Add Phase 10A.6: gain requires trainable depth-aware aux, not semantic credit

9-branch dissection results:
- zero_target crashes (-9.1%): aux must output non-zero
- constant_input neutral (+0.0%): needs at least depth info
- time_only works (+1.0%): h_l not needed, just depth index
- shuffled/fresh_random work (+1.3-1.4%): no semantic content needed
- prefit60_trainable ≈ random_trainable: prefit adds nothing
- All frozen branches crash: trainability is essential

Mechanism: depth-aware trainable auxiliary perturbation that diversifies
block-local updates. Not semantic credit, not pure trainability.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

1 files changed, 853 insertions, 0 deletions

diff --git a/experiments/structured_vs_semantic_aux.py b/experiments/structured_vs_semantic_aux.py
new file mode 100644
index 0000000..15aca16
--- /dev/null
+++ b/experiments/structured_vs_semantic_aux.py
@@ -0,0 +1,853 @@
+"""
+Phase 10A.6: Structured vs Semantic Auxiliary Dissection.
+
+Core question: What kind of structure in the auxiliary signal actually drives
+the blend gain observed in Phase 10A?
+
+9 branches from the same DFA checkpoint at t0=5:
+1.  continue_DFA               — pure DFA baseline
+2.  blend_random_trainable     — random Vec, trained online (same as 10A.5)
+3.  blend_shuffled_trainable   — Vec trained but targets shuffled within batch
+4.  blend_zero_target          — Vec trained with ||a_aux||^2 loss (learns zero)
+5.  blend_fresh_random_target  — Vec trained with fresh i.i.d. random targets each step
+6.  blend_time_only            — auxiliary only sees t=l/L (no h_l)
+7.  blend_constant_input       — auxiliary learns a fixed per-block template (no input)
+8.  blend_prefit60_frozen      — Vec prefit for 60 epochs, then FROZEN
+9.  blend_prefit60_trainable   — Vec prefit for 60 epochs, then continue training
+"""
+import os
+import sys
+import json
+import argparse
+import numpy as np
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+import torch.optim as optim
+from torch.utils.data import DataLoader
+import torchvision
+import torchvision.transforms as transforms
+import copy
+
+sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
+
+from models.residual_mlp import ResidualMLP
+from models.value_net import SinusoidalTimeEmbed
+from metrics.credit_metrics import cosine_similarity_batch, perturbation_correlation
+
+
+# ---------------------------------------------------------------------------
+# Auxiliary network architectures
+# ---------------------------------------------------------------------------
+
+class VectorCreditNet(nn.Module):
+    """Standard Vec: takes (h, t, s) and outputs d_hidden credit vector."""
+    def __init__(self, d_hidden, s_dim, time_embed_dim=32, hidden_dim=256, num_layers=3):
+        super().__init__()
+        self.ln = nn.LayerNorm(d_hidden)
+        self.time_embed = SinusoidalTimeEmbed(time_embed_dim)
+        input_dim = d_hidden + time_embed_dim + s_dim
+        layers = []
+        for i in range(num_layers):
+            in_d = input_dim if i == 0 else hidden_dim
+            layers.append(nn.Linear(in_d, hidden_dim))
+            layers.append(nn.GELU())
+        layers.append(nn.Linear(hidden_dim, d_hidden))
+        self.net = nn.Sequential(*layers)
+
+    def forward(self, h, t, s):
+        return self.net(torch.cat([self.ln(h), self.time_embed(t), s], dim=-1))
+
+
+class TimeOnlyNet(nn.Module):
+    """Auxiliary that only takes t=l/L as input (no h_l, no s).
+    Shared MLP on sinusoidal time embedding -> d_hidden.
+    """
+    def __init__(self, d_hidden, time_embed_dim=32, hidden_dim=256, num_layers=3):
+        super().__init__()
+        self.time_embed = SinusoidalTimeEmbed(time_embed_dim)
+        layers = []
+        for i in range(num_layers):
+            in_d = time_embed_dim if i == 0 else hidden_dim
+            layers.append(nn.Linear(in_d, hidden_dim))
+            layers.append(nn.GELU())
+        layers.append(nn.Linear(hidden_dim, d_hidden))
+        self.net = nn.Sequential(*layers)
+
+    def forward(self, h, t, s):
+        # h and s are ignored — only t is used
+        return self.net(self.time_embed(t))
+
+
+class ConstantNet(nn.Module):
+    """Auxiliary with NO input at all: learns a per-block fixed output template.
+    Each block has an nn.Parameter of shape (d_hidden,).
+    forward(h, t, s) just expands the per-block param to match batch size.
+    Block index is passed as an integer via a separate call to set_block().
