Proof embeddings — vector_behavior
Vectors for the proofs, made with the same models and the same pooling as the statement spaces already in this repo, so the two are directly comparable.
| directory | what one row is | rows | dim |
|---|---|---|---|
proof_emb/e5-large-v2_theorem/ |
one theorem's whole tactic script | 61,542 | 1024 |
proof_emb/e5-large-v2_step/ |
one tactic invocation with its goal state | ~259,580 | 1024 |
proof_emb/e5-mistral-7b-instruct_theorem/ |
one theorem's whole tactic script | 61,542 | 4096 |
Each directory holds embeddings.npy, idx_to_name.json, meta.json, and for the step
granularity step_meta.json.gz with the theorem, step index and premises per row.
Lining a proof up with its statement
Row i of a proof space is the theorem named at idx_to_name.json[i]. The statement
spaces are keyed the same way, so going between them is a name lookup:
import json, numpy as np
P = np.load("proof_emb/e5-large-v2_theorem/embeddings.npy")
pn = json.load(open("proof_emb/e5-large-v2_theorem/idx_to_name.json"))
S = np.load("embeddings/e5_large/embeddings.npy")
sn = json.load(open("embeddings/e5_large/idx_to_name.json"))
si = {n: i for i, n in enumerate(sn)}
both = [(i, si[n]) for i, n in enumerate(pn) if n in si] # 56,467 theorems
pi, sj = zip(*both)
proof_vecs, stmt_vecs = P[list(pi)], S[list(sj)]
56,467 of the 61,542 proved theorems are also in the 99,552-theorem statement pool. The rest have proofs but no statement embedding.
For step rows, idx_to_name.json[i] is "<theorem>#<step index>"; split on # to get
back to the theorem.
Truncation
Proofs are much longer than statements and everything is encoded at 512 tokens, so long
tactic scripts are cut off. The exact count is in each directory's meta.json as
n_truncated / frac_truncated — check it before drawing conclusions about long proofs.
Please read this before using them
In the parent study proofs are held back on purpose. Every claim about discovered structure is checked by asking whether the grouped theorems share proof premises, and that check has force only because no encoder was ever shown a proof.
These vectors break that. Any structure found with them cannot then be validated against proofs — that is confirming a finding with the thing that produced it. Validate with something else: human judgement, a held-out corpus, or the source organisation.
The same applies to real_pairs_verified.json.gz in this repo, which is the answer key
for the pairing step rather than the discovery step.