The literature review is very strange to me. Where is the section on certified robustness against epsilon-ball adversarial examples? The techniques used in that literature (e.g. interval propagation) are nearly identical to what you discuss here.
I was meaning to include such a section, but forgot :). Perhaps I will edit it in. I think such work is qualitatively similar to what we’re trying to do, but that the key difference is that we’re interested in “best guess” estimates, as opposed to formally verified-to-be-correct estimates (mostly because we don’t think formally verified estimates are tractable to produce in general).
Relatedly, what’s the source of hope for these kinds of methods outperforming adversarial training? My sense from the certified defenses literature is that the estimates they produce are very weak, because of the problems with failing to model all the information in activations. (Note I’m not sure how weak the estimates actually are, since they usually report fraction of inputs which could be certified robust, rather than an estimate of the probability that a sampled input will cause a misclassification, which would be more analogous to your setting.)
The main hope comes from the fact that we’re using a “best guess” estimate, instead of trying to certify that the model won’t produce catastrophic actions. For example, Method 1 can be thought of as running a single example with a Gaussian blob around it through the model, but also tracking the “1st order” contributions that come from the Gaussian blob. If we wanted to bound the potential contributions from the Gaussian blob, our estimates would get really broad really fast, as you tend to see with interval propagation.
Although, this also comes with the opposite issue of how to know if the estimates are at all reasonble, especially when you train against them.
If your catastrophe detector involves a weak model running many many inferences, then it seems like the total number of layers is vastly larger than the number of layers in M, which seems like it will exacerbate the problems above by a lot. Any ideas for dealing with this?
I think fundamentally we just need our estimates to “not get that much worse” as things get deeper/more complicated. The main hope for why we can achieve this is that the underlying model itself will not get worse as it gets deeper/the chain of thought gets longer. This implies that there is some sort of stabalization going on, so we will need to capture the effect of this stabalization. It does seem like in order to do this, we will have to model only high level properties of this distribution, instead of trying to model things on the level of activations.
In other words, one issue with interval propagation is that it makes an assumption that can only become less true as you propagate through the model. After a few layers, you’re (perhaps only implicitly) putting high probability on activations that the model will never produce. But as long as your “activation model” is behaving reasonably, then hopefully it will only become more uncertain insofar as the underlying reasoning done by the model becomes more uncertain.
What’s your proposal for the distribution P0 for Method 2 (independent linear features)?
You can either train an SAE on the input distribution, or just try to select the input distribution to maximize the probability of catastrophe produced by the estimation method (perhaps starting with an SAE of the input distribution, or a random one). Probably this wouldn’t work that well in practice.
Why think this is a cost you can pay? Even if we ignore the existence of C and just focus on M, and we just require modeling the correlations between any pair of layers (which of course can be broken by higher-order correlations), that is still quadratic in the number of parameters of M and so has a cost similar to training M in the first place. In practice I would assume it is a much higher cost (not least because C is so much larger than M).
Our ultimate goal is vaguely to “only pay costs that SGD had to pay to produce M” Slightly more specifically, M has a bunch of correlations between its layers. Some of these correlations were actively selected to be those particular values by SGD, and other correlations were kind of random. We want to track the ones that were selected, and just assume the other ones are random. Hopefully, since SGD was not actively manipulating those correlations, the underlying model is in some sense invariant to their precise values, and so a model that treats such correlations as random will predict the same underlying behavior as a model that models the precise values of those correlations.
Fwiw the thing that scares me is the combination of three things:
Producing an accurate estimate requires “understanding” the input
Our standard for the quality of estimates will be very high
The approach is purely algorithmic (rather than e.g. using the flexible intelligence of LLMs / humans)
You presumably agree with (1) and (3). For (2), it seems like there’s a lot of correlations you need to take into account for this to produce estimates that aren’t wildly off:
Underestimates of risk: These are cases where the presumption of independence neglects correlations between things that happen for catastrophe-causing events. For example, maybe a model is planning to defect when RSA-2048 is factored, and it has N different consistency checks it runs to make sure we aren’t fooling it about whether it has been factored. The method has to see that there’s a common cause for all the consistency checks to return 1, otherwise it will underestimate risk by a factor exponential in N. (And tbc I think even separately from more exotic examples like RSA-2048, it will be relatively common for this pattern to arise with networks, e.g. it happens any time that in reality there is a common cause that produces many pieces of evidence, and then the network aggregates those pieces of evidence to infer the common cause.)
Overestimates of risk: These are cases where the presumption of independence neglects correlations that rule out catastrophe, and so lead to overestimates. For example, the model might be willing to make up fake instructions for creating bioweapons to help with scifi writing, but never provide real instructions. So the method needs to capture the “understanding” of which instructions are fake vs real.