+    """
+    def __init__(self, d_hidden, num_blocks):
+        super().__init__()
+        # One template per block
+        self.templates = nn.ParameterList(
+            [nn.Parameter(torch.zeros(d_hidden)) for _ in range(num_blocks)]
+        )
+        self._block_idx = 0
+
+    def set_block(self, l):
+        self._block_idx = l
+
+    def forward(self, h, t, s):
+        batch = h.size(0)
+        return self.templates[self._block_idx].unsqueeze(0).expand(batch, -1)
+
+
+# ---------------------------------------------------------------------------
+# Data
+# ---------------------------------------------------------------------------
+
+def get_cifar10(batch_size=128):
+    transform_train = transforms.Compose([
+        transforms.RandomCrop(32, padding=4), transforms.RandomHorizontalFlip(),
+        transforms.ToTensor(),
+        transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2470, 0.2435, 0.2616))])
+    transform_test = transforms.Compose([
+        transforms.ToTensor(),
+        transforms.Normalize((0.4914, 0.4822, 0.4465), (0.2470, 0.2435, 0.2616))])
+    trainset = torchvision.datasets.CIFAR10(
+        root='./data', train=True, download=True, transform=transform_train)
+    testset = torchvision.datasets.CIFAR10(
+        root='./data', train=False, download=True, transform=transform_test)
+    return (DataLoader(trainset, batch_size=batch_size, shuffle=True,
+                       num_workers=4, pin_memory=True),
+            DataLoader(testset, batch_size=batch_size, shuffle=False,
+                       num_workers=4, pin_memory=True))
+
+
+# ---------------------------------------------------------------------------
+# Evaluation helpers
+# ---------------------------------------------------------------------------
+
+def evaluate(model, test_loader, device):
+    model.eval(); c, t = 0, 0
+    with torch.no_grad():
+        for x, y in test_loader:
+            x = x.view(x.size(0), -1).to(device); y = y.to(device)
+            c += (model(x).argmax(1) == y).sum().item(); t += x.size(0)
+    return c / t
+
+
+def compute_diagnostics(model, aux_net, Bs, test_loader, device,
+                         credit_mode, alpha=0.75, const_net_L=None):
+    """Compute mean Gamma (BP cosine) and mean rho (perturbation correlation)."""
+    model.eval()
+    if aux_net is not None:
+        aux_net.eval()
+    L = model.num_blocks
+
+    # Get one batch
+    for x, y in test_loader:
+        x = x.view(x.size(0), -1).to(device); y = y.to(device); break
+    batch = x.size(0)
+
+    # BP pass to get hidden gradients
+    was_frozen = not next(model.parameters()).requires_grad
+    if was_frozen:
+        for p in model.parameters(): p.requires_grad_(True)
+    model.zero_grad()
+    lo, hbp = model(x, return_hidden=True)
+    for l in range(L + 1): hbp[l].retain_grad()
+    F.cross_entropy(lo, y).backward()
+    bp = {l: hbp[l].grad.detach().clone() for l in range(L + 1)}
+    if was_frozen:
+        for p in model.parameters(): p.requires_grad_(False)
+
+    with torch.no_grad():
+        lo2, hi = model(x, return_hidden=True)
+        eT = lo2.softmax(-1); eT[torch.arange(batch), y] -= 1; s = eT.detach()
+
+    gammas, rhos = [], []
+    for l in range(L):
+        h_l = hi[l].detach()
+        t_l = torch.full((batch,), l / L, device=device)
+
+        if credit_mode == 'dfa':
+            a_l = (s @ Bs[l].T).detach()
+        elif credit_mode == 'blend' and aux_net is not None:
+            a_dfa = (s @ Bs[l].T).detach()
+            if isinstance(aux_net, ConstantNet):
+                aux_net.set_block(l)
+            a_aux = aux_net(h_l, t_l, s).detach()
+            rd = (a_dfa ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+            rv = (a_aux ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+            a_l = alpha * a_aux / rv + (1 - alpha) * a_dfa / rd
+        else:
+            a_l = (s @ Bs[l].T).detach()
+
+        gammas.append(cosine_similarity_batch(a_l, bp[l]))
+
+        def make_fwd(sl):
+            def f(h):
+                with torch.no_grad():
+                    c = h
+                    for i in range(sl, L):
+                        c = c + model.blocks[i](c)
+                    return F.cross_entropy(
+                        model.out_head(model.out_ln(c)), y, reduction='none')
+            return f
+
+        rhos.append(perturbation_correlation(h_l, a_l, make_fwd(l),
+                                              epsilon=1e-3, M=16))
+
+    return float(np.mean(gammas)), float(np.mean(rhos))
+
+
+# ---------------------------------------------------------------------------
+# DFA training + checkpoint
+# ---------------------------------------------------------------------------
+
+def train_dfa_get_checkpoint(model, train_loader, test_loader, device,
+                              total_epochs, t0, lr, wd):
+    d = model.d_hidden; L = model.num_blocks
+    Bs = [torch.randn(d, 10, device=device) / np.sqrt(10) for _ in range(L)]
+    block_opts = [optim.AdamW(b.parameters(), lr=lr, weight_decay=wd)
+                  for b in model.blocks]
+    embed_opt = optim.AdamW(model.embed.parameters(), lr=lr, weight_decay=wd)
+    head_opt = optim.AdamW(
+        list(model.out_head.parameters()) + list(model.out_ln.parameters()),
