A Mystery About High Dimensional Concept Encoding

Fabien Roger

Epistemic status: I ran some experiments with surprising results, and I don’t have a clear intuition of what it means for the way concepts are encoded in model activations. Help is welcome!

[EDIT] I made a mistake while analyzing the data, and it changes some of the early interpretations of the results. It doesn't change the fact that using a classifier is a poor way of finding the directions which matter most, but it lifts most of the mystery.

[EDIT 2] I found a satisfying explanation of the phenomenon in Haghighatkhah, 2022. Helpful pictures are included in the paper.

The mystery

If you want to find the “direction” corresponding to a concept in a Large Language Model, “natural” methods fail to find a crucial direction: you need to remove >5 dimensions for the model’s ability to use the concept to be affected. This seems to show that the concept is encoded in “a large number of dimensions”. But adversarial methods are able to find one direction which is quite significant (large effect when “removed”). How is that? What does that mean about how information is encoded by LLM?

More details

Let’s say you want to remove the concept of gender from a GPT-2’s activations between layers 23 and 24 (out of 48). (Both are >100 dimensional vectors). A natural thing to do is to have a bunch of sentences about guys and girls, train a linear classifier to predict if the sentence is about guys or girls, and use the direction the linear classifier gives you as the “direction corresponding to the concept of gender”. Then, you can project GPT-2’s activation (at inference time) on the plane orthogonal to the direction to have the model not take gender into account anymore.

This naive attempt fails: you can train a classifier to classify sentences as “guy-sentence” or “girl-sentence” based on the projected activations, and it will get 90% accuracy (down from 95%), and if you project GPT-2’s activation in the middle of the network, it will make only a tiny difference in the output of the network. This is a method called INLP (Ravfogel, 2020) (the original technique removes multiple directions to obtain a measurable effect).

But if you jointly train the projection and the linear classifier in an adversarial setup, you will get very different results: accuracy drops to ~50%, and GPT-2’s behavior changes much more, and sometimes outputs “she” when “he” is more appropriate. This is called RLACE (Ravfogel, 2022).

Why is that?

The best explanation I have found to explain this discrepancy is that INLP (= using a classifier) finds the direction with ~~the largest difference~~ a clear separation, and it has almost no impact on model behavior. While RLACE (= using an adversarialy trained classifier and projection) finds a different direction (cosine similarity of 0.6), a direction where there is ~~a clear separation~~ a large difference, and it has a much greater impact on model behavior.

[Edit (original images were wrong: titles were swapped)]

[Edit] Here is what it looks like in the plane defined by the directions found by INLP and RLACE: INLP finds a clear separation, and RLACE uses changes with large magnitude as well as very large features.

Is this something special about the distribution of neural activations?

No: if you use another “natural” distribution like GLOVE word encodings (which Ravfogel’s papers study), you will find that INLP fails to remove linearly available information, while RLACE is much better at it.

However, that’s not that surprising given the explanation above: the directions where there is a crisp distinction between two opposite concepts are not the one along which the magnitude of the changes is larger.

But just because information is linearly available doesn’t mean the network will be able to use it, especially if the direction you remove is one where the magnitude of the activations is the large: I’m surprised by how little INLP affects model behavior.

What does that mean about how concepts are encoded?

I have already seen people claiming that the large features seen in LLMs are probably the sign that models are encoding crisp concepts. I think that this experiment provides evidence of the opposite: it seems that projecting along directions where activations differ a lot is less impactful than projecting along directions where activations differ less, but in a crisper way. I would have expected the opposite to be true, and I’m open to explanations of why networks don’t seem to use directions along which activations maximally vary. (This part of the mystery was entirely due to a mistake I made while analyzing the results.)

[Edit] I have already seen people claiming that the large features seen in LLMs are probably the sign that models are encoding crisp concepts. This experiment seems to support this conclusion: projecting down the directions where there is a crisp distinction make little to no difference, but projecting down the directions where there are large activations seems to affect model behavior a lot: the model seems to not rely on the crisp feature it builds, and instead relies on other features with large magnitude.

