Add Phase 2 explore experiments: synthetic nonlinearity ladder + CIFAR depth scan

- synth_nonlinearity_ladder.py: teacher-student with phi_alpha(z) = (1-a)z + a*tanh(z)
  Sweeps alpha x depth to find where state bridge / credit bridge fail
- cifar_depth_scan.py: CIFAR-10 with L={2,4,6,8,12}, d={256,512}
  Finds Goldilocks regime for credit bridge vs DFA
- plot_synth_ladder.py: phase diagram visualization

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

1 files changed, 822 insertions, 0 deletions

diff --git a/experiments/synth_nonlinearity_ladder.py b/experiments/synth_nonlinearity_ladder.py
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+++ b/experiments/synth_nonlinearity_ladder.py
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+"""
+Synthetic Nonlinearity Ladder: teacher-student classification with controllable nonlinearity.
+
+Teacher dynamics:
+  h_{l+1}^* = h_l^* + W_l^* phi_alpha(h_l^*)
+  phi_alpha(z) = (1-alpha)*z + alpha*tanh(z)
+
+alpha=0 -> linear, alpha=1 -> fully nonlinear.
+Sweep (alpha, L) to find where state bridge fails and credit bridge degrades.
+
+Methods: BP, DFA, State Bridge, Credit Bridge (all reuse project conventions).
+"""
+import os
+import sys
+import json
+import argparse
+import time
+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, TensorDataset
+import copy
+
+sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
+
+from models.residual_mlp import ResidualMLP, ResidualBlock
+from models.value_net import ValueNet, create_ema_model, update_ema
+from models.state_bridge import StateBridgeNet
+from metrics.credit_metrics import (
+    cosine_similarity_batch, perturbation_correlation, nudging_test,
+    offline_bp_cosine, feature_drift
+)
+
+
+# =============================================================================
+# Teacher network and data generation
+# =============================================================================
+class TeacherNet:
+    """Fixed teacher network with controllable nonlinearity."""
+
+    def __init__(self, d_hidden, num_blocks, num_classes, alpha, seed=0):
+        rng = np.random.RandomState(seed)
+        self.d_hidden = d_hidden
+        self.num_blocks = num_blocks
+        self.num_classes = num_classes
+        self.alpha = alpha
+
+        # Teacher block weights: scaled for stability
+        self.Ws = []
+        for l in range(num_blocks):
+            W = rng.randn(d_hidden, d_hidden).astype(np.float32)
+            # Scale so spectral norm of residual part is small
+            W = W / (np.linalg.norm(W, ord=2) + 1e-8) * 0.3
+            self.Ws.append(torch.from_numpy(W))
+
+        # Output projection
+        U = rng.randn(num_classes, d_hidden).astype(np.float32)
+        U = U / (np.linalg.norm(U, ord=2) + 1e-8)
+        self.U = torch.from_numpy(U)
+
+    def to(self, device):
+        self.Ws = [W.to(device) for W in self.Ws]
+        self.U = self.U.to(device)
+        return self
+
+    def phi(self, z):
+        """Controllable activation: (1-alpha)*z + alpha*tanh(z)."""
+        return (1 - self.alpha) * z + self.alpha * torch.tanh(z)
+
+    def forward(self, h0):
+        """Forward pass through teacher, returns logits and hidden states."""
+        h = h0
+        hiddens = [h]
+        for l in range(self.num_blocks):
+            f = F.linear(self.phi(h), self.Ws[l])
+            h = h + f
+            hiddens.append(h)
+        logits = F.linear(h, self.U)
+        return logits, hiddens
+
+
+def generate_dataset(teacher, num_samples, d_hidden, device, seed=0):
+    """Generate classification dataset from teacher network."""
+    torch.manual_seed(seed)
+    X = torch.randn(num_samples, d_hidden, device=device)
+    with torch.no_grad():
+        logits, _ = teacher.forward(X)
+        Y = logits.argmax(dim=-1)
+    return X, Y
+
+
+# =============================================================================
+# Student network (same architecture family as teacher)
+# =============================================================================
+class StudentBlock(nn.Module):
+    """Residual block with pre-LayerNorm + phi_alpha."""
