Zach Furman
This proposal looks really promising to me. This might be obvious to everyone, but I think much better interpretability research is really needed to make this possible in a safe(ish) way. (To verify the shard does develop, isn’t misaligned, etc.) We’d just need to avoid the temptation to take the fancy introspection and interpretability tools this would require and use them as optimization targets, which would obviously make them useless as safeguards.
No substantive reply, but I do want to thank you for commenting here—original authors publicly responding to analysis of their work is something I find really high value in general. Especially academics that are outside the usual LW/AF sphere, which I would guess you are given your account age.
I don’t think the game is an alarming capability gain at all—I agree with LawrenceC’s comment below. It’s more of a “gain-of-function research” scenario to me. Like, maybe we shouldn’t deliberately try to train a model to be good at this? If you’ve ever played Diplomacy, you know the whole point of the game is manipulating and backstabbing your way to world domination. I think it’s great that the research didn’t actually seem to come up with any scary generalizable techniques or dangerous memetics, but I think ideally shouldn’t even be trying in the first place.
Why does GPT-3 use the same matrix for word embedding and final predictions? I would expect this to constrain the model, and the only potential upsides I can see are saving parameters (lol) and preserving interpretability (lmao)[8]. Other resources like A Mathematical Framework for Transformer Circuits use different embedding/unembedding matrices—their and . Perhaps this is not necessary for GPT-3 since the final feed-forward network can perform an appropriate linear transformation, and in A Mathematical Framework they are looking at transformers without FFNs. But some properties (e.g. words being linear combinations of other words) cannot be changed by such a linear transformation, so having an entire new unembedding matrix could still add value.
This is called “tied embeddings”. You’re right that models don’t need to have this constraint, and some don’t—for instance, GPT-NeoX. I’m not sure whether or not this actually improves performance in practice though.
This is something I’ve been thinking about recently. In particular, you can generalize this by examining temporary conserved quantities, such as phases of matter (typically produced by spontaneous symmetry-breaking). This supports a far richer theory of information-accessible-at-a-distance than only permanently conserved quantities like energy can provide, and allows for this information to have dynamics like a stochastic process. In fact, if you know a bit of solid-state physics you probably realize exactly how much of our observed macroscopic properties (e.g. object color) are determined by things like spontaneous symmetry-breaking. You can make all of this more rigorous and systematic by connecting to ergodic theory, but this is probably deserving of a full paper, if I can get around to it. Happy to discuss more with anyone else.
But in the last few years, we’ve gotten: [...]
Robots (Boston Dynamics)
Broadly agree with this post, though I’ll nitpick the inclusion of robotics here. I don’t think it’s progressing nearly as fast as ML, and it seems fairly uncontroversial that we’re not nearly as close to human-level motor control as we are to (say) human-level writing. I only bring this up because a decent chunk of bad reasoning (usually underestimation) I see around AGI risk comes from skepticism about robotics progress, which is mostly irrelevant in my model.
The field of complex systems seems like a great source of ideas for interpretability and alignment. In lieu of a longer comment, I’ll just leave this great review by Teehan et al. on emergent structures in LLMs. Section 3 in particular is great.
Dropping some late answers here—though this isn’t my subfield, so forgive me if I mess things up here.
Correct me if I’m wrong, but it struck while reading this that you can think of a neural network as learning two things at once:
a classification of the input into 2^N different classes (where N is the total number of neurons), each of which gets a different function applied to it
those functions themselves
This is exactly what a spline is! This is where the spline view of neural networks comes from (mentioned in Appendix C of the post). What you call “classes” the literature typically calls the “partition.” Also, while deep networks can theoretically have exponentially many elements in the partition (w.r.t. the number of neurons), in practice, they instead are closer to linear.
Can the functions and classes be decoupled?
To my understanding this is exactly what previous (non-ML) research on splines did, with things like free-knot splines. Unfortunately this is computationally intractable. So instead much research focused on fixing the partition (say, to a uniform grid), and changing only the functions. A well-known example here is the wavelet transform. But then you lose the flexibility to change the partition—incredibly important if some regions need higher resolution than others!
From this perspective the coupling of functions to the partition is exactly what makes neural networks good approximators in the first place! It allows you to freely move the partition, like with free-knot splines, but in a way that’s still computationally tractable. Intuitively, neural networks have the ability to use high resolution where it’s needed most, like how 3D meshes of video game characters have the most polygons in their face.
How much of the power of neural networks comes from their ability to learn to classify something into exponentially many different classes vs from the linear transformations that each class implements?
There are varying answers here, depending on what you mean by “power”: I’d say either the first or neither. If you mean “the ability to approximate efficiently,” then I would probably say that the partition matters more—assuming the partition is sufficiently fine, each linear transformation only performs a “first order correction” to the mean value of the partition.
But I don’t really think this is where the “magic” of deep learning comes from. In fact this approximation property holds for all neural networks, including shallow ones. It can’t capture what I see as the most important properties, like what makes deep networks generalize well OOD. For that you need to look elsewhere. It appears like deep neural networks have an inductive bias towards simple algorithms, i.e. those with a low (pseudo) Kolmogorov complexity. (IMO, from the spline perspective, a promising direction to explain this could be via compositionality and degeneracy of spline operators.)
