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"""GPT-2 W_U row-norm frequency check.
At-scale test of the jspace-nanogpt geometric finding: at char scale,
the unembedding row norms anti-correlate with token frequency
(r(||W_U[k]||, log10 f) = -0.693, Spearman -0.808) and this geometry is
LEARNED (r ~ 0 at init). Does it generalize to a real LM with
V = 50,257?
Cheap by design: load lm_head/wte rows, take row norms, correlate against
unigram token counts from a corpus. No Jacobian, no training, no GPU.
Usage:
.venv/bin/python src/wu_row_norm_check.py [--models gpt2,gpt2-medium]
Corpus: wikitext-103-raw-v1 (train) from HF. Counts are token-level
unigram frequencies after GPT-2 byte-level BPE encoding.
"""
import argparse
import time
import numpy as np
import safetensors.torch
import torch
from huggingface_hub import hf_hub_download
from transformers import GPT2TokenizerFast
WIKITEXT_REPO = "Salesforce/wikitext"
WIKITEXT_PARQUETS = [
"wikitext-103-raw-v1/train-00000-of-00002.parquet",
"wikitext-103-raw-v1/train-00001-of-00002.parquet",
]
def pearson(x, y):
x = x - x.mean()
y = y - y.mean()
denom = np.sqrt((x * x).sum() * (y * y).sum())
return float((x * y).sum() / denom) if denom > 0 else float("nan")
def spearman(x, y):
def rankdata(a):
order = np.argsort(a, kind="mergesort")
ranks = np.empty_like(order, dtype=float)
ranks[order] = np.arange(1, a.size + 1)
return ranks
return pearson(rankdata(x), rankdata(y))
def load_wte(model_id: str) -> np.ndarray:
path = hf_hub_download(model_id, "model.safetensors")
st = safetensors.torch.load_file(path)
candidates = ["transformer.wte.weight", "wte.weight", "model.embed_tokens.weight"]
key = next((k for k in candidates if k in st), None)
if key is None:
raise KeyError(
f"no wte/embedding weight found in {model_id}; "
f"have: {sorted(st.keys())[:10]} ..."
)
wte = st[key]
print(f"[{model_id}] {key} {tuple(wte.shape)} dtype={wte.dtype}")
# GPT-2 ties lm_head to wte, so row norms of wte == row norms of W_U.
return torch.norm(wte.float(), dim=1).numpy()
def load_corpus() -> list[str]:
import pyarrow.parquet as pq
texts: list[str] = []
for name in WIKITEXT_PARQUETS:
path = hf_hub_download(WIKITEXT_REPO, name, repo_type="dataset")
print(f"loading corpus shard from {path}")
table = pq.read_table(path, columns=["text"])
texts.extend(table.column("text").to_pylist())
print(f"corpus: {len(texts)} rows")
return texts
def count_tokens(tokenizer, texts: list[str], batch_size: int = 1000) -> np.ndarray:
counts = np.zeros(tokenizer.vocab_size, dtype=np.int64)
n_tokens = 0
t0 = time.time()
for start in range(0, len(texts), batch_size):
chunk = texts[start : start + batch_size]
enc = tokenizer(chunk, add_special_tokens=False)
for ids in enc["input_ids"]:
np.add.at(counts, ids, 1)
n_tokens += len(ids)
if (start // batch_size) % 20 == 0:
print(
f" rows {start}/{len(texts)} tokens {n_tokens:,} "
f"elapsed {time.time() - t0:.0f}s"
)
print(f"done: {n_tokens:,} tokens in {time.time() - t0:.0f}s")
return counts
def report(model_id: str, norms: np.ndarray, counts: np.ndarray, tokenizer):
freqs = counts.astype(np.float64)
seen = freqs > 0
logf = np.log10(freqs + 1.0) # smoothed; +1 keeps unseen tokens finite
def r_raw(mask):
return pearson(freqs[mask], norms[mask])
def r_log(mask):
return pearson(logf[mask], norms[mask])
def r_sp(mask):
return spearman(freqs[mask], norms[mask])
n = norms.size
n_seen = int(seen.sum())
print(f"\n===== {model_id} ===== V={n} tokens seen={n_seen} "
f"({100 * n_seen / n:.1f}%)")
print(f" r(raw freq, norm) all V: {r_raw(np.ones(n, bool)):+.3f}")
print(f" r(raw freq, norm) seen only: {r_raw(seen):+.3f}")
print(f" r(log10 freq, norm) all V: {r_log(np.ones(n, bool)):+.3f}")
print(f" r(log10 freq, norm) seen only: {r_log(seen):+.3f}")
for thr in (5, 100, 1000):
m = freqs >= thr
print(f" r(log10 freq, norm) freq>={thr:<6} "
f"(n={int(m.sum()):>5}): {r_log(m):+.3f}")
print(f" Spearman(raw, norm) seen only: {r_sp(seen):+.3f}")
# Decile table: quantiles of log-frequency vs mean norm.
if n_seen > 10:
qs = np.quantile(logf[seen], np.linspace(0, 1, 11))
idx = np.digitize(logf, qs[1:-1])
print(" log10-freq decile -> mean norm:")
for d in range(10):
m = (idx == d) & seen
if m.sum() == 0:
continue
lo, hi = qs[d], qs[d + 1]
print(f" [{lo:5.2f},{hi:5.2f}] n={int(m.sum()):>5} "
f"mean norm={norms[m].mean():.3f}")
# Top tokens by norm (narrative color).
order = np.argsort(norms)[::-1][:15]
print(" top-15 tokens by row norm (token | norm | count | rank-by-freq):")
for i in order:
tok = tokenizer.decode([int(i)])
rank = int((freqs > freqs[i]).sum()) + 1
print(f" {tok!r:>14} {norms[i]:.3f} {int(freqs[i]):>8,} #{rank:,}")
return {
"model": model_id,
"r_raw_all": r_raw(np.ones(n, bool)),
"r_log_all": r_log(np.ones(n, bool)),
"r_log_seen": r_log(seen),
"spearman_seen": r_sp(seen),
"n_seen": n_seen,
}
def main():
ap = argparse.ArgumentParser()
ap.add_argument("--models", default="gpt2", help="comma-separated HF ids")
ap.add_argument("--no-corpus", action="store_true",
help="skip tokenization (use saved counts if present)")
args = ap.parse_args()
tokenizer = GPT2TokenizerFast.from_pretrained("openai-community/gpt2")
if args.no_corpus:
counts = np.load("/tmp/wu_counts.npy")
else:
texts = load_corpus()
counts = count_tokens(tokenizer, texts)
np.save("/tmp/wu_counts.npy", counts)
results = []
for mid in args.models.split(","):
mid = mid.strip()
norms = load_wte(mid)
results.append(report(mid, norms, counts, tokenizer))
print("\n===== SUMMARY =====")
for r_ in results:
print(
f"{r_['model']}: r(raw)={r_['r_raw_all']:+.3f} "
f"r(log10, all V)={r_['r_log_all']:+.3f} "
f"r(log10, seen)={r_['r_log_seen']:+.3f} "
f"Spearman(seen)={r_['spearman_seen']:+.3f}"
)
if __name__ == "__main__":
main()
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