+
+    def __init__(self, d_hidden, alpha):
+        super().__init__()
+        self.ln = nn.LayerNorm(d_hidden)
+        self.w = nn.Linear(d_hidden, d_hidden, bias=False)
+        self.alpha = alpha
+        # Small init for stability
+        nn.init.normal_(self.w.weight, std=0.01)
+
+    def phi(self, z):
+        return (1 - self.alpha) * z + self.alpha * torch.tanh(z)
+
+    def forward(self, h):
+        """Returns residual F_l(h), NOT h + F_l(h)."""
+        return self.w(self.phi(self.ln(h)))
+
+
+class StudentNet(nn.Module):
+    """Student network: L residual blocks + linear output head."""
+
+    def __init__(self, d_hidden, num_classes, num_blocks, alpha):
+        super().__init__()
+        self.blocks = nn.ModuleList([StudentBlock(d_hidden, alpha) for _ in range(num_blocks)])
+        self.out_head = nn.Linear(d_hidden, num_classes)
+        self.num_blocks = num_blocks
+        self.d_hidden = d_hidden
+
+    def forward(self, x, return_hidden=False):
+        h = x  # No embedding needed, input is already d_hidden
+        hiddens = [h] if return_hidden else None
+        for block in self.blocks:
+            f = block(h)
+            h = h + f
+            if return_hidden:
+                hiddens.append(h)
+        logits = self.out_head(h)
+        if return_hidden:
+            return logits, hiddens
+        return logits
+
+    def forward_from_layer(self, h, start_layer):
+        """Run forward from a given layer to output."""
+        for i in range(start_layer, self.num_blocks):
+            f = self.blocks[i](h)
+            h = h + f
+        return self.out_head(h)
+
+
+# =============================================================================
+# Training methods
+# =============================================================================
+def evaluate(model, test_loader, device):
+    model.eval()
+    correct, total = 0, 0
+    with torch.no_grad():
+        for x, y in test_loader:
+            x, y = x.to(device), y.to(device)
+            logits = model(x)
+            correct += (logits.argmax(1) == y).sum().item()
+            total += x.size(0)
+    return correct / total
+
+
+def train_bp(model, train_loader, test_loader, device, args):
+    """Standard BP training."""
+    optimizer = optim.AdamW(model.parameters(), lr=args.lr, weight_decay=args.wd)
+    scheduler = optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=args.epochs)
+    log = {'train_loss': [], 'train_acc': [], 'test_acc': []}
+
+    for epoch in range(1, args.epochs + 1):
+        model.train()
+        total_loss, correct, total = 0, 0, 0
+        for x, y in train_loader:
+            x, y = x.to(device), y.to(device)
+            logits = model(x)
+            loss = F.cross_entropy(logits, y)
+            optimizer.zero_grad()
+            loss.backward()
+            optimizer.step()
+            total_loss += loss.item() * x.size(0)
+            correct += (logits.argmax(1) == y).sum().item()
+            total += x.size(0)
+        scheduler.step()
+        log['train_loss'].append(total_loss / total)
+        log['train_acc'].append(correct / total)
+        log['test_acc'].append(evaluate(model, test_loader, device))
+        if epoch % 20 == 0 or epoch == 1:
+            print(f"    [BP] Ep {epoch}: loss={log['train_loss'][-1]:.4f} "
+                  f"train={log['train_acc'][-1]:.4f} test={log['test_acc'][-1]:.4f}")
+    return log
+
+
+def train_dfa(model, train_loader, test_loader, device, args):
+    """DFA training with fixed random feedback matrices."""
