Thanks for running these experiments and writing this up! I’m very excited to see this sort of followup work, and I think there are a lot of useful results here. I agree with most of this, and mostly just have a few nitpicks about how you interpret some things.

Reactions to the summary of your experimental results:

• CCS does so better than random, but not by a huge margin: on average, random linear probes have a 75% accuracy on some “easy” datasets;
  • I think it’s cool that random directions sometimes do so well; this provides a bit of additional evidence that high-accuracy directions can be quite salient.
  • It’s not too surprising to me that this holds for UQA (which is instruction-tuned, so it should intuitively have a particularly salient truth-y direction) and the easiest datasets like IMDB, but I doubt this holds for most models and datasets. At the very least I recall looking at this in one narrow setting before and got close to random performance (though I don’t remember what setting that was exactly). I’d be curious to see this for more model/dataset pairs.
  • This is more of a nitpick with your phrasing, but FWIW based on the plot it does still look to me like CCS is better by a large margin (e.g. 75% accuracy to 95% accuracy is a 5x reduction in error) even in the settings where random directions do best. The takeaway for me here is mostly just that random direction can sometimes be surprisingly good -- which I agree is interesting.
• CCS does not find the single linear probe with high accuracy: there are more than 20 orthogonal linear probes (i.e. using completely different information) that have similar accuracies as the linear probe found by CCS (for most datasets);
  • Yep, I agree; we definitely weren’t claiming to find a uniquely good direction. I also quite like the recursive CCS experiment, and would love to see more experiments along these lines.
  • I think it’s interesting that you can find 20 orthogonal probes each with high accuracy. But I’m especially interested in how many functionally equivalent directions there are. For example, if this 20 dimensional subspace actually corresponds to roughly the same clustering into true and false, then I would say they are ~equivalent for my purposes.
• CCS does not always find a probe with low test CCS loss (Figure 1 of the paper is misleading). CSS finds probes which are sometimes overconfident in inconsistent predictions on the test set, resulting in a test loss that is sometimes higher than always predicting a constant probability;
  • We indeed forgot to specify that figure 1 is with the train set — that was a good catch that we’ll specify in the arxiv version soon (we’ve already done so for the camera ready version). 
  • I think some of your experiments here are also interesting and helpful.  That said, I do want to emphasize that I don’t find train-test distinctions particularly essential here because our method is unsupervised; I ultimately just want to find a direction that gives correct predictions to superhuman examples, and we can always provide those superhuman examples as part of the training data.
  • Another way of putting this is that I view our method as being an unsupervised clustering method, for which I mostly just care about finding high-accuracy clusters. We also show  it generalizes/transfers, but IMO that’s of secondary importance.
  • I also think it's interesting to look at loss rather than just accuracy (which we didn't do much), but I do ultimately think accuracy is quite a bit more important overall.
• CCS’ performance on GPT-J heavily depends on the last tokens of the input, especially when looking at the last layers’ activations (the setting used in the paper).
  • Thanks, these are helpful results. The experiment showing that intermediate layers can be better in some ways also feel similar to our finding that intermediate layers do better than later layers when using a misleading prompt. In general I would indeed like to see more work trying to figure out what’s going on with autoregressive models like GPT-J.

Reactions to your main takeaways:

• However, we still don’t know if this feature corresponds to the model’s “beliefs”.
  • I agree. (I also still doubt current models have “beliefs” in any deep sense)
• Future work should compare their work against the random probe baseline. Comparing to a 50% random guessing baseline is misleading, as random probes have higher accuracy than that.
  • I agree, this seems like a good point.
• CCS will likely miss important information about the model’s beliefs because there is more than one linear probe which achieves low loss and high CCS accuracy, i.e. there is more than one truth-like feature… There are many orthogonal linear probes which achieve low loss and high CCS accuracy, i.e. there are many truth-like features. Narrowing down which linear probe corresponds to the model’s beliefs might be hard.
  • I think your experiments here are quite interesting, but I still don’t think they show that there are many functionally different truth-like features, which is what I mostly care about. This is also why I don’t think this provides much evidence that “Narrowing down which linear probe corresponds to the model’s beliefs might be hard.” (If you have two well-separated clusters in high dimensional space, I would expect there to be a large space of separating hyperplanes — this is my current best guess for what’s going on with your results.)
• There exists a direction which contains all linearly available information about truth, i.e. you can’t train a linear classifier to classify true from untrue texts after projecting the activations along this direction. CCS doesn’t find it. This means CCS is ill-suited for ablation-related experiments.
  • I definitely agree that vanilla CCS is ill-suited for ablation-related experiments; I think even supervised linear probes are probably not what we want for ablation-related experiments, and CCS is clearly worse than logistic regression.
  • I like this experiment. This suggests to me that there really is just functionally one truth-like feature/direction. I agree your results imply that vanilla CCS is not finding this direction geometrically, but your results make me more optimistic we can actually find this direction using CCS and maybe just a little bit more work. For example, I’d be curious to see what happens if you first get predictions from CCS, then use those predictions to get two clusters, then take the difference in means between those induced clusters. Do you get a better direction?
    • More generally I'm still interested in whether this has meaningfully different predictions from what CCS finds or not.
• Future work should use more data or more regularization than the original paper did if it wants to find features which are actually truth-like.
  • This seems like a useful finding!
• To get clean results, use CCS on UQA, and don’t get too close to GPT models. Investigating when and why CCS sometimes fails with GPT models could be a promising research direction.
  • I basically agree, though I would suggest studying non-instruction tuned encoder or encoder-decoder models like T5 or (vanilla) DeBERTa as well, since instruction tuning might affect things.
• When using CCS on GPT models, don’t use CCS only on the last layer, as probes trained on activations earlier in the network are less sensitive to the format of the input.
  • This also seems like an interesting finding, thanks!

There were a number of iterations with major tweaks. It went something like:

• I spent a while thinking about the problem conceptually, and developed a pretty strong intuition that something like this should be possible. 
• I tried to show it experimentally. There were no signs of life for a while (it turns out you need to get a bunch of details right to see any real signal -- a regime that I think is likely my comparative advantage) but I eventually got it to sometimes work using a PCA-based method. I think it took some work to make that more reliable, which led to what we refer to in the paper as CRC-TPC. 
• That method had some issues, but we also found that there was also low-hanging fruit in the sense that a good direction often appeared in one of the top 2 principal components (instead of just the top one). It also seemed kind of weird to really care about high-variance directions even when variance isn't necessarily functionally meaningful (since you can rescale subsequent layers). 
• This led to CRC-BSS, which is scale-invariant. This worked better (a bit more reliable, seemed to work well in cases where the good direction was in the top 2 principal components, etc.). But it was still based on the original intuition of clustering. 
• I started developing the intuition that "old school" or "geometric" unsupervised methods -- like clustering -- can be decent but that they're not really the right way to think about things relative to a more "functional" deep learning perspective. I also thought we should be able to do something similar without explicitly relying on linear structure in the representations, and eventually started thinking about my interpretation of what CRC is doing as finding a direction satisfying consistency properties. After another round of experimentation with the method, this finally led to CCS. 

Each stage required a number of iterations to get various details right (and even then, I'm pretty sure I could continue to improve things with more iterations like that, but decided that's not really the point of the paper or my comparative advantage). 

In general I do a lot of back and forth between thinking conceptually about the problem for long periods of time to develop intuitions (I'm extremely intuitions-driven) and periods where I focus on experiments that were inspired by those intuitions.

I feel like I have more to say on this topic, so maybe I'll write a future post about it with more details, but I'll leave it at that for now. Hopefully this is helpful.