Hope this helps!
Since nobody here has made the connection yet, I feel obliged to write something, late as I am.
To make the problem more tractable, suppose we restrict our set of coordinate changes to ones where the resulting functions can still (approximately) be written as a neural network. (These are usually called “reparameterizations.”) This occurs when multiple neural networks implement (approximately) the same function; they’re redundant. One trivial example of this is the invariance of ReLU networks to scaling one layer by a constant, and the next layer by the inverse of that constant.
Then, in the language of parametric statistics, this phenomenon has a name: non-identifiability! Lucky for us, there’s a decent chunk of literature on identifiability in neural networks out there. At first glance, we have what seems like a somewhat disappointing result: ReLU networks are identifiable up to permutation and rescaling symmetries.
But there’s a catch—this is only true except for a set of measure zero. (The other catch is that the results don’t cover approximate symmetries.) This is important because there are reasons to suggest real neural networks are pushed close to this set during training. This set of measure zero corresponds to “reducible” or “degenerate” neural networks—those that can be expressed with fewer parameters. And hey, funny enough, aren’t neural networks quite easily pruned?
In other parts of the literature, this problem has been phrased differently, under the framework of “structure-function symmetries” or “canonicalization.” It’s also often covered when discussing the concepts of “inverse stability” and “stable recovery.” For more on this, including a review of the literature, I highly recommend Matthew Farrugia-Roberts’ excellent master’s thesis on the topic.
(Separately, I’m currently working on the issue of coordinate-free sparsity. I believe I have a solution to this—stay tuned, or reach out if interested.)
My summary (endorsed by Jesse):
1. ERM can be derived from Bayes by assuming your “true” distribution is close to a deterministic function plus a probabilistic error, but this fact is usually obscured
2. Risk is not a good inner product (naively) - functions with similar risk on a given loss function can be very different
3. The choice of functional norm is important, but uniform convergence just picks the sup norm without thinking carefully about it
4. There are other important properties of models/functions than just risk
5. Learning theory has failed to find tight (generalization) bounds, and bounds might not even be the right thing to study in the first place
In other words, does there exist any dataset such that generating extrapolations from it leads to good outcomes, even in the hands of bad actors?
I think this is an important question to ask, but “even in the hands of bad actors” is just too difficult a place to start. I’m sure you’re aware, but it’s an unsolved problem whether there exists a dataset / architecture / training procedure such that “generating extrapolations from it leads to good outcomes,” for sufficiently capable ML models, even in the hands of good actors. (And the “bad actor” piece can at least plausibly be solved by social coordination, whereas the remaining portion is a purely technical problem you can’t dodge.)
But if you drop the bad actor part, I think this question is a good one to ask (but still difficult)! I think answering this question requires a better understanding of how neural networks generalize, but I can at least see worlds where the answer is “yes”. (Though there are still pitfalls in how you instantiate this in reality—does your dataset need to be perfectly annotated, so that truth-telling is incentivized over sycophancy/deception? Does it require SGD to always converge to the same generalization behavior? etc.)
To be clear, I don’t know the answer to this!
Spitballing here, the key question to me seems to be about the OOD generalization behavior of ML models. Models that receive similarly low loss on the training distribution still have many different ways they can behave on real inputs, so we need to know what generalization strategies are likely to be learned for a given architecture, training procedure, and dataset. There is some evidence in this direction, suggesting that ML models are biased towards a simplicity prior over generalization strategies.
If this is true, then the incredibly handwave-y solution is to just create a dataset where the simplest (good) process for estimating labels is to emulate an aligned human. At first pass this actually looks quite easy—it’s basically what we’re doing with language models already.
Unfortunately there’s quite a lot we swept under the rug. In particular this may not scale up as models get more powerful—the prior towards simplicity can be overcome if it results in lower loss, and if the dataset contains some labels that humans unknowingly rated incorrectly, the best process for estimating labels involves saying what humans believe is true rather than what actually is. This can already be seen with the sycophancy problems today’s LLMs are having.
There’s a lot of other thorny problems in this vein that you can come up with with a few minutes of thinking. That being said, it doesn’t seem completely doomed to me! There just needs to be a lot more work here. (But I haven’t spent too long thinking about this, so I could be wrong.)
For anyone who wants to play around with this themselves, you might be interested in a small Colab notebook I made, with some interactive 2D and 3D plots.
A bit of a side note, but I don’t even think you need to appeal to new architectures—it looks like the NTK approximation performs substantially worse even with just regular MLPs (see this paper, among others).
Great discussion here!