+    d = model.d_hidden
+    L = model.num_blocks
+    C = args.num_classes
+
+    Bs = [torch.randn(d, C, device=device) / np.sqrt(C) for _ in range(L)]
+    block_opts = [optim.AdamW(block.parameters(), lr=args.lr, weight_decay=args.wd)
+                  for block in model.blocks]
+    head_opt = optim.AdamW(model.out_head.parameters(), lr=args.lr, weight_decay=args.wd)
+
+    all_schedulers = ([optim.lr_scheduler.CosineAnnealingLR(o, T_max=args.epochs) for o in block_opts]
+                      + [optim.lr_scheduler.CosineAnnealingLR(head_opt, T_max=args.epochs)])
+
+    log = {'train_loss': [], 'train_acc': [], 'test_acc': []}
+
+    for epoch in range(1, args.epochs + 1):
+        model.train()
+        total_loss, correct, total = 0, 0, 0
+        for x, y in train_loader:
+            x, y = x.to(device), y.to(device)
+            batch = x.size(0)
+
+            with torch.no_grad():
+                logits, hiddens = model(x, return_hidden=True)
+                loss_val = F.cross_entropy(logits, y)
+                e_T = logits.softmax(dim=-1)
+                e_T[torch.arange(batch), y] -= 1
+
+            # Update output head (h_L detached)
+            hL_det = hiddens[-1].detach()
+            logits_out = model.out_head(hL_det)
+            loss_out = F.cross_entropy(logits_out, y)
+            head_opt.zero_grad()
+            loss_out.backward()
+            head_opt.step()
+
+            # Update each block with DFA local surrogate
+            for l in range(L):
+                h_l = hiddens[l].detach()
+                a_dfa = (e_T @ Bs[l].T).detach()
+                rms = (a_dfa ** 2).mean(dim=-1, keepdim=True).sqrt() + 1e-6
+                a_norm = a_dfa / rms
+                f_l = model.blocks[l](h_l)
+                local_loss = (f_l * a_norm).sum(dim=-1).mean()
+                block_opts[l].zero_grad()
+                local_loss.backward()
+                torch.nn.utils.clip_grad_norm_(model.blocks[l].parameters(), 1.0)
+                block_opts[l].step()
+
+            total_loss += loss_val.item() * batch
+            correct += (logits.argmax(1) == y).sum().item()
+            total += batch
+
+        for s in all_schedulers:
+            s.step()
+        log['train_loss'].append(total_loss / total)
+        log['train_acc'].append(correct / total)
+        log['test_acc'].append(evaluate(model, test_loader, device))
+        if epoch % 20 == 0 or epoch == 1:
+            print(f"    [DFA] Ep {epoch}: loss={log['train_loss'][-1]:.4f} "
+                  f"train={log['train_acc'][-1]:.4f} test={log['test_acc'][-1]:.4f}")
+    return log, Bs
+
+
+def train_state_bridge(model, train_loader, test_loader, device, args):
+    """State Bridge training."""
+    d = model.d_hidden
+    L = model.num_blocks
+    C = args.num_classes
+
+    state_pred = StateBridgeNet(d_hidden=d, s_dim=C, time_embed_dim=32,
+                                hidden_dim=256, num_layers=3).to(device)
+
+    block_opts = [optim.AdamW(block.parameters(), lr=args.lr, weight_decay=args.wd)
+                  for block in model.blocks]
+    head_opt = optim.AdamW(model.out_head.parameters(), lr=args.lr, weight_decay=args.wd)
+    state_opt = optim.Adam(state_pred.parameters(), lr=args.lr_fb)
+
+    all_schedulers = ([optim.lr_scheduler.CosineAnnealingLR(o, T_max=args.epochs) for o in block_opts]
+                      + [optim.lr_scheduler.CosineAnnealingLR(head_opt, T_max=args.epochs)])
+
+    log = {'train_loss': [], 'train_acc': [], 'test_acc': [], 'state_pred_error': []}
