code/gpt2_align.py

"""GPT-2 (Conv1D, transposed-weight) symmetry factors. mergeschool's generic aligners assume the
row-major nn.Linear convention, so the residual/MLP/head maps are written out explicitly here for
the goldfish family. Every factor below is exact (LayerNorm is permutation-equivariant; GELU is
elementwise; GPT-2 uses learned positional embeddings so head permutation is exact)."""
import numpy as np
import sys
sys.path.insert(0, "/root/mergeability/src")
from mergeschool.core import alignment as AL


def _pre(n):
    p = n.split(".")
    for i, x in enumerate(p):
        if x.isdigit():
            return ".".join(p[:i + 1]) + "."
    return None


def layers_of(sd):
    return sorted({int(k.split(".")[2]) for k in sd if k.startswith("transformer.h.")})


# --------------------------------------------------------------- residual basis (d)
def apply_resid(sd, d, perm=None, R=None):
    """Carry sd into another model's residual basis. perm: index array (exact). R: (d,d) orthogonal
    with acts_B @ R ~ acts_A (exact up to LayerNorm's elementwise scale, which is left alone)."""
    out = {}
    P = (lambda W, ax: np.take(W, perm, axis=ax)) if perm is not None else None
    for name, W in sd.items():
        W = np.asarray(W, float)
        n = name
        try:
            if n.endswith("wte.weight") or n.endswith("wpe.weight") or n.endswith("lm_head.weight"):
                out[n] = P(W, 1) if P else W @ R
            elif ("ln_" in n or n.endswith("ln_f.weight") or n.endswith("ln_f.bias")) and W.ndim == 1:
                out[n] = P(W, 0) if P else W            # norm affine: exact under perm, kept under R
            elif n.endswith("attn.c_attn.weight") or n.endswith("mlp.c_fc.weight"):
                out[n] = P(W, 0) if P else R.T @ W      # (d, out): residual is the INPUT axis
            elif n.endswith("attn.c_proj.weight") or n.endswith("mlp.c_proj.weight"):
                out[n] = P(W, 1) if P else W @ R        # (in, d): residual is the OUTPUT axis
            elif (n.endswith("attn.c_proj.bias") or n.endswith("mlp.c_proj.bias")) and W.shape[0] == d:
                out[n] = P(W, 0) if P else W @ R
            else:
                out[n] = W
        except Exception:
            out[n] = W
    return out


# --------------------------------------------------------------- free MLP hidden axis (4d)
def mlp_match(sd_a, sd_b):
    perms = {}
    for L in layers_of(sd_a):
        fa, fb = f"transformer.h.{L}.mlp.c_fc.weight", f"transformer.h.{L}.mlp.c_proj.weight"
        A = np.asarray(sd_a[fa], float).T @ np.asarray(sd_b[fa], float)          # (4d,d)@(d,4d)
        A = A + np.asarray(sd_a[fb], float) @ np.asarray(sd_b[fb], float).T
        perms[L] = AL._assignment(A)
    return perms


def apply_mlp(sd, perms):
    out = dict(sd)
    for L, q in perms.items():
        out[f"transformer.h.{L}.mlp.c_fc.weight"] = np.asarray(sd[f"transformer.h.{L}.mlp.c_fc.weight"], float)[:, q]
        out[f"transformer.h.{L}.mlp.c_fc.bias"] = np.asarray(sd[f"transformer.h.{L}.mlp.c_fc.bias"], float)[q]
        out[f"transformer.h.{L}.mlp.c_proj.weight"] = np.asarray(sd[f"transformer.h.{L}.mlp.c_proj.weight"], float)[q]
    return out


# --------------------------------------------------------------- attention heads
def head_match(sd_a, sd_b, d, nh):
    hd, perms = d // nh, {}
    for L in layers_of(sd_a):
        ca, cp = f"transformer.h.{L}.attn.c_attn.weight", f"transformer.h.{L}.attn.c_proj.weight"
        gain = np.zeros((nh, nh))
        for blk in range(3):                                   # q | k | v, each (d, d)
            A = np.asarray(sd_a[ca], float)[:, blk * d:(blk + 1) * d].reshape(d, nh, hd)
            B = np.asarray(sd_b[ca], float)[:, blk * d:(blk + 1) * d].reshape(d, nh, hd)
            gain += np.einsum("xiy,xjy->ij", A, B)
        A = np.asarray(sd_a[cp], float).reshape(nh, hd, d)
        B = np.asarray(sd_b[cp], float).reshape(nh, hd, d)
        gain += np.einsum("ixy,jxy->ij", A, B)
        perms[L] = AL._assignment(gain)
    return perms


def apply_head(sd, perms, d, nh):
    hd, out = d // nh, dict(sd)
    for L, h in perms.items():
        ca, cb = f"transformer.h.{L}.attn.c_attn.weight", f"transformer.h.{L}.attn.c_attn.bias"
        cp = f"transformer.h.{L}.attn.c_proj.weight"
        W = np.asarray(sd[ca], float).copy()
        Bv = np.asarray(sd[cb], float).copy()
        for blk in range(3):
            s = slice(blk * d, (blk + 1) * d)
            W[:, s] = W[:, s].reshape(d, nh, hd)[:, h].reshape(d, d)
            Bv[s] = Bv[s].reshape(nh, hd)[h].reshape(d)
        out[ca], out[cb] = W, Bv
        out[cp] = np.asarray(sd[cp], float).reshape(nh, hd, d)[h].reshape(d, d)
    return out


# --------------------------------------------------------------- composition with accept-each
def align_full(sd_a, sd_b, d, nh, acts_a=None, acts_b=None, method="permutation", body_keys=None,
               accept_each=True):
    info = {"residual": False, "mlp": 0, "heads": 0, "rejected": []}
    sd = dict(sd_b)

    def keep(cand, tag):
        if not accept_each:
            return cand, True
        if AL.block_normalised_distance(sd_a, cand, body_keys) <= AL.block_normalised_distance(sd_a, sd, body_keys):
            return cand, True
        info["rejected"].append(tag)
        return sd, False

    if acts_a is not None and acts_b is not None:
        kind, obj = AL.residual_basis_map(acts_a, acts_b, method=method)
        cand = apply_resid(sd, d, perm=(obj if kind == "perm" else None), R=(obj if kind == "R" else None))
        sd, ok = keep(cand, "residual"); info["residual"] = ok
    mp = mlp_match(sd_a, sd)
    sd, ok = keep(apply_mlp(sd, mp), "mlp"); info["mlp"] = len(mp) if ok else 0
    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)