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"""Cycle-gain decomposition of the nudge loop at the DOMINANT MODE (user directive: measure
the explosion's cause). Run the trainer-faithful nudged relax, let the residual converge to the
dominant mode, then difference consecutive sweeps to get per-stage amplification factors ALONG
THE ACTUAL MODE (norms audits failed; alignment is everything):
gH = |dd_11| / |dz_11| top stage: beta*NBT*CE-curvature read
gV(l) = |dd_l| / |dd_{l+1}| down-chain vjp through block l+1
gF(l) = |do_l| / |dz_{l-1}| up-chain rebuild through block l
closure: gH * prod(gV) ~ dd-chain, rebuild adds dd_l -> next dz; rho_meas from residuals.
Plus per-head carrier analysis for blocks 8-11 (share of the mode through each head, its
max|logit| and attention entropy) -> names the physical carrier (switching-regime heads?).
Control column for the batch-noise question: per-batch BP u1 vs 8-batch-mean BP u1 overlap."""
import argparse, pickle
import numpy as np, torch, torch.nn as nn, torch.nn.functional as F
from pathlib import Path
ap = argparse.ArgumentParser()
ap.add_argument('--ckpts', default='plain:195000,cent:195000,plain:210000')
ap.add_argument('--K', type=int, default=16)
ap.add_argument('--beta', type=float, default=3e-3)
a = ap.parse_args()
dev = 'cuda'
torch.manual_seed(7)
B, T = 8, 256
class RMSNorm(nn.Module):
def __init__(self, C, eps=1e-6):
super().__init__(); self.g = nn.Parameter(torch.ones(C)); self.eps = eps
def forward(self, x):
return x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps) * self.g
class SwiGLU(nn.Module):
def __init__(self, C):
super().__init__()
h = ((8 * C // 3) + 63) // 64 * 64
self.w1 = nn.Linear(C, h, bias=False); self.w3 = nn.Linear(C, h, bias=False)
self.w2 = nn.Linear(h, C, bias=False)
def forward(self, x):
return self.w2(F.silu(self.w1(x)) * self.w3(x))
class Olmo2Attn(nn.Module):
def __init__(self, C, H, T):
super().__init__()
self.H, self.hd = H, C // H
self.qkv = nn.Linear(C, 3 * C, bias=False); self.proj = nn.Linear(C, C, bias=False)
self.qn, self.kn = RMSNorm(C), RMSNorm(C)
inv = 1.0 / (500000.0 ** (torch.arange(0, self.hd, 2).float() / self.hd))
fr = torch.outer(torch.arange(T).float(), inv)
self.register_buffer('rc', fr.cos(), persistent=False)
self.register_buffer('rs', fr.sin(), persistent=False)
def rope(self, x):
Tn = x.shape[2]
x1, x2 = x[..., ::2], x[..., 1::2]
c, s = self.rc[None, None, :Tn].to(x.dtype), self.rs[None, None, :Tn].to(x.dtype)
return torch.stack((x1 * c - x2 * s, x1 * s + x2 * c), dim=-1).flatten(-2)
def heads(self, x):
"""per-head attention outputs (pre-proj) + logit stats + entropy"""
Bn, Tn, C = x.shape
q, k, v = self.qkv(x).split(C, dim=2)
q, k = self.qn(q), self.kn(k)
q = self.rope(q.view(Bn, Tn, self.H, self.hd).transpose(1, 2))
k = self.rope(k.view(Bn, Tn, self.H, self.hd).transpose(1, 2))
v = v.view(Bn, Tn, self.H, self.hd).transpose(1, 2)
lg = (q @ k.transpose(-2, -1)) / (self.hd ** 0.5)
mask = torch.ones(Tn, Tn, dtype=torch.bool, device=x.device).tril()