Leaving a meta-comment about priors: on one hand, almost-linear features seem very plausible (a priori) for almost-linear neural networks; on the other, linear algebra is probably the single mathematical tool I’d expect ML researchers to be incredibly well-versed in, and the fact that we haven’t found a “smoking gun” at this point with so much potential scrutiny makes me suspect.And while this is a very natural hypothesis to test, and I’m excited for people to do so, it seems possible that the field’s familiarity with linear methods is a hammer that makes everything look like a nail. It’s easy to focus on linear interpretability because the alternative seems too hard (a response I often get) - I think this is wrong, and there are tractable directions in the nonlinear case too, as long as you’re willing to go slightly further afield.
I also have some skepticism on the object-level here too, but it was taking me too long to write it up, so that will have to wait. I think this is definitely a topic worth spending more time on—appreciate the post!
Exponential growth is a fairly natural thing to expect here, roughly for the same reason that vanishing/exploding gradients happen (input/output sensitivity is directly related to param/output sensitivity). Based on this hypothesis, I’m preregistering the prediction that (all other things equal) the residual stream in post-LN transformers will exhibit exponentially shrinking norms, since it’s known that post-LN transformers are more sensitive to vanishing gradient problems compared to pre-LN ones.
Edit: On further thought, I still think this intuition is correct, but I expect the prediction is wrong—the notion of relative residual stream size in a post-LN transformer is a bit dubious, since the size of the residual stream is entirely determined by the layer norm constants, which are a bit arbitrary because they can be rolled into other weights. I think the proper prediction is more around something like Lyapunov exponents.
Yep, pre-LN transformers avoid the vanishing gradient problem.
Haven’t checked this myself, but the phenomenon seems to be fairly clean? See figure 3.b in the paper I linked, or figure 1 in this paper.
I actually wouldn’t think of vanishing/exploding gradients as a pathological training problem but a more general phenomenon about any dynamical system. Some dynamical systems (e.g. the sigmoid map) fall into equilibria over time, getting exponentially close to one. Other dynamical systems (e.g. the logistic map) become chaotic, and similar trajectories diverge exponentially over time. If you check, you’ll find the first kind leads to vanishing gradients (at each iteration of the map), and the second to exploding ones. This a forward pass perspective on the problem—the usual perspective on the problem considers only implications for the backward pass, since that’s where the problem usually shows up.
Notice above that the system with exponential decay in the forward pass had vanishing gradients (growing gradient norms) in the backward pass—the relationship is inverse. If you start with toy single-neuron networks, you can prove this to yourself pretty easily.
The predictions here are still complicated by a few facts—first, exponential divergence/convergence of trajectories doesn’t necessarily imply exponentially growing/shrinking norms. Second, the layer norm complicates things, confining some dynamics to a hypersphere (modulo the zero-mean part). Haven’t fully worked out the problem for myself yet, but still think there’s a relationship here.
If anyone wants an interactive visual for the correlation upper and lower bounds, I made one for myself here: https://www.math3d.org/chXa4xZrC.
The x, y, and z axes are the correlations between X and Y, and Y and Z, and X and Z respectively. Everything inside the blue surface is possible. There are also some sliders to help visualize level sets.
This is definitely the core challenge of the language model approach, and may be the reason it fails. I actually believe language models aren’t the most likely approach to achieve superintelligence. But I also place a non-trivial probability on this occurring, which makes it worth thinking about for me.
Let me try to explain why I don’t rule this possibility out. Obviously GPT-3 doesn’t know more than a human, as evident in its sub-human performance on common tasks and benchmarks. But suppose we instead have a much more advanced system, a near-optimal sequence predictor for human-written text. Your argument is still correct—it can’t output anything more than a human would know, because that wouldn’t achieve minimum loss on the training data. But does that imply it can’t know more than humans? That is, is it impossible for it to make use of facts that humans don’t realize as an intermediate step in outputting text that only includes facts humans do realize?
I think not necessarily. As an extreme example, one particular optimal sequence predictor would be a perfect simulation, atom-for-atom, of the entire universe at the time a person was writing the text they wrote. Trivially, this sequence predictor “knows” more than humans do, since it “knows” everything, but it will also never output that information in the predicted text.
More practically, sequence prediction is just compression. More effective sequence prediction means more effective compression. The more facts about the world you know, the less data is required to describe each individual piece of text. For instance, knowing the addition algorithm is a more space-efficient way to predict all strings like “45324 + 58272 =” than memorization. As the size of the training data you’re given approaches infinity, assuming a realistic space-bounded sequence predictor, the only way its performance can improve is with better world/text modeling. The fact that humans don’t know a certain fact wouldn’t prohibit it from being discovered if it allows more efficient sequence prediction.
Will we reach this superhuman point in practice? I don’t know. It may take absurd amounts of computation and training data to reach this point, or just more than alternative approaches. But it doesn’t seem impossible to me in theory.
Even if we reach this point, this still leaves the original problem—the model will not output anything more than a human would know, even if it has that knowledge internally. But even without fancy future interpretability tools, we may be heading in that direction with things like InstructGPT, where the model was fine-tuned to spit out things it was capable of saying, but wouldn’t have said under pure sequence prediction.
This whole argument, together with rapid recent progress, is enough for me to not immediately write off language models, and consider strategies to take advantage of them if this scenario were to occur.