+        lr=lr, weight_decay=wd)
+    scheds = ([optim.lr_scheduler.CosineAnnealingLR(o, T_max=total_epochs)
+               for o in block_opts] +
+              [optim.lr_scheduler.CosineAnnealingLR(embed_opt, T_max=total_epochs),
+               optim.lr_scheduler.CosineAnnealingLR(head_opt, T_max=total_epochs)])
+    ckpt = None
+    for epoch in range(1, total_epochs + 1):
+        model.train(); tl, c, t = 0, 0, 0
+        for x, y in train_loader:
+            x = x.view(x.size(0), -1).to(device); y = y.to(device); b = x.size(0)
+            with torch.no_grad():
+                lo, hi = model(x, return_hidden=True); lv = F.cross_entropy(lo, y)
+                eT = lo.softmax(-1); eT[torch.arange(b), y] -= 1
+            hL = hi[-1].detach()
+            lo2 = F.cross_entropy(model.out_head(model.out_ln(hL)), y)
+            head_opt.zero_grad(); lo2.backward(); head_opt.step()
+            for l in range(L):
+                a = (eT @ Bs[l].T).detach()
+                rm = (a ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+                f = model.blocks[l](hi[l].detach())
+                ll = (f * (a / rm)).sum(-1).mean()
+                block_opts[l].zero_grad(); ll.backward()
+                torch.nn.utils.clip_grad_norm_(model.blocks[l].parameters(), 1.0)
+                block_opts[l].step()
+            a0 = (eT @ Bs[0].T).detach()
+            r0 = (a0 ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+            el = (model.embed(x) * (a0 / r0)).sum(-1).mean()
+            embed_opt.zero_grad(); el.backward(); embed_opt.step()
+            tl += lv.item() * b; c += (lo.argmax(1) == y).sum().item(); t += b
+        for s in scheds: s.step()
+        if epoch == t0:
+            acc = evaluate(model, test_loader, device)
+            ckpt = {'model': copy.deepcopy(model.state_dict()),
+                    'Bs': [B.clone() for B in Bs], 'acc': acc}
+            print(f"  [DFA] Checkpoint at epoch {t0}: acc={acc:.4f}")
+        if epoch % 10 == 0:
+            print(f"  [DFA] Epoch {epoch}: acc={evaluate(model, test_loader, device):.4f}")
+    return Bs, ckpt
+
+
+# ---------------------------------------------------------------------------
+# Offline Vec prefit
+# ---------------------------------------------------------------------------
+
+def offline_fit_vec(vec_net, model, Bs, train_loader, device, epochs, lr_fb, M, eps_pert=1e-3):
+    """Pre-train VectorCreditNet using perturbation targets (no forward net training)."""
+    L = model.num_blocks
+    vec_opt = optim.Adam(vec_net.parameters(), lr=lr_fb)
+    model.eval()
+    print(f"  [prefit] Starting Vec prefit for {epochs} epochs...")
+    for epoch in range(1, epochs + 1):
+        vec_net.train(); total_loss = 0.0; nb = 0
+        for x, y in train_loader:
+            x = x.view(x.size(0), -1).to(device); y = y.to(device); batch = x.size(0)
+            with torch.no_grad():
+                lo, hi = model(x, return_hidden=True)
+                eT = lo.softmax(-1); eT[torch.arange(batch), y] -= 1; s = eT.detach()
+            hL = hi[-1].detach()
+
+            # Terminal anchor
+            t_L = torch.ones(batch, device=device)
+            a_term = vec_net(hL, t_L, s)
+            hL_req = hL.clone().requires_grad_(True)
+            ce = F.cross_entropy(model.out_head(model.out_ln(hL_req)), y,
+                                  reduction='sum')
+            dL = torch.autograd.grad(ce, hL_req)[0].detach()
+            loss_term = ((a_term - dL) ** 2).sum(-1).mean()
+
+            # Perturbation loss at a random layer
+            lt = np.random.randint(0, L)
+            h_l = hi[lt].detach()
+            t_l = torch.full((batch,), lt / L, device=device)
+            a_l = vec_net(h_l, t_l, s)
+            lp2 = torch.tensor(0.0, device=device)
+            for _ in range(M):
+                v = torch.randn_like(h_l)
+                v = v / (v.norm(-1, keepdim=True) + 1e-8)
+                with torch.no_grad():
+                    lp = F.cross_entropy(
+                        model.forward_from_layer(h_l + eps_pert * v, lt), y, reduction='none')
+                    lm = F.cross_entropy(
+                        model.forward_from_layer(h_l - eps_pert * v, lt), y, reduction='none')
+                    gj = (lp - lm) / (2 * eps_pert)
+                lp2 = lp2 + (((a_l * v).sum(-1) - gj.detach()) ** 2).mean()
+            lp2 /= M
+            vl = loss_term + lp2
+            vec_opt.zero_grad(); vl.backward()
+            torch.nn.utils.clip_grad_norm_(vec_net.parameters(), 1.0)
+            vec_opt.step()
+            total_loss += vl.item(); nb += 1
+        if epoch % 10 == 0 or epoch == epochs:
+            print(f"  [prefit] Epoch {epoch}/{epochs}: loss={total_loss/nb:.4f}")
+    vec_net.eval()
+    return vec_net
+
+
+# ---------------------------------------------------------------------------
+# Estimate shuffled-target RMS (for fresh_random sigma matching)
+# ---------------------------------------------------------------------------
+
+def estimate_shuffled_rms(model, Bs, train_loader, device, M=4, eps_pert=1e-3, n_batches=5):
+    """Estimate RMS of shuffled perturbation targets to match for fresh_random branch."""
