updated ZH and ZL.
30:54
So it's in a different part of the latent space. >> Cool.
30:59
Yeah, and that's the key like mini batch construction through memory space concept. Yeah, cool.
31:06
>> And then at test time, it's simply the three loops.
31:08
So there's your outer final loop, which turns out like just at train time doesn't matter.
31:12
Train time recursion was important, but test time recursion was actually not that important, which is kind of kind of counterintuitive.
31:18
And then the HRM inside that has your two other loops. >> Makes sense. >> And and that's it. So pretty simple.
31:25
>> Now that makes more sense.
31:27
>> The only two changes, the main two changes here is that they collapse L net and H net into just net. >> Great.
31:34
>> They and it's important detail, these are four transformer layers, this is four transformer layers, and this is just one transformer layer.
31:40
And Alexia actually shows that going deeper actually didn't help.
31:44
>> Yeah, and actually on some tasks, it was just a feed forward net actually worked just as well as a transformer there, right?
31:48
It was like on Sudoku I think, yeah.
31:50
>> Sudoku MLP actually outperformed the the attention.
31:52
It was it it scored zero on the maze.
31:56
The MLP scored zero on the maze.
31:56
And so there's it's not clear, it's not obvious that the transformer is always better.
32:03
So there's the weight sharing, and then instead of going back just the one two, the H this back propping through just these two, you actually back prop through one latent recursion step all the way through one latent recursion step.
32:16
So let me just walk through this a little bit.
32:19
So we have same thing here. >> point, yeah.
32:23
>> It's mainly the same thing here.
32:23
We're doing this six times.
32:27
And then we we go one more time here.
32:30
And then we do our deep recursion. This is the outer loop. N sub times.
32:36
And so again, we have the no grad, we have the detach, and then this is where it's different.
32:40
So, I I am calling this latent recursion after the detach. >> Yeah.
32:45
So, it's one full recursive loop is happening with that problem.
32:49
>> And so, that's the main uh difference in the optimization.
32:51
Otherwise, it's effectively the same.
32:54
And then it outputs, and then you're good to go, and you train it [snorts] uh exactly as the same way before.
33:00
And then at test time, it's the same thing uh again.
33:02
And so, largely the same. >> Cool.
33:05
And so, in many ways, it's sort of a simplification, right?
33:07
You're collapsing certain parts of it.
33:08
You're simplifying this net architecture.
33:14
It's slightly more complicated along this back back through time this back back prop through time part because you're actually back propping through more than you did before, but it's like taking a bunch of lessons from the first one and basically simplifying most of it.
33:25
>> Which is actually why she need I think is why she needs to make the model smaller.
33:28
And so, it's a 28 million parameter model for HRM.
33:30
Now, she brings it down to a 7 million parameter model.
33:34
It actually gets from 70% to 87% on uh um on our prize uh one, and uh and does actually quite well on our prize two as well.
33:42
And so, um yeah, so she makes the small the model model, you know, uh three, four times smaller, um but because it has that recursion, um it it actually outperforms.
33:52
And there is one There's this uh researcher named Melly Mitchell that writes this book uh talking about this very phenomenon, which is like it is um sufficient, not necessary to go uh bigger and get better performance, um and it is sufficient and not necessary to to add more recursion.
34:12
And so, where I'm really excited is what happens if you do both.
34:14
And you're still limited by back prop through time.
34:17
Even uh Alexia is is limited by back prop that last step um from a memory perspective for sure.
34:24
Um and so, if you can make the model really big, and you have a lots of recursion, and we do something else other than backprop through time.
34:32
Uh then we can get exact all the benefits of this and all the benefits of the giant LLMs and then you can get some crazy stuff.
34:39
>> So now to wrap up, why don't we talk a little bit about the bigger picture?
34:43
What does this mean for the field of AI research?
34:45
How should people think about where these models fit into the current span of research happening, especially given that it seems like a bit of a departure from a lot of the methods that people are used to hearing about and increasingly seeing products that people use?
34:57
>> Well, I think for one, uh this from the arguments that Schmidhuber makes and what we've talked about today, recursion is important and it's not going away.
35:05
And it they clearly the benefit is here of adding recursion to models and you've seen things like the recursion language models at Google um that are are pretty powerful and cool.
35:13
Um and so uh that's that's definitely one piece that's I don't think going away anytime soon.
35:18
Um the next one is this outer refinement loop, like back T TBTT, like T equals one truncated backprop through time T equals one.
35:26
I think that that is a really powerful idea, the fact that that works so well.
35:29
Uh we have yet to really explore it that extremely really understand what's happening there.
35:36
Um and then the third is that idea of like, okay, we know that recursion works.
35:39
We have these tiny recursive models that are 7 million parameters, they can solve what a 100 million 100 billion 100 >> 100 billion, >> billion parameter model can't solve trained on the entire internet and a 7 million parameter wins.
35:56
Like the right answer is to like take the amazingness here and take the amazingness here, which probably is already in Gemini already or some of these it might be at least in some part.
36:06
Um but when you when you take um the benefit of both these TRMs and these giant models and you actually slam together, I think that it's just going to take off.
36:16
It's going to be really huge.
36:19
>> Yeah, one of the things that's really interesting about these TRMs and each TRMs is they're not general purpose models, right?
36:22
These were task-specific models, right?
36:24
The model trained to do Sudoku cannot do ARC Prize inherently, it has to be trained on the our prize set to do so.
36:30
Versus the alarms that are used on these tasks are general purpose models that maybe get some additional fine-tuning data or in-context learning data on those tasks.
36:39
And so, I think that's where the interesting overlap might come is if you can make these more general purpose agents that can somehow be general purpose in the way that the sort of next token prediction algorithm has given us and do more complex reasoning to achieve that.
36:52
Seems like you can have really fish-dark architectures to do scalable reasoning. >> Right.
36:57
And And like a lot of the view of what these alarms are doing is finding really amazing embedding representation spaces. >> Yes.
37:05
>> But reasoning inside that that space is actually not done all that much.
37:09
>> Yeah, it's it's always through the token space that happens. >> the token space.
37:11
And so, like what you can imagine is we found mapping from token space or from vision from pixels some really cool latent space where like things are just nicely semantically separated and we can, you know, makes it really easy for downstream tasks to do, but now in that space use this like tiny reasoning models use some some type of recursion inside that and train those those those that model on that a little small model on that reasoning space.
37:38
>> [music] >> I think that's going to be the way to work.
37:40
>> Pranshu, thanks so much for breaking it all down for us.
37:41
See you all in the next episode of Decoded. Thank you. >> [music]