+
+    for epoch in range(1, args.epochs + 1):
+        model.train()
+        state_pred.train()
+        total_loss, correct, total = 0, 0, 0
+        total_se = 0
+
+        for x, y in train_loader:
+            x, y = x.to(device), y.to(device)
+            batch = x.size(0)
+
+            with torch.no_grad():
+                logits, hiddens = model(x, return_hidden=True)
+                loss_val = F.cross_entropy(logits, y)
+                e_T = logits.softmax(dim=-1)
+                e_T[torch.arange(batch), y] -= 1
+                s = e_T.detach()
+
+            hL_det = hiddens[-1].detach()
+
+            # Train state predictor
+            state_loss = 0.0
+            for l in range(L):
+                h_l_det = hiddens[l].detach()
+                t_l = torch.full((batch,), l / L, device=device)
+                pred_hL = state_pred(h_l_det, t_l, s)
+                target = hL_det
+                target_norm = target.norm(dim=-1, keepdim=True).clamp(min=1.0)
+                state_loss = state_loss + (((pred_hL - target) / target_norm) ** 2).sum(dim=-1).mean()
+            state_loss = state_loss / L
+            state_opt.zero_grad()
+            state_loss.backward()
+            state_opt.step()
+            total_se += state_loss.item() * batch
+
+            # Compute credits
+            credits = []
+            for l in range(L):
+                h_l_det = hiddens[l].detach().requires_grad_(True)
+                t_l = torch.full((batch,), l / L, device=device)
+                pred_hL = state_pred(h_l_det, t_l, s)
+                pred_logits = model.out_head(pred_hL)
+                pred_loss = F.cross_entropy(pred_logits, y, reduction='sum')
+                a_l = torch.autograd.grad(pred_loss, h_l_det, create_graph=False)[0]
+                credits.append(a_l.detach())
+
+            # Update output head
+            logits_out = model.out_head(hL_det)
+            loss_out = F.cross_entropy(logits_out, y)
+            head_opt.zero_grad()
+            loss_out.backward()
+            head_opt.step()
+
+            # Update blocks
+            for l in range(L):
+                h_l = hiddens[l].detach()
+                a = credits[l]
+                rms = (a ** 2).mean(dim=-1, keepdim=True).sqrt() + 1e-6
+                a_norm = a / rms
+                f_l = model.blocks[l](h_l)
+                local_loss = (f_l * a_norm).sum(dim=-1).mean()
+                block_opts[l].zero_grad()
+                local_loss.backward()
+                torch.nn.utils.clip_grad_norm_(model.blocks[l].parameters(), 1.0)
+                block_opts[l].step()
+
+            total_loss += loss_val.item() * batch
+            correct += (logits.argmax(1) == y).sum().item()
+            total += batch
+
+        for sch in all_schedulers:
+            sch.step()
+
+        log['train_loss'].append(total_loss / total)
+        log['train_acc'].append(correct / total)
+        log['test_acc'].append(evaluate(model, test_loader, device))
+        log['state_pred_error'].append(total_se / total)
+        if epoch % 20 == 0 or epoch == 1:
+            print(f"    [SB] Ep {epoch}: loss={log['train_loss'][-1]:.4f} "
+                  f"train={log['train_acc'][-1]:.4f} test={log['test_acc'][-1]:.4f} "
+                  f"se={log['state_pred_error'][-1]:.6f}")
+    return log, state_pred
+
+
+def train_credit_bridge(model, train_loader, test_loader, device, args):
+    """Credit Bridge training with terminal gradient matching + bridge consistency."""