+    model.eval(); L = model.num_blocks
+    rms_vals = []
+    for i, (x, y) in enumerate(train_loader):
+        if i >= n_batches: break
+        x = x.view(x.size(0), -1).to(device); y = y.to(device); batch = x.size(0)
+        with torch.no_grad():
+            lo, hi = model(x, return_hidden=True)
+        lt = np.random.randint(0, L)
+        h_l = hi[lt].detach()
+        for _ in range(M):
+            v = torch.randn_like(h_l)
+            v = v / (v.norm(-1, keepdim=True) + 1e-8)
+            with torch.no_grad():
+                lp = F.cross_entropy(
+                    model.forward_from_layer(h_l + eps_pert * v, lt), y, reduction='none')
+                lm = F.cross_entropy(
+                    model.forward_from_layer(h_l - eps_pert * v, lt), y, reduction='none')
+                gj = (lp - lm) / (2 * eps_pert)
+            # Shuffled
+            gj_sh = gj[torch.randperm(batch, device=device)]
+            rms_vals.append(gj_sh.pow(2).mean().sqrt().item())
+    return float(np.mean(rms_vals)) if rms_vals else 0.01
+
+
+# ---------------------------------------------------------------------------
+# Branch runner
+# ---------------------------------------------------------------------------
+
+def run_branch(model, aux_net, Bs, train_loader, test_loader, device,
+               t0, total_epochs, branch_type, alpha, lr, lr_fb, wd, M,
+               branch_name='', fresh_sigma=0.01):
+    """
+    Run a training branch from a loaded checkpoint.
+
+    branch_type options:
+      'dfa'                   — pure DFA
+      'blend_trainable'       — blend with Vec trained online (perturbation targets)
+      'blend_shuffled'        — blend with Vec trained on shuffled targets
+      'blend_zero_target'     — blend with Vec trained toward zero (||a_aux||^2)
+      'blend_fresh_random'    — blend with Vec trained on fresh random targets each step
+      'blend_time_only'       — blend with TimeOnlyNet trained online
+      'blend_constant'        — blend with ConstantNet trained online
+      'blend_frozen'          — blend with pre-fit Vec, frozen
+      'blend_prefit_trainable'— blend with pre-fit Vec, continue training
+    """
+    d = model.d_hidden; L = model.num_blocks; eps_pert = 1e-3
+
+    # Determine which aux nets need training
+    trainable_types = {'blend_trainable', 'blend_shuffled', 'blend_zero_target',
+                       'blend_fresh_random', 'blend_time_only', 'blend_constant',
+                       'blend_prefit_trainable'}
+    aux_trained = (branch_type in trainable_types) and (aux_net is not None)
+
+    block_opts = [optim.AdamW(b.parameters(), lr=lr, weight_decay=wd)
+                  for b in model.blocks]
+    embed_opt = optim.AdamW(model.embed.parameters(), lr=lr, weight_decay=wd)
+    head_opt = optim.AdamW(
+        list(model.out_head.parameters()) + list(model.out_ln.parameters()),
+        lr=lr, weight_decay=wd)
+    aux_opt = optim.Adam(aux_net.parameters(), lr=lr_fb) if aux_trained else None
+
+    scheds = ([optim.lr_scheduler.CosineAnnealingLR(o, T_max=total_epochs)
+               for o in block_opts] +
+              [optim.lr_scheduler.CosineAnnealingLR(embed_opt, T_max=total_epochs),
+               optim.lr_scheduler.CosineAnnealingLR(head_opt, T_max=total_epochs)])
+    # Advance schedulers to match checkpoint epoch
+    for _ in range(t0):
+        for s in scheds: s.step()
+
+    log = {'test_acc': [], 'train_loss': [], 'gamma': [], 'rho': [], 'alpha_eff': []}
+    diag_epochs = set(
+        list(range(t0 + 1, min(t0 + 6, total_epochs + 1))) +
+        [t0 + 8, t0 + 10, t0 + 15, t0 + 20] +
+        list(range(t0 + 10, total_epochs + 1, 10)) +
+        [total_epochs])
+
+    for epoch in range(t0 + 1, total_epochs + 1):
+        model.train()
+        if aux_net is not None and aux_trained:
+            aux_net.train()
+        elif aux_net is not None:
+            aux_net.eval()
+
+        tl, c, t = 0, 0, 0
+        epoch_aux_norms, epoch_dfa_norms = [], []
+
+        for x, y in train_loader:
+            x = x.view(x.size(0), -1).to(device); y = y.to(device); batch = x.size(0)
+            with torch.no_grad():
+                lo, hi = model(x, return_hidden=True); lv = F.cross_entropy(lo, y)
+                eT = lo.softmax(-1); eT[torch.arange(batch), y] -= 1; s = eT.detach()
+            hL = hi[-1].detach()
+
+            # ----------------------------------------------------------------
+            # Train auxiliary network (if applicable)
+            # ----------------------------------------------------------------
+            if aux_opt is not None:
+                if branch_type in ('blend_trainable', 'blend_prefit_trainable',
+                                   'blend_time_only'):
+                    # Standard perturbation targets
+                    t_L = torch.ones(batch, device=device)
+                    a_term = aux_net(hL, t_L, s)
+                    hL_req = hL.clone().requires_grad_(True)
+                    ce = F.cross_entropy(
+                        model.out_head(model.out_ln(hL_req)), y, reduction='sum')
+                    dL = torch.autograd.grad(ce, hL_req)[0].detach()
+                    loss_term = ((a_term - dL) ** 2).sum(-1).mean()
+                    lt = np.random.randint(0, L)
