IC-867In GPT-2 prefix-tuned on the emotion dataset, attention over prefix positions is nearly constant across inputs, collapsing the effective bias subspace to a single direction in most layers

Aleksandar Petrov, Philip Torr, Adel Bibi

SourceWhen Do Prompting and Prefix-Tuning Work? A Theory of Capabilities and Limitations

The paper trains a prefix of size 10 on GPT-2 for the emotion classification task and examines the range of attention (1st to 99th percentile) over the 10 prefix positions across 12 layers. For most layers, including layer 1, the attention each prefix position receives is almost constant regardless of the input, meaning the effective bias is a single fixed vector applied to the attention layer output. Only layer 3 shows three prefix positions with large variation, yielding a 3-dimensional effective subspace where the input governs which bias vector is selected. This suggests GPT-2 does not fully utilize the representational capacity available to the prefix.

Evidence
correlational
Key metric
GPT-2 prefix size 10, emotion dataset: layer 1 attention over prefix positions is nearly constant (collapsed subspace); layer 3 has three prefix positions with large variation (3-dimensional effective subspace); range shown as 1st to 99th percentile across 12 layers
Caveat
Single prefix trained on one dataset (emotion). The paper notes this is for illustration and does not test other tasks or prefix sizes on GPT-2.
Model
GPT-2
Methods
Prefix Tuning / Li & Liang 2021 (Prefix-tuning) [primary]
Related work
Prefix Tuning / Li & Liang 2021 (Prefix-tuning) [builds-on]
Related findings
IC-866
Extraction
automatic-extraction