+    d = model.d_hidden
+    L = model.num_blocks
+    C = args.num_classes
+    warmup_epochs = max(1, args.epochs // 5)
+
+    value_net = ValueNet(d_hidden=d, s_dim=C, time_embed_dim=32,
+                         hidden_dim=256, num_layers=3).to(device)
+    value_net_ema = create_ema_model(value_net)
+
+    Bs_fallback = [torch.randn(d, C, device=device) / np.sqrt(C) for _ in range(L)]
+
+    block_opts = [optim.AdamW(block.parameters(), lr=args.lr, weight_decay=args.wd)
+                  for block in model.blocks]
+    head_opt = optim.AdamW(model.out_head.parameters(), lr=args.lr, weight_decay=args.wd)
+    value_opt = optim.Adam(value_net.parameters(), lr=args.lr_fb)
+
+    all_schedulers = ([optim.lr_scheduler.CosineAnnealingLR(o, T_max=args.epochs) for o in block_opts]
+                      + [optim.lr_scheduler.CosineAnnealingLR(head_opt, T_max=args.epochs)])
+
+    lam = args.lam
+    K_samples = args.K
+    sigma_bridge = args.sigma_bridge
+    ema_momentum = args.ema_momentum
+    term_grad_weight = args.term_grad_weight
+
+    log = {'train_loss': [], 'train_acc': [], 'test_acc': [],
+           'value_loss': [], 'term_loss': [], 'bridge_loss': [], 'tgrad_loss': []}
+
+    for epoch in range(1, args.epochs + 1):
+        model.train()
+        value_net.train()
+        total_loss, correct, total = 0, 0, 0
+        total_vloss, total_term, total_bridge, total_tgrad = 0, 0, 0, 0
+
+        if epoch <= warmup_epochs:
+            credit_blend = 0.0
+        else:
+            credit_blend = min(1.0, (epoch - warmup_epochs) / max(1, warmup_epochs))
+
+        for x, y in train_loader:
+            x, y = x.to(device), y.to(device)
+            batch = x.size(0)
+
+            with torch.no_grad():
+                logits, hiddens = model(x, return_hidden=True)
+                loss_val = F.cross_entropy(logits, y)
+                e_T = logits.softmax(dim=-1)
+                e_T[torch.arange(batch), y] -= 1
+                s = e_T.detach()
+                true_loss = F.cross_entropy(logits, y, reduction='none').detach()
+
+            hL_det = hiddens[-1].detach()
+
+            # ---- Train value net ----
+            t_L = torch.ones(batch, device=device)
+            V_terminal = value_net(hL_det, t_L, s)
+            loss_term = ((V_terminal - true_loss) ** 2).mean()
+
+            loss_tgrad = torch.tensor(0.0, device=device)
+            if term_grad_weight > 0:
+                hL_req = hL_det.clone().requires_grad_(True)
+                V_at_L = value_net(hL_req, t_L, s)
+                grad_V_L = torch.autograd.grad(V_at_L.sum(), hL_req, create_graph=True)[0]
+                hL_req2 = hL_det.clone().requires_grad_(True)
+                logits_tgt = model.out_head(hL_req2)
+                ce_loss = F.cross_entropy(logits_tgt, y, reduction='sum')
+                a_L_exact = torch.autograd.grad(ce_loss, hL_req2, create_graph=False)[0].detach()
+                loss_tgrad = ((grad_V_L - a_L_exact) ** 2).sum(dim=-1).mean()
+
+            loss_bridge = 0.0
+            for l in range(L):
+                h_l_det = hiddens[l].detach()
+                t_l = torch.full((batch,), l / L, device=device)
+                t_l_next = torch.full((batch,), (l + 1) / L, device=device)
+                V_l = value_net(h_l_det, t_l, s)
+
+                with torch.no_grad():
+                    h_next_det = hiddens[l + 1].detach()
+                    log_terms = []
+                    for k in range(K_samples):
+                        noise = sigma_bridge * torch.randn_like(h_next_det)
+                        V_next = value_net_ema(h_next_det + noise, t_l_next, s)
+                        log_terms.append(-V_next / lam)
+                    log_stack = torch.stack(log_terms, dim=-1)
+                    V_target = -lam * (torch.logsumexp(log_stack, dim=-1) - np.log(K_samples))
+
+                loss_bridge = loss_bridge + ((V_l - V_target.detach()) ** 2).mean()