+                    h_l = hi[lt].detach()
+                    t_l = torch.full((batch,), lt / L, device=device)
+                    a_l = aux_net(h_l, t_l, s)
+                    lp2 = torch.tensor(0.0, device=device)
+                    for _ in range(M):
+                        v = torch.randn_like(h_l)
+                        v = v / (v.norm(-1, keepdim=True) + 1e-8)
+                        with torch.no_grad():
+                            lp = F.cross_entropy(
+                                model.forward_from_layer(h_l + eps_pert * v, lt),
+                                y, reduction='none')
+                            lm = F.cross_entropy(
+                                model.forward_from_layer(h_l - eps_pert * v, lt),
+                                y, reduction='none')
+                            gj = (lp - lm) / (2 * eps_pert)
+                        lp2 = lp2 + (((a_l * v).sum(-1) - gj.detach()) ** 2).mean()
+                    lp2 /= M
+                    vl = loss_term + lp2
+
+                elif branch_type == 'blend_shuffled':
+                    # Perturbation targets shuffled within batch
+                    t_L = torch.ones(batch, device=device)
+                    a_term = aux_net(hL, t_L, s)
+                    hL_req = hL.clone().requires_grad_(True)
+                    ce = F.cross_entropy(
+                        model.out_head(model.out_ln(hL_req)), y, reduction='sum')
+                    dL = torch.autograd.grad(ce, hL_req)[0].detach()
+                    dL_sh = dL[torch.randperm(batch, device=device)]
+                    loss_term = ((a_term - dL_sh) ** 2).sum(-1).mean()
+                    lt = np.random.randint(0, L)
+                    h_l = hi[lt].detach()
+                    t_l = torch.full((batch,), lt / L, device=device)
+                    a_l = aux_net(h_l, t_l, s)
+                    lp2 = torch.tensor(0.0, device=device)
+                    for _ in range(M):
+                        v = torch.randn_like(h_l)
+                        v = v / (v.norm(-1, keepdim=True) + 1e-8)
+                        with torch.no_grad():
+                            lp = F.cross_entropy(
+                                model.forward_from_layer(h_l + eps_pert * v, lt),
+                                y, reduction='none')
+                            lm = F.cross_entropy(
+                                model.forward_from_layer(h_l - eps_pert * v, lt),
+                                y, reduction='none')
+                            gj = (lp - lm) / (2 * eps_pert)
+                        # Shuffle targets within batch to break semantic correlation
+                        gj_sh = gj[torch.randperm(batch, device=device)]
+                        lp2 = lp2 + (((a_l * v).sum(-1) - gj_sh.detach()) ** 2).mean()
+                    lp2 /= M
+                    vl = loss_term + lp2
+
+                elif branch_type == 'blend_zero_target':
+                    # Minimize ||a_aux||^2 — teaches the network to output zero
+                    lt = np.random.randint(0, L)
+                    h_l = hi[lt].detach()
+                    t_l = torch.full((batch,), lt / L, device=device)
+                    if isinstance(aux_net, ConstantNet):
+                        aux_net.set_block(lt)
+                    a_l = aux_net(h_l, t_l, s)
+                    vl = (a_l ** 2).sum(-1).mean()
+
+                elif branch_type == 'blend_fresh_random':
+                    # Fresh i.i.d. random targets sampled every step
+                    lt = np.random.randint(0, L)
+                    h_l = hi[lt].detach()
+                    t_l = torch.full((batch,), lt / L, device=device)
+                    a_l = aux_net(h_l, t_l, s)
+                    # Sample random target with RMS matched to shuffled scale
+                    rand_target = torch.randn(batch, device=device) * fresh_sigma
+                    lp2 = torch.tensor(0.0, device=device)
+                    for _ in range(M):
+                        v = torch.randn_like(h_l)
+                        v = v / (v.norm(-1, keepdim=True) + 1e-8)
+                        # Fresh random target per direction per step
+                        gj_rand = torch.randn(batch, device=device) * fresh_sigma
+                        lp2 = lp2 + (((a_l * v).sum(-1) - gj_rand) ** 2).mean()
+                    lp2 /= M
+                    vl = lp2
+
+                elif branch_type == 'blend_constant':
+                    # ConstantNet: train per-block templates
+                    # Train all blocks this step (cheap since it's just parameters)
+                    vl = torch.tensor(0.0, device=device)
+                    lt = np.random.randint(0, L)
+                    h_l = hi[lt].detach()
+                    t_l = torch.full((batch,), lt / L, device=device)
+                    aux_net.set_block(lt)
+                    a_l = aux_net(h_l, t_l, s)
+                    lp2_inner = torch.tensor(0.0, device=device)
+                    for _ in range(M):
+                        v = torch.randn_like(h_l)
+                        v = v / (v.norm(-1, keepdim=True) + 1e-8)
+                        with torch.no_grad():
+                            lp = F.cross_entropy(