References and notebooks with the experiments

The paper describing RLACE, and comparing it with INLP: Linear Adversarial Concept Erasure (Ravfogel 2022) https://arxiv.org/pdf/2201.12091.pdf. Note: This paper also shows that RLACE gives the same results as INLP if you choose some special loss function for RLACE. So the difference between RLACE and INLP has to do about “how” you mix guys’ and girls’ datapoints, and RLACE default loss (which encourages data “separation”) is better than the loss which encourages large difference before projection.
The paper describing INLP: Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection (Ravfogel 2020) https://arxiv.org/pdf/2004.07667.pdf
Experiments with projecting GPT-2’s activations by RLACE and INLP. For simplicity, INLP is used without “neutral” sentences. Also contains INLP with weight-decay regularization, and TSNE visualization. (Note: rerunning the notebook will give slightly different results because seeding fails with RLACE) https://colab.research.google.com/drive/1EvF61IOG9G9hXsGliNaS2Wv-sD9ZXugl?usp=sharing
More experiments with RLACE on GPT-2’s activations: results are not conclusive, but at least RLACE always “does something” (while that’s not true with INLP). https://colab.research.google.com/drive/1R5PmdKdgVxVMoxmrFPZARZk-V38tdztN?usp=sharing

Appendix

Is it something specific to gender?

I tried exactly one more concept: political left vs political right, and I got the exact same results. See here: https://colab.research.google.com/drive/1wXQiiqU9Iy0lPCC92JvtK20kH5HKfWQr?usp=sharing

[Edit] Is it something specific to model trained with dropout?

Question asked by Neel Nada

No, similar results were found with GPT-Neo-125M (which I think is trained without dropout). Results can be found here https://colab.research.google.com/drive/1we8CrqMjgDUW2n5HIqlcoSeZxxODqXul?usp=sharing

Note: in the experiments I ran on GPT-Neo-125M, RLACE found a direction with extremely large direction, and impacted abilities of the model on all themes. I don't know if it's related to dropout or not.

[Edit] Can you have a bigger impact by swapping instead of projecting to zero?

Question asked by Neel Nada

Yes! After the prompt "Ezra is such a prick! Yesterday", the original model uses uses "he" to describe the subject on 3/3 completion, 2/3 with the model where data is "projected to median along the direction", and 0/3 with the model where data is "swapped along the direction" (with RLACE). It doesn't change the fact that INLP has a very small impact. And it doesn't

See here for more examples https://colab.research.google.com/drive/1IHL7HIWo6Ez0QHajMaSRoQZRyTg-CEOA?usp=sharing

[Edit] Here are some generations

For each distinct prompts, each model generates three completions with different seeds (each line is done with the same seed).