+            loss_bridge = loss_bridge / L
+
+            value_loss = loss_term + loss_bridge + term_grad_weight * loss_tgrad
+            value_opt.zero_grad()
+            value_loss.backward()
+            torch.nn.utils.clip_grad_norm_(value_net.parameters(), 1.0)
+            value_opt.step()
+            update_ema(value_net, value_net_ema, ema_momentum)
+
+            total_vloss += value_loss.item() * batch
+            total_term += loss_term.item() * batch
+            total_bridge += (loss_bridge.item() if isinstance(loss_bridge, torch.Tensor) else loss_bridge) * batch
+            total_tgrad += loss_tgrad.item() * batch
+
+            # ---- Compute credits ----
+            cb_credits = []
+            for l in range(L):
+                h_l_det = hiddens[l].detach().requires_grad_(True)
+                t_l = torch.full((batch,), l / L, device=device)
+                V_l = value_net(h_l_det, t_l, s)
+                a_l = torch.autograd.grad(V_l.sum(), h_l_det, create_graph=False)[0]
+                cb_credits.append(a_l.detach())
+
+            dfa_credits = [(e_T @ Bs_fallback[l].T).detach() for l in range(L)]
+
+            credits = []
+            for l in range(L):
+                if credit_blend >= 1.0:
+                    a = cb_credits[l]
+                elif credit_blend <= 0.0:
+                    a = dfa_credits[l]
+                else:
+                    cb_rms = (cb_credits[l] ** 2).mean(dim=-1, keepdim=True).sqrt() + 1e-6
+                    dfa_rms = (dfa_credits[l] ** 2).mean(dim=-1, keepdim=True).sqrt() + 1e-6
+                    a = credit_blend * (cb_credits[l] / cb_rms) + (1 - credit_blend) * (dfa_credits[l] / dfa_rms)
+                credits.append(a)
+
+            # ---- Update output head ----
+            logits_out = model.out_head(hL_det)
+            loss_out = F.cross_entropy(logits_out, y)
+            head_opt.zero_grad()
+            loss_out.backward()
+            head_opt.step()
+
+            # ---- Update blocks ----
+            for l in range(L):
+                h_l = hiddens[l].detach()
+                a = credits[l]
+                rms = (a ** 2).mean(dim=-1, keepdim=True).sqrt() + 1e-6
+                a_norm = a / rms
+                f_l = model.blocks[l](h_l)
+                local_loss = (f_l * a_norm).sum(dim=-1).mean()
+                block_opts[l].zero_grad()
+                local_loss.backward()
+                torch.nn.utils.clip_grad_norm_(model.blocks[l].parameters(), 1.0)
+                block_opts[l].step()
+
+            total_loss += loss_val.item() * batch
+            correct += (logits.argmax(1) == y).sum().item()
+            total += batch
+
+        for sch in all_schedulers:
+            sch.step()
+
+        log['train_loss'].append(total_loss / total)
+        log['train_acc'].append(correct / total)
+        log['test_acc'].append(evaluate(model, test_loader, device))
+        log['value_loss'].append(total_vloss / total)
+        log['term_loss'].append(total_term / total)
+        log['bridge_loss'].append(total_bridge / total)
+        log['tgrad_loss'].append(total_tgrad / total)
+        if epoch % 20 == 0 or epoch == 1:
+            phase = "warmup" if epoch <= warmup_epochs else f"blend={credit_blend:.2f}"
+            print(f"    [CB] Ep {epoch} ({phase}): loss={log['train_loss'][-1]:.4f} "
+                  f"train={log['train_acc'][-1]:.4f} test={log['test_acc'][-1]:.4f} "
+                  f"vloss={log['value_loss'][-1]:.6f}")
+    return log, value_net, value_net_ema
+
+
+# =============================================================================
+# Diagnostics (per-layer)
+# =============================================================================
+def compute_diagnostics(model, method_name, test_loader, device, args,
+                        value_net=None, state_predictor=None, dfa_Bs=None):
+    """Compute per-layer diagnostic metrics."""