+                                model.forward_from_layer(h_l + eps_pert * v, lt),
+                                y, reduction='none')
+                            lm = F.cross_entropy(
+                                model.forward_from_layer(h_l - eps_pert * v, lt),
+                                y, reduction='none')
+                            gj = (lp - lm) / (2 * eps_pert)
+                        lp2_inner = lp2_inner + (
+                            ((a_l * v).sum(-1) - gj.detach()) ** 2).mean()
+                    vl = lp2_inner / M
+                else:
+                    vl = None
+
+                if vl is not None:
+                    aux_opt.zero_grad(); vl.backward()
+                    torch.nn.utils.clip_grad_norm_(aux_net.parameters(), 1.0)
+                    aux_opt.step()
+
+            # ----------------------------------------------------------------
+            # Compute credits for each block
+            # ----------------------------------------------------------------
+            dfa_credits = [(eT @ Bs[l].T).detach() for l in range(L)]
+            credits = []
+            for l in range(L):
+                a_dfa = dfa_credits[l]
+                rms_d = (a_dfa ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+
+                if branch_type == 'dfa':
+                    credits.append(a_dfa / rms_d)
+                else:
+                    # All blend branches
+                    h_l = hi[l].detach()
+                    t_l = torch.full((batch,), l / L, device=device)
+                    with torch.no_grad():
+                        if isinstance(aux_net, ConstantNet):
+                            aux_net.set_block(l)
+                        a_aux = aux_net(h_l, t_l, s).detach()
+                    rms_v = (a_aux ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+                    a_blend = alpha * a_aux / rms_v + (1 - alpha) * a_dfa / rms_d
+                    credits.append(a_blend)
+
+                # Track norms for alpha_eff
+                a_c = credits[-1]
+                if branch_type == 'dfa':
+                    epoch_aux_norms.append(0.0)
+                    epoch_dfa_norms.append(a_c.norm().item())
+                else:
+                    a_dfa_n = a_dfa / rms_d
+                    rms_v2 = (a_aux ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+                    epoch_aux_norms.append((alpha * a_aux / rms_v2).norm().item())
+                    epoch_dfa_norms.append(((1 - alpha) * a_dfa_n).norm().item())
+
+            # ----------------------------------------------------------------
+            # Update output head (local exact gradient — allowed)
+            # ----------------------------------------------------------------
+            lo2 = F.cross_entropy(model.out_head(model.out_ln(hL)), y)
+            head_opt.zero_grad(); lo2.backward(); head_opt.step()
+
+            # ----------------------------------------------------------------
+            # Update blocks with local surrogate
+            # a_total is already blended; normalize before inner product
+            # ----------------------------------------------------------------
+            for l in range(L):
+                a = credits[l]
+                rm = (a ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+                f = model.blocks[l](hi[l].detach())
+                ll = (f * (a / rm)).sum(-1).mean()
+                block_opts[l].zero_grad(); ll.backward()
+                torch.nn.utils.clip_grad_norm_(model.blocks[l].parameters(), 1.0)
+                block_opts[l].step()
+
+            # Update embedding with block-0 credit
+            a0 = credits[0]
+            r0 = (a0 ** 2).mean(-1, keepdim=True).sqrt() + 1e-6
+            el = (model.embed(x) * (a0 / r0)).sum(-1).mean()
+            embed_opt.zero_grad(); el.backward(); embed_opt.step()
+
+            tl += lv.item() * batch; c += (lo.argmax(1) == y).sum().item(); t += batch
+
+        for sch in scheds: sch.step()
+        ta = evaluate(model, test_loader, device)
+        log['test_acc'].append(ta); log['train_loss'].append(tl / t)
+
+        mean_aux = np.mean(epoch_aux_norms) if epoch_aux_norms else 0.0
+        mean_dfa = np.mean(epoch_dfa_norms) if epoch_dfa_norms else 1.0
+        aeff = mean_aux / (mean_aux + mean_dfa + 1e-12)
+        log['alpha_eff'].append((epoch, aeff))
+
+        if epoch in diag_epochs:
+            cm = 'blend' if branch_type != 'dfa' else 'dfa'
+            gamma, rho = compute_diagnostics(
+                model, aux_net if branch_type != 'dfa' else None,
+                Bs, test_loader, device, cm, alpha)
+            log['gamma'].append((epoch, gamma)); log['rho'].append((epoch, rho))
+            if epoch <= t0 + 15 or epoch % 20 == 0 or epoch == total_epochs:
+                print(f"    [{branch_name}] Ep {epoch}: acc={ta:.4f}, "
+                      f"G={gamma:.4f}, r={rho:.4f}, aeff={aeff:.3f}")
+        elif epoch % 10 == 0 or epoch == total_epochs:
+            print(f"    [{branch_name}] Ep {epoch}: acc={ta:.4f}")
+
+    return log
+
+
+# ---------------------------------------------------------------------------
+# Main experiment
+# ---------------------------------------------------------------------------