prompts	default model	edit model with RLACE	edit model with INLP
In a shocking finding, scientist discovered a herd of unicorns	. Not only that, but these unicorns are being stalked by a demonic being. To put things into perspective, a human being that crosses into this land	. Not only that, but these unicorns are being treated as a valuable resource by the farmers in the area and are being used to provide food to local villagers	. Not only that, but these unicorns are being stalked by a pack of wolves!" "They are hunting unicorns that have been caught between
In a shocking finding, scientist discovered a herd of unicorns	had been kept as virtual pets on the dark web. 'The fact that they aren't real and that they really only exist on the dark web is	had been kept, without any food or water, in their own urine since they were born." The study found that newborn unicorns were kept in their	had been kept as virtual pets on the dark web. 'The fact that they aren't real and that they really only exist on the dark web is
In a shocking finding, scientist discovered a herd of unicorns	in the United States that was previously almost unheard of because they live in the mountainous regions of central Mexico. The unicorns in the area are more closely	in the United States that weighs 2,500lb (1,250kg) each Professor of Veterinary Science at California State University and her team, with	in the United States that was previously almost unheard of because they live in the mountainous regions of central Mexico. The unicorns in the area are more closely
Brigitta is such a prick! Yesterday,	after I'd left, she began to talk to me with a sort of pride and arrogance, making me feel like I'd been hit by a speeding train.	after I'd left, she began to talk to me with a sort of pride and arrogance, making me feel like I'd been hit by a speeding train.	after I'd left, she began to talk to me with a sort of pride and arrogance, making me feel like I'd been hit by a speeding train.
Brigitta is such a prick! Yesterday,	she and her mate were out on the deck. I was having tea at the front of their cabin. I heard them talk. One was saying that they had	by the way, I had my three-day old daughter with me, but we made the mistake of going out together in this fashion. After we had parted	by the way, I had my three-day old daughter with me, and we made the three-hour journey to see this great lady, and what did
Brigitta is such a prick! Yesterday,	as I was coming home from the office, she called with her husband to my room and took one of my coats from my dressing-table. She sat close	as I was coming home from the office, she called with her child to my room, and when I went up to her and opened the door, she came	as I was coming home from the office, she called with her husband to my room, where I was lying. She began by saying that her brother and himself
Ezra is such a prick! Yesterday,	he was complaining about being at a bar, and being offered a job. How did he know it was from him?! Oh, I'm so glad there were	after I'd gotten back at them for having stolen my stuff, I went over to Ezra's house and said goodbye to him. I had already told him that	he was complaining about being at a bar, and being offered a job. How did he know it was a bar?! Oh, I don't know. So
Ezra is such a prick! Yesterday,	Ezra and I, as well as three of the staff, were walking to his office to make an appointment when we were accosted by a black woman who	she and her pals pulled a fake hooker out her front door to make money for the trip to San Diego. They left this little lady tied to their car	Ezra and I, as well as three of the staff, were walking to his office to make an appointment when we were accosted by a black woman who
Ezra is such a prick! Yesterday,	as I was coming home from the office, he called with his wife to my lodgings one evening. He said he wished I would give him a hand	as I was coming home from the office, he called with his wife to my lodgings one night. He said he would let me know the next morning	as I was coming home from the office, he called with his wife to my lodgings one evening. He said he wished I would give him a hand

[-]Neel Nanda2y40

Interesting results, thanks for sharing! To clarify, what exactly are you doing after identifying a direction vector? Projecting and setting its coordinate to zero? Actively reversing it?

And how do these results compare to the dumb approach of just taking the gradient of the logit difference at that layer, and using that as your direction?

Some ad-hoc hypotheses for what might be going on:

An underlying thing is probably that the model is representing several correlated features - is_woman, is_wearing_a_dress, has_long_hair, etc. Even if you can properly isolate the is_woman direction, just deleting this may not matter that much, esp if the answer is obvious?
- I'm not sure which method this will harm more though, since presumably they'll pick up on a direction that's the average of all features weighted by their correlation with is_woman, ish.
IMO, a better metric here is the difference in the she vs he logits, rather than just the accuracy - that may be a better way of picking up on whether you've found a meaningful direction?
GPT-2 is trained with dropout on the residual stream, which may fuck with things? It's presumably learned at least some redundancy to cope with ablations.
- To test this, try replicating on GPT-Neo 125M? That doesn't have dropout.
Gender is probably just a pretty obvious thing, that's fairly overdetermined, and breaking an overdetermined thing by removing a particular concept is hard.
I have a fuzzy intuition that it's easier to break models than to insert/edit a concept? I'd weakly predict that your second method will damage model performance in general more, even on non-gender-y tasks. Maybe it's learned to shove the model off distribution in a certain way, or exploits some feature of how the model is doing superposition where it adds in two features the model doesn't expect to see at the same time, which fucks with things? Idk, these are all random ad-hoc guesses.
- Another way of phrasing this - I'd weakly predict that for any set of, say, 10 prompts, even with no real connection, you could learn a direction that fucks with all of them, just because it's not that hard to break a model with access to its internal activations (if this is false, I'd love to know!). Clearly, that direction isn't going to have any conceptual meaning!
One concrete experiment to test the above - what happens if you reverse the direction, rather than removing it? (Ie, take v - 2(v . gender_dir) gender_dir, not v - (v . gender_dir) gender_dir). If RLACE can significantly reverse accuracy to favour she over he incorrectly, that feels interesting to me!

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