+    model.eval()
+    if value_net is not None:
+        value_net.eval()
+    if state_predictor is not None:
+        state_predictor.eval()
+
+    d = model.d_hidden
+    L = model.num_blocks
+    C = args.num_classes
+
+    # Get one batch
+    for x, y in test_loader:
+        x, y = x.to(device), y.to(device)
+        break
+
+    batch = x.size(0)
+
+    # BP gradients (for offline BP cosine)
+    # Manual forward to get gradable hidden states
+    h = x.detach().requires_grad_(True)
+    hiddens_bp = [h]
+    for block in model.blocks:
+        f = block(hiddens_bp[-1])
+        h_next = hiddens_bp[-1] + f
+        hiddens_bp.append(h_next)
+    logits_bp = model.out_head(hiddens_bp[-1])
+    loss_bp = F.cross_entropy(logits_bp, y)
+    bp_grads = {}
+    grads = torch.autograd.grad(loss_bp, hiddens_bp, retain_graph=False)
+    for l in range(L + 1):
+        bp_grads[l] = grads[l].detach().clone()
+
+    # Clean forward
+    with torch.no_grad():
+        logits, hiddens = model(x, return_hidden=True)
+        e_T = logits.softmax(dim=-1)
+        e_T[torch.arange(batch), y] -= 1
+        s = e_T.detach()
+
+    results = {
+        'bp_cosine': [],
+        'perturbation_rho': [],
+        'nudging': {'0.001': [], '0.003': [], '0.01': []},
+    }
+
+    # State bridge prediction error (if applicable)
+    if method_name == 'state_bridge' and state_predictor is not None:
+        state_pred_errors = []
+        for l in range(L):
+            h_l_det = hiddens[l].detach()
+            t_l = torch.full((batch,), l / L, device=device)
+            with torch.no_grad():
+                pred_hL = state_predictor(h_l_det, t_l, s)
+                hL_det = hiddens[-1].detach()
+                err = ((pred_hL - hL_det) ** 2).sum(dim=-1).mean().item()
+                state_pred_errors.append(err)
+        results['state_pred_error_per_layer'] = state_pred_errors
+
+    for l in range(L):
+        h_l = hiddens[l].detach()
+        t_l = torch.full((batch,), l / L, device=device)
+
+        if method_name == 'bp':
+            a_l = bp_grads[l]
+        elif method_name == 'dfa':
+            a_l = (e_T @ dfa_Bs[l].T).detach()
+        elif method_name == 'state_bridge':
+            h_l_req = h_l.clone().requires_grad_(True)
+            pred_hL = state_predictor(h_l_req, t_l, s)
+            pred_logits = model.out_head(pred_hL)
+            pred_loss = F.cross_entropy(pred_logits, y, reduction='sum')
+            a_l = torch.autograd.grad(pred_loss, h_l_req, create_graph=False)[0].detach()
+        elif method_name == 'credit_bridge':
+            h_l_req = h_l.clone().requires_grad_(True)
+            V_l = value_net(h_l_req, t_l, s)
+            a_l = torch.autograd.grad(V_l.sum(), h_l_req, create_graph=False)[0].detach()
+        else:
+            raise ValueError(f"Unknown method: {method_name}")
+
+        # BP cosine
+        bp_cos = cosine_similarity_batch(a_l, bp_grads[l])
+        results['bp_cosine'].append(bp_cos)
+
+        # Forward function for perturbation and nudging
+        def make_fwd_fn(start_l):
+            def fwd_fn(h):
+                with torch.no_grad():
+                    curr = h
+                    for i in range(start_l, L):
+                        curr = curr + model.blocks[i](curr)
+                    out = model.out_head(curr)
+                    return F.cross_entropy(out, y, reduction='none')
+            return fwd_fn
+
+        fwd_fn = make_fwd_fn(l)
+        rho = perturbation_correlation(h_l, a_l, fwd_fn, epsilon=1e-3, M=16)
+        results['perturbation_rho'].append(rho)
+
+        for eta in [0.001, 0.003, 0.01]:
+            nud = nudging_test(h_l, a_l, fwd_fn, eta=eta)
+            results['nudging'][str(eta)].append(nud)
+
+    return results
+
+
+# =============================================================================
+# Main experiment runner
+# =============================================================================
+def run_single(alpha, L, seed, args, device):
+    """Run all methods for a single (alpha, L, seed) configuration."""
