# 27

I made a series of mech interp puzzles for my MATS scholars, which seemed well received, so I thought I'd share them more widely! I'll be posting a sequence of puzzles, approx one a week - these are real questions about models which I think are interesting, and where thinking about them should teach you some real principle about how to think about mech interp. Here's a short one to start:

Mech Interp Puzzle 1: This is a histogram of the pairwise cosine similarity of the embedding of tokens in GPT-Neo (125M language model). Note that the mean is very high! (>0.9) Is this surprising? Why does this happen?

Bonus question: Here's the same histogram for GPT-2 Small, with a mean closer to 0.3. Is this surprising? What, if anything, can you infer from the fact that they differ?

Code:

``````!pip install transformer_lens plotly
from transformer_lens import HookedTransformer
import plotly.express as px
import torch
model = HookedTransformer.from_pretrained("gpt-neo-small")
subsample = torch.randperm(model.cfg.d_vocab)[:5000].to(model.cfg.device)
W_E = model.W_E[subsample] # Take a random subset of 5,000 for memory reasons
W_E_normed = W_E / W_E.norm(dim=-1, keepdim=True) # [d_vocab, d_model]
cosine_sims = W_E_normed @ W_E_normed.T # [d_vocab, d_vocab]
px.histogram(cosine_sims.flatten().detach().cpu().numpy(), title="Pairwise cosine sims of embedding")
``````

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