AF - Calendar feature geometry in GPT-2 layer 8 residual stream SAEs by Patrick Leask

The Nonlinear Library: Alignment Forum

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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Calendar feature geometry in GPT-2 layer 8 residual stream SAEs, published by Patrick Leask on August 17, 2024 on The AI Alignment Forum.
TL;DR: We demonstrate that the decoder directions of GPT-2 SAEs are highly structured by finding a historical date direction onto which projecting non-date related features lets us read off their historical time period by comparison to year features.
Calendar years are linear: there are as many years between 2000 and 2024, as there are between 1800 and 1824. Linear probes can be used to predict years of particular events from the activations of language models. Since calendar years are linear, one might think the same of other time-based features such as weekday features, however weekday activations in sparse autoencoders (SAEs) were recently found to be arranged in a circular configuration in their top principal components.
Inspired by this, we looked into weekdays, months, and most interestingly calendar years from the perspective of SAE feature decoder similarity.
For each group of calendar features, we found interesting patterns of feature splitting between sparse autoencoders of different sizes. For calendar years, we found a timeline direction that meaningfully ordered events, individuals, and concepts with respect to their historical period, which furthermore does not correspond to a principal component of the decoder directions. Finally, we introduce a simple method for finding some of these interpretable directions.
Features at different scales
We started by replicating the weekday results by performing PCA on the decoder directions of features that had high activations when prompted with days of the week, using the same GPT-2 SAEs as in this post, ranging from 768 to 98304 features. In the 768 feature SAE, we found a single weekday feature that activated strongly on all days of the week.
In the largest SAE, we found 10 weekday features, 3 of which activated on all days of the week, with the remaining 7 activating on a single day of the week each.
We found a group of features that activate primarily on specific days of the week by taking the top 20 activating samples for each feature and checking that the max activating token in each of these samples was the specific weekday. We found the first two principal components for this set of features, and projected the features that activate on any day or number of days from all SAEs onto these directions.
The labeled features are those that activate on a single day across all SAEs, with the multi-day features unlabeled to maintain legibility.
The smallest SAE (blue) has a single feature that activates on all weekday tokens, and lies near the mean of all the weekday features. The largest SAEs learn features for each day of the week, plus additional multi-day features. Across SAE sizes, the single day features form clusters.
In each of these examples, the smallest SAE has a single feature that splits into many specific features that seem of roughly the same importance. With calendar years, however, the situation is more complex. The same method of finding the principal components for single year features between 1900 and 2020 only succeeds in a few 21st century features, and nothing from the 20th century.
There is also a group of single year features in a smaller SAE in the center of the plot, suggesting these principal components do not explain variance in them.
The plot below shows the years for which each of the features is active, with the x-axis being years from 1950 to 2020, the y-axis being separate features, and the colored bars indicating the periods of year for which that feature is active. Only in the largest SAEs do you see more than a few single calendar year features, with most of the features activating on ranges of years, or other patterns such as the start and end...