lgm = lg.masked_fill(~mask, float('-inf'))
p = lgm.softmax(-1)
y = p @ v # (B,H,T,hd)
ent = -(p.clamp_min(1e-12).log() * p).sum(-1).mean(dim=(0, 2)) # (H,)
mx = lg.masked_fill(~mask, 0).abs().amax(dim=(0, 2, 3)) # (H,)
return y, mx, ent
def forward(self, x):
Bn, Tn, C = x.shape
q, k, v = self.qkv(x).split(C, dim=2)
q, k = self.qn(q), self.kn(k)
q = self.rope(q.view(Bn, Tn, self.H, self.hd).transpose(1, 2))
k = self.rope(k.view(Bn, Tn, self.H, self.hd).transpose(1, 2))
v = v.view(Bn, Tn, self.H, self.hd).transpose(1, 2)
y = F.scaled_dot_product_attention(q, k, v, is_causal=True)
return self.proj(y.transpose(1, 2).contiguous().view(Bn, Tn, C))
class Olmo2Block(nn.Module):
def __init__(self, C, H, T):
super().__init__()
self.attn = Olmo2Attn(C, H, T); self.ff = SwiGLU(C)
self.na, self.nf = RMSNorm(C), RMSNorm(C)
def forward(self, z):
z = z + self.na(self.attn(z))
return z + self.nf(self.ff(z))
first = True
for spec in a.ckpts.split(','):
lineage, step = spec.split(':'); step = int(step)
ck = torch.load(f'runs/fw72m_{lineage}_s{step}.pt', map_location='cpu', weights_only=False)
cfg = ck['config']; C, H, L = cfg['C'], cfg['H'], cfg['L']
if first:
DD = Path('/home/yurenh2/ept/ep_run/data') / cfg.get('data', 'fineweb_edu')
vocab = pickle.load(open(DD / 'meta.pkl', 'rb'))['vocab_size']
data = np.memmap(DD / 'val.bin', dtype=np.uint16, mode='r')
ix = torch.randint(len(data) - T - 1, (B,))
x = torch.stack([torch.from_numpy(data[i:i + T].astype(np.int64)) for i in ix]).to(dev)
y = torch.stack([torch.from_numpy(data[i + 1:i + 1 + T].astype(np.int64)) for i in ix]).to(dev)
first = False
tok = nn.Embedding(vocab, C).to(dev); tok.load_state_dict(ck['tok'])
blocks = nn.ModuleList([Olmo2Block(C, H, T) for _ in range(L)]).to(dev)
blocks.load_state_dict(ck['blocks'], strict=False)
W_out = ck['wout'].to(dev)
ln_f = RMSNorm(C).to(dev); ln_f.load_state_dict(ck['lnf'])
NBT = B * T
def readout(z): return ln_f(z) @ W_out.t()
f_ins, f_outs = [], []
prev = tok(x).detach()
for b in blocks:
i = prev.detach().requires_grad_(True)
o = b(i)
f_ins.append(i); f_outs.append(o)
prev = o.detach()
ins, outs = f_ins, f_outs
zs = [o.detach().float() for o in f_outs]
d = [None] * L
hist = [] # (zs_copy, d_copy, os_copy) per sweep
res_seq = []
for k in range(a.K):
zc = zs[L - 1].detach().requires_grad_(True)
ce_k = F.cross_entropy(readout(zc).reshape(-1, vocab), y.reshape(-1))
d[L - 1] = (-a.beta * NBT * torch.autograd.grad(ce_k, zc)[0]).detach().float()
for l in range(L - 2, -1, -1):
d[l] = torch.autograd.grad(outs[l + 1], ins[l + 1], grad_outputs=d[l + 1],
retain_graph=True)[0].detach().float()
prev = tok(x).detach()
n_ins, n_outs, os_now, rnum, rden = [], [], [], 0.0, 0.0
for l in range(L):
i = prev.detach().requires_grad_(True)
o = blocks[l](i)
n_ins.append(i); n_outs.append(o)
znew = o.detach().float() + d[l]
os_now.append(o.detach().float())
rnum += float((znew - zs[l]).norm()); rden += float(zs[l].norm())
zs[l] = znew
prev = zs[l]
ins, outs = n_ins, n_outs