+
+def run_experiment(args):
+    device = torch.device(f'cuda:{args.gpu}' if torch.cuda.is_available() else 'cpu')
+    print(f"Using device: {device}")
+    os.makedirs(args.output_dir, exist_ok=True)
+    torch.manual_seed(args.seed); np.random.seed(args.seed)
+    torch.cuda.manual_seed_all(args.seed)
+
+    train_loader, test_loader = get_cifar10(args.batch_size)
+    input_dim = 32 * 32 * 3; L = args.num_blocks; d = args.d_hidden
+
+    # ----------------------------------------------------------------
+    # Step 1: Train DFA and capture checkpoint at t0
+    # ----------------------------------------------------------------
+    print(f"\n{'='*60}\nTraining DFA baseline (checkpoint at t0={args.t0})\n{'='*60}")
+    model_dfa = ResidualMLP(input_dim, d, 10, L).to(device)
+    Bs, ckpt = train_dfa_get_checkpoint(
+        model_dfa, train_loader, test_loader, device,
+        args.epochs, args.t0, args.lr, args.wd)
+    print(f"  Checkpoint acc at t0={args.t0}: {ckpt['acc']:.4f}")
+
+    # ----------------------------------------------------------------
+    # Step 2: Offline prefit of Vec (for prefit60 branches)
+    # ----------------------------------------------------------------
+    print(f"\n{'='*60}\nOffline prefit of Vec (60 epochs)\n{'='*60}")
+    torch.manual_seed(args.seed + 7777)
+    vec_prefit = VectorCreditNet(d_hidden=d, s_dim=10).to(device)
+    # Load checkpoint model for prefit (weights at t0, forward net frozen)
+    model_prefit = ResidualMLP(input_dim, d, 10, L).to(device)
+    model_prefit.load_state_dict(ckpt['model'])
+    model_prefit.eval()
+    for p in model_prefit.parameters(): p.requires_grad_(False)
+    vec_prefit = offline_fit_vec(
+        vec_prefit, model_prefit, ckpt['Bs'],
+        train_loader, device, epochs=60, lr_fb=args.lr_fb, M=args.M)
+    del model_prefit
+
+    # ----------------------------------------------------------------
+    # Step 3: Estimate sigma for fresh_random (match shuffled-target RMS)
+    # ----------------------------------------------------------------
+    model_ref = ResidualMLP(input_dim, d, 10, L).to(device)
+    model_ref.load_state_dict(ckpt['model']); model_ref.eval()
+    for p in model_ref.parameters(): p.requires_grad_(False)
+    fresh_sigma = estimate_shuffled_rms(model_ref, ckpt['Bs'], train_loader, device)
+    print(f"  fresh_random sigma (matched to shuffled RMS): {fresh_sigma:.5f}")
+    del model_ref
+
+    # ----------------------------------------------------------------
+    # Step 4: Define and run all 9 branches
+    # ----------------------------------------------------------------
+    # Each entry: (branch_name, branch_type, aux_factory_fn)
+    # aux_factory_fn returns a fresh aux_net (or None for dfa)
+    VEC_SEED = args.seed + 7777
+
+    def make_vec():
+        torch.manual_seed(VEC_SEED)
+        return VectorCreditNet(d_hidden=d, s_dim=10).to(device)
+
+    def make_time_only():
+        torch.manual_seed(VEC_SEED)
+        return TimeOnlyNet(d_hidden=d).to(device)
+
+    def make_constant():
+        torch.manual_seed(VEC_SEED)
+        return ConstantNet(d_hidden=d, num_blocks=L).to(device)
+
+    def make_prefit_frozen():
+        net = copy.deepcopy(vec_prefit)
+        for p in net.parameters(): p.requires_grad_(False)
+        net.eval()
+        return net
+
+    def make_prefit_trainable():
+        return copy.deepcopy(vec_prefit)
+
+    branches = [
+        # (name, branch_type, aux_factory)
+        ('continue_DFA',               'dfa',                    lambda: None),
+        ('blend_random_trainable',      'blend_trainable',        make_vec),
+        ('blend_shuffled_trainable',    'blend_shuffled',         make_vec),
+        ('blend_zero_target_trainable', 'blend_zero_target',      make_vec),
+        ('blend_fresh_random_target',   'blend_fresh_random',     make_vec),
+        ('blend_time_only_trainable',   'blend_time_only',        make_time_only),
+        ('blend_constant_input',        'blend_constant',         make_constant),
+        ('blend_prefit60_frozen',       'blend_frozen',           make_prefit_frozen),
+        ('blend_prefit60_trainable',    'blend_prefit_trainable', make_prefit_trainable),
+    ]
+
+    all_results = {}
+    for bname, btype, aux_factory in branches:
+        print(f"\n{'='*60}\n{bname}\n{'='*60}")
+        # Fresh model from checkpoint
+        model_b = ResidualMLP(input_dim, d, 10, L).to(device)
+        model_b.load_state_dict(ckpt['model'])
+        aux_net_b = aux_factory()
+
+        log = run_branch(
+            model_b, aux_net_b, ckpt['Bs'],
+            train_loader, test_loader, device,
+            args.t0, args.epochs, btype,
+            args.alpha, args.lr, args.lr_fb, args.wd, args.M,
+            branch_name=bname, fresh_sigma=fresh_sigma)
+        all_results[bname] = log
+        print(f"  {bname} final acc: {log['test_acc'][-1]:.4f}")
+
+    # ----------------------------------------------------------------
+    # Step 5: Summary table
+    # ----------------------------------------------------------------
+    dfa_final = all_results['continue_DFA']['test_acc'][-1]
+
+    print(f"\n{'='*95}")
+    print("SUMMARY — Phase 10A.6: Structured vs Semantic Auxiliary")
+    print(f"{'='*95}")
