This research was completed for London AI Safety Research (LASR) Labs 2024. The team was supervised by @Stefan Heimershiem (Apollo Research). Find out more about the program and express interest in upcoming iterations here.
This video is a short overview of the project presented on the final day of the LASR Labs. Note that the paper was updated since then.
We study the effects of perturbing Transformer activations, building upon recent work by Gurnee, Lindsey, and Heimersheim & Mendel. Specifically, we interpolate between model-generated residual stream activations, and measure the change in the model output. Our initial results suggest that:
The residual stream of a trained Transformer can be divided into stable regions. Within these regions, small changes in model activations lead to minimal changes in output. However, at region boundaries, small changes can lead to significant output differences.
These regions emerge during training and evolves with model scale. Randomly initialized models do not exhibit these stable regions, but as training progresses or model size increases, the boundaries between regions become sharper.
These stable regions appear to correspond to semantic distinctions. Dissimilar prompts occupy different regions, and activations from different regions produce different next token predictions.
While further investigation is needed, these regions appear to be much larger than polytopes studied by Hanin & Rolnick and Black et al.
We believe that studying stable regions can improve our understanding of how neural networks work. The extent to which this understanding is useful for safety is an active topic of discussion 123.
The updated paper with additional plots in the appendix is not yet visible or arxiv, but you can read it here.
Is this consistent with the interpretation of self-attention as approximating (large) steps in a Hopfield network?
I have an old hypothesis about this which I might finally get to see tested. The idea is that the feedforward networks of a transformer create little attractor basins. Reasoning is twofold: the QK-circuit only passes very limited information to the OV circuit as to what information is present in other streams, which introduces noise into the residual stream during attention layers. Seeing this, I guess that another reason might be due to inferring concepts from limited information:
Consider that the prompts “The German physicist with the wacky hair is called” and “General relativity was first laid out by” will both lead to “Albert Einstein”. Both of them will likely land in different parts of an attractor basin which will converge.
You can measure which parts of the network are doing the compression using differential optimization, in which we take d[OUTPUT]/d[INPUT] as normal, and compare to d[OUTPUT]/d[INPUT] when the activations of part of the network are “frozen”. Moving from one region to another you’d see a positive value while in one basin, a large negative value at the border, and then another positive value in the next region.
I believe there are two phenomena happening during training
Predictions corresponding to the same stable region become more similar, i.e. stable regions become more stable. We can observe this in the animations.
Existing regions split, resulting in more regions.
I hypothesize that
could be some kind of error correction. Models learn to rectify errors coming from superposition interference or another kind of noise.
could be interpreted as more capable models picking up on subtler differences between the prompts and adjusting their predictions.