res_seq.append(rnum / max(rden, 1e-9))
hist.append(([z.clone() for z in zs], [di.clone() for di in d], os_now))
rho = res_seq[-1] / max(res_seq[-2], 1e-12)
zA, dA, oA = hist[-2]; zB, dB, oB = hist[-1]
dz = [zB[l] - zA[l] for l in range(L)]
dd = [dB[l] - dA[l] for l in range(L)]
do = [oB[l] - oA[l] for l in range(L)]
gH = float(dd[L - 1].norm() / max(dz[L - 1].norm(), 1e-12))
gV = [float(dd[l].norm() / max(dd[l + 1].norm(), 1e-12)) for l in range(L - 1)]
gF = [float(do[l].norm() / max(dz[l - 1].norm(), 1e-12)) for l in range(1, L)]
print(f'{lineage} s{step//1000}k | rho {rho:.4f} | gH(top read) {gH:.4f}', flush=True)
print(' gV vjp l<-l+1 (11<-top .. 0<-1): ' + ' '.join(f'{v:.2f}' for v in reversed(gV)), flush=True)
print(' gF fwd l-1->l (1 .. 11): ' + ' '.join(f'{v:.2f}' for v in gF), flush=True)
# per-head carriers, blocks 8-11: mode share through each head + logit/entropy state
for l in range(8, 12):
at = blocks[l].attn
xin = zA[l - 1]
with torch.no_grad():
y0, mx, ent = at.heads(xin)
y1, _, _ = at.heads(xin + dz[l - 1])
share = torch.linalg.vector_norm(y1 - y0, dim=(0, 2, 3))
share = (share / share.sum()).cpu().numpy()
order = np.argsort(-share)[:3]
cells = ' '.join(f'h{h}:share {share[h]:.2f} maxlg {float(mx[h]):.0f} ent {float(ent[h]):.2f}'
for h in order)
print(f' blk{l} carriers: {cells}', flush=True)
del tok, blocks, W_out, ln_f, ins, outs, f_ins, f_outs, zs, d, hist
torch.cuda.empty_cache()
# batch-noise control (the "shared with BP" question): per-batch BP u1 vs mean-BP u1
ck = torch.load('runs/fw72m_plain_s195000.pt', map_location='cpu', weights_only=False)
cfg = ck['config']; C, H, L = cfg['C'], cfg['H'], cfg['L']
tok = nn.Embedding(vocab, C).to(dev); tok.load_state_dict(ck['tok'])
blocks = nn.ModuleList([Olmo2Block(C, H, T) for _ in range(L)]).to(dev)
blocks.load_state_dict(ck['blocks'], strict=False)
W_out = ck['wout'].to(dev)
ln_f = RMSNorm(C).to(dev); ln_f.load_state_dict(ck['lnf'])
params = list(blocks.parameters())
names = [n for n, _ in blocks.named_parameters()]
SEL = [i for i, n in enumerate(names) if n in ('0.attn.qkv.weight', '8.attn.qkv.weight')]
gs = {i: [] for i in SEL}
for _ in range(8):
ixb = torch.randint(len(data) - T - 1, (B,))
xb = torch.stack([torch.from_numpy(data[i:i + T].astype(np.int64)) for i in ixb]).to(dev)
yb = torch.stack([torch.from_numpy(data[i + 1:i + 1 + T].astype(np.int64)) for i in ixb]).to(dev)
z = tok(xb)
for b in blocks: z = b(z)
ce = F.cross_entropy((ln_f(z) @ W_out.t()).reshape(-1, vocab), yb.reshape(-1))
g = torch.autograd.grad(ce, params, allow_unused=True)
for i in SEL: gs[i].append(g[i].detach().cpu())
for i in SEL:
gbar = torch.stack(gs[i]).mean(0)
u = torch.linalg.svd(gbar, full_matrices=False).U[:, 0]
ovs = [abs(float(u @ torch.linalg.svd(g, full_matrices=False).U[:, 0])) for g in gs[i]]
print(f'BP-batch-noise control {names[i]}: per-batch u1 vs mean u1 overlap = {np.mean(ovs):.3f}', flush=True)
print('CYCLE_DONE', flush=True)
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