Size Comparison Congruence —- SUMMARIZE:

• Dot products of tokens after embedding layer
  • large
  • tokens in general
  • average over dataset of single tokens
  • For multiple tokens for a word, get the average of each token's embeddings
  • Dot Product of large synonyms
• Dot products of token and all neurons (congruence)
  • Compute dot products for "tall" and "large", and compare the similarities (eg. which are in the top) AND identify their common top neurons
• Dot products of input after first MLP layer

• GPT-2-Large

GPT-2-Small

https://colab.research.google.com/drive/18JcQcn7TKhN-1ULNjqQqvst9yJ6ZDhAA

Dot products of tokens after embedding layer

• In “large”, we run a few tests to find that adjectives with semantic similarity to “large” in terms of size, such as “huge”, have a high dot product. We take the dot product right after the first embedding layer.
• In “average over dataset of single tokens”, we generate 100 random tokens put through the first embedding layer and plot the histogram of their dot products.
• In Dot Product of large synonyms, we obtain this dot product histogram only for single tokens that are synonyms of “large”

Histogram of dot product of 100 random tokens

AVG: 4.9035

dot product histogram only for single tokens that are synonyms of “large”

AVG: >6

We observe that the “large synonyms” have dot product that’s higher than average

TO DO: Perform actual hypothesis testing to get p-value

ISSUE: This takes pairs as observations, meaning many observations are repeated in pairs. What problems arise from this? [try to identify as many issues as poss]

• To ChatGPT: I am taking the dot product of 100 items, and making a histogram of the dot products. This takes pairs as observations, meaning many observations are repeated in pairs. Can I do hypothesis testing on this to see how many deviations away a subset is from the average value? What problems arise from this?