+    print(f"{'Branch':<34} {'@20':>6} {'final':>7} {'diff':>7} "
+          f"{'mG_5:15':>9} {'mr_5:15':>9} {'aeff':>7}")
+    print("-" * 83)
+
+    for bname, log in all_results.items():
+        accs = log['test_acc']
+        idx20 = max(0, 20 - args.t0 - 1)
+        acc20 = accs[idx20] if len(accs) > idx20 else accs[-1]
+        final = accs[-1]
+        diff = final - dfa_final
+        gammas_e = [g for e, g in log['gamma'] if args.t0 < e <= args.t0 + 15]
+        rhos_e = [r for e, r in log['rho'] if args.t0 < e <= args.t0 + 15]
+        aeffs_e = [a for e, a in log['alpha_eff'] if args.t0 < e <= args.t0 + 15]
+        mg = float(np.mean(gammas_e)) if gammas_e else float('nan')
+        mr = float(np.mean(rhos_e)) if rhos_e else float('nan')
+        mae = float(np.mean(aeffs_e)) if aeffs_e else float('nan')
+        print(f"{bname:<34} {acc20:>6.4f} {final:>7.4f} {diff:>+7.4f} "
+              f"{mg:>9.4f} {mr:>9.4f} {mae:>7.3f}")
+
+    # ----------------------------------------------------------------
+    # Step 6: Save results
+    # ----------------------------------------------------------------
+    save_data = {
+        'args': vars(args),
+        'dfa_ckpt_acc': float(ckpt['acc']),
+        'fresh_sigma': float(fresh_sigma),
+    }
+    for bname, log in all_results.items():
+        save_data[bname] = {
+            'test_acc': log['test_acc'],
+            'train_loss': log['train_loss'],
+            'gamma': log['gamma'],
+            'rho': log['rho'],
+            'alpha_eff': log['alpha_eff'],
+        }
+    out_path = os.path.join(args.output_dir,
+                            f'structured_aux_t{args.t0}_s{args.seed}.json')
+    with open(out_path, 'w') as f:
+        json.dump(save_data, f, indent=2, default=float)
+    print(f"\nSaved to {out_path}")
+
+    # ----------------------------------------------------------------
+    # Step 7: Judgment
+    # ----------------------------------------------------------------
+    print(f"\n{'='*60}\nJUDGMENT\n{'='*60}")
+    r = {bname: log['test_acc'][-1] for bname, log in all_results.items()}
+    dfa = r['continue_DFA']
+    rt = r.get('blend_random_trainable', float('nan'))
+    sh = r.get('blend_shuffled_trainable', float('nan'))
+    zt = r.get('blend_zero_target_trainable', float('nan'))
+    fr = r.get('blend_fresh_random_target', float('nan'))
+    to = r.get('blend_time_only_trainable', float('nan'))
+    cn = r.get('blend_constant_input', float('nan'))
+    pf = r.get('blend_prefit60_frozen', float('nan'))
+    pt = r.get('blend_prefit60_trainable', float('nan'))
+
+    print(f"  DFA={dfa:.4f}  rt={rt:.4f}  sh={sh:.4f}  zt={zt:.4f}  "
+          f"fr={fr:.4f}  to={to:.4f}  cn={cn:.4f}  pf={pf:.4f}  pt={pt:.4f}")
+
+    # Key comparisons
+    thr = 0.003
+    if abs(rt - sh) < thr and abs(rt - fr) < thr:
+        print("  -> random_trainable ≈ shuffled ≈ fresh_random: "
+              "gain is NOT from semantic content, likely norm/regularization")
+    elif rt > sh + thr and rt > fr + thr:
+        print("  -> random_trainable > shuffled AND fresh_random: "
+              "some semantic structure in Vec helps")
+
+    if abs(rt - zt) < thr:
+        print("  -> zero_target ≈ random_trainable: "
+              "the implicit regularization is from the blend ratio, not signal direction")
+    elif zt < dfa - thr:
+        print("  -> zero_target HURTS vs DFA: driving aux toward zero is not just neutral")
+
+    if abs(rt - to) < thr:
+        print("  -> time_only ≈ random_trainable: "
+              "depth schedule alone captures most of the benefit")
+    if abs(rt - cn) < thr:
+        print("  -> constant_input ≈ random_trainable: "
+              "fixed per-block template sufficient (no input processing needed)")
+
+    if pt > pf + thr:
+        print("  -> prefit60_trainable > prefit60_frozen: "
+              "continued training after prefit improves further")
+    elif abs(pt - pf) < thr:
+        print("  -> prefit60_trainable ≈ prefit60_frozen: "
+              "prefit quality saturates, additional online training neutral")
+
+    if pt > rt + thr:
+        print("  -> prefit60_trainable > random_trainable: "
+              "warm-start from prefit helps over training from scratch")
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description='Phase 10A.6: Structured vs Semantic Auxiliary Dissection')
+    parser.add_argument('--num_blocks', type=int, default=4)
+    parser.add_argument('--d_hidden', type=int, default=256)
+    parser.add_argument('--batch_size', type=int, default=128)
+    parser.add_argument('--epochs', type=int, default=100)
+    parser.add_argument('--t0', type=int, default=5)
+    parser.add_argument('--alpha', type=float, default=0.75)
+    parser.add_argument('--lr', type=float, default=1e-3)
+    parser.add_argument('--lr_fb', type=float, default=1e-3)
+    parser.add_argument('--wd', type=float, default=0.01)
+    parser.add_argument('--M', type=int, default=4)
+    parser.add_argument('--seed', type=int, default=42)
+    parser.add_argument('--gpu', type=int, default=2)
+    parser.add_argument('--output_dir', type=str, default='results/structured_aux')
+    args = parser.parse_args()
+    run_experiment(args)
+
+
+if __name__ == '__main__':
+    main()