RESULT 25: bias decomposition probe — 100% between-block transmission (TRANS=EP 0.9987, ANCHOR=1.0000, K1=BP exactly, K3=K8 saturated)

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn

1 files changed, 190 insertions, 0 deletions

diff --git a/ep_run/probe_blockcos.py b/ep_run/probe_blockcos.py
new file mode 100644
index 0000000..b55107a
--- /dev/null
+++ b/ep_run/probe_blockcos.py
@@ -0,0 +1,190 @@
+"""Error-source decomposition for cascade-EP: WITHIN-block vs BETWEEN-block.
+
+Key code fact: the theta-read is exact autograd of the block-local energy, so ALL
+finite-beta error enters through STATE DISPLACEMENT. That factorizes exactly:
+  grad(anchor, cot) = sum_l <cot_l, d o_l(anchor_l)/d theta_l>
+  (free,   c)  = BP            (exact cotangents at free states)
+  (nudged, d)  = EP            (EP-transmitted d at beta-displaced anchors)
+  (free,   d)  = TRANS-only    -> isolates BETWEEN-block transmission error (d quality)
+  (nudged, c)  = ANCHOR-only   -> isolates WITHIN-block anchor displacement error
+cos(each, BP) tells which factor dominates. Plus per-block cos-by-depth profile:
+transmission compounding must show as decay toward block 0 (furthest from loss).
+Self-check: (free, c) rebuilt through the same code path must give cos==1 vs BP.
+Usage: probe_blockcos.py [--ckpt runs/stage1b_ep_muon_s45000.pt] [--K 3] [--nb 4]
+"""
+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('--ckpt', default='runs/stage1b_ep_muon_s45000.pt')
+ap.add_argument('--K', type=int, default=3)
+ap.add_argument('--nb', type=int, default=4)
+ap.add_argument('--betas', default='1e-3,3e-3')
+a = ap.parse_args()
+dev = 'cuda'
+torch.manual_seed(7)
+
+ck = torch.load(a.ckpt, map_location='cpu', weights_only=False)
+DD = Path('/home/yurenh2/ept/ep_run/data') / ck.get('config', {}).get('data', 'tinystories_bpe')
+vocab = pickle.load(open(DD / 'meta.pkl', 'rb'))['vocab_size']
+B, T = 8, 256
+
+def get_batch():
+    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])
+    y = torch.stack([torch.from_numpy(data[i + 1:i + 1 + T].astype(np.int64)) for i in ix])
+    return x.to(dev), y.to(dev)
+
+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 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))
+
+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'])
+NBT = B * T
+params = [p for p in blocks.parameters()]
+pcounts = [sum(1 for _ in blocks[l].parameters()) for l in range(L)]
+
+def readout(z): return ln_f(z) @ W_out.t()
+
+def flat(gs): return torch.cat([g.reshape(-1).double() for g in gs])
+
+def cos(ga, gb):
+    va, vb = flat(ga), flat(gb)
+    return float((va @ vb) / (va.norm() * vb.norm() + 1e-30))
+
+def cos_by_block(ga, gb):
+    out, i = [], 0
+    for l in range(L):
+        sa = ga[i:i + pcounts[l]]; sb = gb[i:i + pcounts[l]]
+        out.append(cos(sa, sb)); i += pcounts[l]
+    return out
+
+def grads_from(outs_list, cots):
+    """sum_l <cot_l, o_l> -> d/dtheta. Positive scale/sign of cots irrelevant for cos."""
+    obj = sum((o * c.detach()).sum() for o, c in zip(outs_list, cots))
+    gs = torch.autograd.grad(obj, params, allow_unused=True, retain_graph=True)
+    return [g.float() if g is not None else torch.zeros_like(p) for g, p in zip(gs, params)]
+
+def run_case(x, y, beta):
+    # --- BP reference + exact cotangents c_l at free states (whole-chain graph) ---
+    z = tok(x)
+    zs_bp = []
+    for b in blocks:
+        z = b(z); zs_bp.append(z)
+    ce = F.cross_entropy(readout(zs_bp[-1]).reshape(-1, vocab), y.reshape(-1))
+    g_bp = [g.float() for g in torch.autograd.grad(ce, params, retain_graph=True, allow_unused=False)]
+    c = [g.detach() for g in torch.autograd.grad(ce, zs_bp, retain_graph=False)]
+
+    # --- free block-wise pass (graph per block, EP-style detach between blocks) ---
+    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()
+
+    # self-check: (free, c) through this path must equal BP
+    g_chk = grads_from(f_outs, c)
+    chk = cos(g_chk, g_bp)
+
+    # --- EP nudged relaxation (harness-faithful): K sweeps of derive-d + rebuild ---
+    ins, outs = f_ins, f_outs
+    zs = [o.detach().float() for o in f_outs]
+    d = [None] * L
+    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] = (-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 = [], []
+        for l in range(L):
+            i = prev.detach().requires_grad_(True)
+            o = blocks[l](i)
+            n_ins.append(i); n_outs.append(o)
+            zs[l] = (o.detach().float() + d[l])
+            prev = zs[l]
+        ins, outs = n_ins, n_outs
+
+    md = [-di for di in d]  # -d ~ +beta*NBT*(transmitted cotangent); scale washes out in cos
+    g_ep    = grads_from(outs,   md)   # (nudged anchor, EP d)      = EP
+    g_trans = grads_from(f_outs, md)   # (free anchor,  EP d)       = transmission-only error
+    g_loc   = grads_from(outs,   c)    # (nudged anchor, exact c)   = anchor-only error
+    return g_bp, g_ep, g_trans, g_loc, chk
+
+batches = [get_batch() for _ in range(a.nb)]
+for beta in [float(s) for s in a.betas.split(',')]:
+    agg = {'ep': [], 'trans': [], 'loc': [], 'chk': []}
+    prof_ep, prof_trans, prof_loc = [], [], []
+    for x, y in batches:
+        g_bp, g_ep, g_trans, g_loc, chk = run_case(x, y, beta)
+        agg['ep'].append(cos(g_ep, g_bp)); agg['trans'].append(cos(g_trans, g_bp))
+        agg['loc'].append(cos(g_loc, g_bp)); agg['chk'].append(chk)
+        prof_ep.append(cos_by_block(g_ep, g_bp))
+        prof_trans.append(cos_by_block(g_trans, g_bp))
+        prof_loc.append(cos_by_block(g_loc, g_bp))
+        del g_bp, g_ep, g_trans, g_loc
+        torch.cuda.empty_cache()
+    m = {k: sum(v) / len(v) for k, v in agg.items()}
+    print(f"[beta={beta:g} K={a.K}] selfcheck(free,c)={m['chk']:.6f}  "
+          f"EP={m['ep']:.4f}  TRANS-only={m['trans']:.4f}  ANCHOR-only={m['loc']:.4f}", flush=True)
+    for name, prof in [('EP   ', prof_ep), ('TRANS', prof_trans), ('ANCHR', prof_loc)]:
+        mp = [sum(p[l] for p in prof) / len(prof) for l in range(L)]
+        print(f"  {name} by block (0=bottom..{L-1}=top): " +
+              " ".join(f"{v:.3f}" for v in mp), flush=True)
+print("DONE_BLOCKCOS", flush=True)