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code/gpt2_align.py

@@ -123,3 +123,18 @@ def align_full(sd_a, sd_b, d, nh, acts_a=None, acts_b=None, method="permutation"
     hp = head_match(sd_a, sd, d, nh)
     sd, ok = keep(apply_head(sd, hp, d, nh), "heads"); info["heads"] = len(hp) if ok else 0
     return sd, info
+
+
+# --------------------------------------------------------------- embedding-row Procrustes
+def emb_procrustes(sd_a, sd_b, tok_a, tok_b, key="transformer.wte.weight", max_anchors=None):
+    """Fit the residual-basis rotation from the EMBEDDING ROWS of shared surface forms, data-free.
+
+    Rows of the two embedding tables that spell the same string are the one correspondence two
+    monolingual tokenizers genuinely share, so `min_R ||E_a[anchors] - E_b[anchors] R||` is a
+    legitimate estimate of the basis map with no corpus and no forward pass. Returns (R, n_anchors).
+    """
+    anchors = AL.vocab_anchors(tok_a, tok_b, max_anchors)
+    ia = [i for i, _ in anchors]; ib = [j for _, j in anchors]
+    Ea = np.asarray(sd_a[key], float)[ia]
+    Eb = np.asarray(sd_b[key], float)[ib]
+    return AL.procrustes_align(Ea, Eb)["R"], len(anchors)