Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning

• Although pretrained language models can be fine-tuned to produce state-of-the-art results for a very wide range of language understanding tasks, the dynamics of this process are not well understood, especially in the low data regime. Why can we use relatively vanilla gradient descent algorithms (e.g., without strong regularization) to tune a model with hundreds of millions of parameters on datasets with only hundreds or thousands of labeled examples? In this paper, we argue that analyzing fine-tuning through the lens of intrinsic dimension provides us with empirical and theoretical intuitions to explain this remarkable phenomenon. We empirically show that common pre-trained models have a very low intrinsic dimension; in other words, there exists a low dimension reparameterization that is as effective for fine-tuning as the full parameter space. For example, by optimizing only 200 trainable parameters randomly projected back into the full space, we can tune a RoBERTa model to achieve 90\% of the full parameter performance levels on MRPC. Furthermore, we empirically show that pre-training implicitly minimizes intrinsic dimension and, perhaps surprisingly, larger models tend to have lower intrinsic dimension after a fixed number of pre-training updates, at least in part explaining their extreme effectiveness. Lastly, we connect intrinsic dimensionality with low dimensional task representations and compression based generalization bounds to provide intrinsic-dimension-based generalization bounds that are independent of the full parameter count.

GPT Agents

• Working on getting the data out of the database in a useful way, so I learned how to create a view that combines multiple rows:

create or replace view combined as
    select distinct t_1.root_id, t_1.experiment_id, t_1.probe as 'probe', DATE_FORMAT(t_1.content, "%M, %Y") as 'date', t_2.content as 'text'
        from table_output as t_1
        inner join table_output as t_2
        on t_1.root_id = t_2.root_id and t_1.tag = 'date' and t_2.tag = 'trimmed';

• What’s nice about this is that I can now order results by date which gives a better way of looking through the data
• Imported the query output spreadsheet into NVivo and flailed with the importer a bit. I think I need to create a script that iterates over all the probes and creates a spreadsheet for each. It also needs to split off the probe from the content. Maybe remove the links as well? I’m conflicted about that because linking is an important thing. Maybe produce two files?

Book

• Working on coding the Biden-Trump debate in NVivo. Had to buy a transcription license. Can’t upload the video???