I agree this isn’t a proof of impossibility, since a purely algorithmic approach (SGD) produced the “understanding” in the first place, so in theory a purely algorithmic approach could still capture all that understanding to produce accurate estimates. But it does seem heuristically like you should assign a fairly low probability that this pans out.
Yes I agree with what you have written, and do think it’s overall not that likely that everything pans out as hoped. We do also have other hopes for how this general picture can still cohere if the specific path doesn’t work out, eg we’re open to learning some stuff empirically and adding an “algorithmic cherry on top” to produce the estimate.
I was meaning to include such a section, but forgot :). Perhaps I will edit it in. I think such work is qualitatively similar to what we’re trying to do, but that the key difference is that we’re interested in “best guess” estimates, as opposed to formally verified-to-be-correct estimates (mostly because we don’t think formally verified estimates are tractable to produce in general).
The main hope comes from the fact that we’re using a “best guess” estimate, instead of trying to certify that the model won’t produce catastrophic actions. For example, Method 1 can be thought of as running a single example with a Gaussian blob around it through the model, but also tracking the “1st order” contributions that come from the Gaussian blob. If we wanted to bound the potential contributions from the Gaussian blob, our estimates would get really broad really fast, as you tend to see with interval propagation.
Although, this also comes with the opposite issue of how to know if the estimates are at all reasonble, especially when you train against them.
I think fundamentally we just need our estimates to “not get that much worse” as things get deeper/more complicated. The main hope for why we can achieve this is that the underlying model itself will not get worse as it gets deeper/the chain of thought gets longer. This implies that there is some sort of stabalization going on, so we will need to capture the effect of this stabalization. It does seem like in order to do this, we will have to model only high level properties of this distribution, instead of trying to model things on the level of activations.
In other words, one issue with interval propagation is that it makes an assumption that can only become less true as you propagate through the model. After a few layers, you’re (perhaps only implicitly) putting high probability on activations that the model will never produce. But as long as your “activation model” is behaving reasonably, then hopefully it will only become more uncertain insofar as the underlying reasoning done by the model becomes more uncertain.
You can either train an SAE on the input distribution, or just try to select the input distribution to maximize the probability of catastrophe produced by the estimation method (perhaps starting with an SAE of the input distribution, or a random one). Probably this wouldn’t work that well in practice.
Our ultimate goal is vaguely to “only pay costs that SGD had to pay to produce M” Slightly more specifically, M has a bunch of correlations between its layers. Some of these correlations were actively selected to be those particular values by SGD, and other correlations were kind of random. We want to track the ones that were selected, and just assume the other ones are random. Hopefully, since SGD was not actively manipulating those correlations, the underlying model is in some sense invariant to their precise values, and so a model that treats such correlations as random will predict the same underlying behavior as a model that models the precise values of those correlations.
Fwiw the thing that scares me is the combination of three things:
Producing an accurate estimate requires “understanding” the input
Our standard for the quality of estimates will be very high
The approach is purely algorithmic (rather than e.g. using the flexible intelligence of LLMs / humans)
You presumably agree with (1) and (3). For (2), it seems like there’s a lot of correlations you need to take into account for this to produce estimates that aren’t wildly off:
Underestimates of risk: These are cases where the presumption of independence neglects correlations between things that happen for catastrophe-causing events. For example, maybe a model is planning to defect when RSA-2048 is factored, and it has N different consistency checks it runs to make sure we aren’t fooling it about whether it has been factored. The method has to see that there’s a common cause for all the consistency checks to return 1, otherwise it will underestimate risk by a factor exponential in N. (And tbc I think even separately from more exotic examples like RSA-2048, it will be relatively common for this pattern to arise with networks, e.g. it happens any time that in reality there is a common cause that produces many pieces of evidence, and then the network aggregates those pieces of evidence to infer the common cause.)
Overestimates of risk: These are cases where the presumption of independence neglects correlations that rule out catastrophe, and so lead to overestimates. For example, the model might be willing to make up fake instructions for creating bioweapons to help with scifi writing, but never provide real instructions. So the method needs to capture the “understanding” of which instructions are fake vs real.
I agree this isn’t a proof of impossibility, since a purely algorithmic approach (SGD) produced the “understanding” in the first place, so in theory a purely algorithmic approach could still capture all that understanding to produce accurate estimates. But it does seem heuristically like you should assign a fairly low probability that this pans out.
Yes I agree with what you have written, and do think it’s overall not that likely that everything pans out as hoped. We do also have other hopes for how this general picture can still cohere if the specific path doesn’t work out, eg we’re open to learning some stuff empirically and adding an “algorithmic cherry on top” to produce the estimate.