+    d = args.d_hidden
+    C = args.num_classes
+
+    print(f"\n  === alpha={alpha}, L={L}, seed={seed} ===")
+    t0 = time.time()
+
+    # Generate data from teacher
+    teacher = TeacherNet(d, L, C, alpha, seed=0).to(device)  # Fixed teacher seed=0
+    X_train, Y_train = generate_dataset(teacher, args.n_train, d, device, seed=seed)
+    X_test, Y_test = generate_dataset(teacher, args.n_test, d, device, seed=seed + 10000)
+
+    train_ds = TensorDataset(X_train, Y_train)
+    test_ds = TensorDataset(X_test, Y_test)
+    train_loader = DataLoader(train_ds, batch_size=args.batch_size, shuffle=True)
+    test_loader = DataLoader(test_ds, batch_size=args.batch_size, shuffle=False)
+
+    results = {}
+
+    # ---- BP ----
+    print("    --- BP ---")
+    torch.manual_seed(seed)
+    model_bp = StudentNet(d, C, L, alpha).to(device)
+    bp_log = train_bp(model_bp, train_loader, test_loader, device, args)
+    bp_diag = compute_diagnostics(model_bp, 'bp', test_loader, device, args)
+    results['bp'] = {'log': bp_log, 'diagnostics': bp_diag}
+
+    # ---- DFA ----
+    print("    --- DFA ---")
+    torch.manual_seed(seed)
+    model_dfa = StudentNet(d, C, L, alpha).to(device)
+    dfa_log, dfa_Bs = train_dfa(model_dfa, train_loader, test_loader, device, args)
+    dfa_diag = compute_diagnostics(model_dfa, 'dfa', test_loader, device, args, dfa_Bs=dfa_Bs)
+    results['dfa'] = {'log': dfa_log, 'diagnostics': dfa_diag}
+
+    # ---- State Bridge ----
+    print("    --- State Bridge ---")
+    torch.manual_seed(seed)
+    model_sb = StudentNet(d, C, L, alpha).to(device)
+    sb_log, state_pred = train_state_bridge(model_sb, train_loader, test_loader, device, args)
+    sb_diag = compute_diagnostics(model_sb, 'state_bridge', test_loader, device, args,
+                                   state_predictor=state_pred)
+    results['state_bridge'] = {'log': sb_log, 'diagnostics': sb_diag}
+
+    # ---- Credit Bridge ----
+    print("    --- Credit Bridge ---")
+    torch.manual_seed(seed)
+    model_cb = StudentNet(d, C, L, alpha).to(device)
+    cb_log, vnet, vnet_ema = train_credit_bridge(model_cb, train_loader, test_loader, device, args)
+    cb_diag = compute_diagnostics(model_cb, 'credit_bridge', test_loader, device, args,
+                                   value_net=vnet)
+    results['credit_bridge'] = {'log': cb_log, 'diagnostics': cb_diag}
+
+    elapsed = time.time() - t0
+    print(f"  === Done alpha={alpha}, L={L}, seed={seed} in {elapsed:.1f}s ===")
+
+    # Summary
+    for m in ['bp', 'dfa', 'state_bridge', 'credit_bridge']:
+        test_acc = results[m]['log']['test_acc'][-1]
+        mean_gamma = np.mean(results[m]['diagnostics']['bp_cosine'])
+        mean_rho = np.mean(results[m]['diagnostics']['perturbation_rho'])
+        mean_nudge = np.mean(results[m]['diagnostics']['nudging']['0.01'])
+        print(f"    {m:20s}: acc={test_acc:.4f} Gamma={mean_gamma:.4f} "
+              f"rho={mean_rho:.4f} nudge={mean_nudge:.6f}")
+
+    return results
+
+
+def serialize(obj):
+    if isinstance(obj, dict):
+        return {str(k): serialize(v) for k, v in obj.items()}
+    elif isinstance(obj, list):
+        return [serialize(v) for v in obj]
+    elif isinstance(obj, (np.floating, np.integer)):
+        return float(obj)
+    elif isinstance(obj, np.ndarray):
+        return obj.tolist()
+    elif isinstance(obj, torch.Tensor):
+        return obj.cpu().numpy().tolist()
+    return obj
+
+
+def main():
+    parser = argparse.ArgumentParser(description='Synthetic Nonlinearity Ladder')
+    parser.add_argument('--alphas', type=float, nargs='+', default=[0.0, 0.5, 1.0])
+    parser.add_argument('--depths', type=int, nargs='+', default=[2, 8])
+    parser.add_argument('--seeds', type=int, nargs='+', default=[42])
+    parser.add_argument('--d_hidden', type=int, default=128)
+    parser.add_argument('--num_classes', type=int, default=10)
+    parser.add_argument('--n_train', type=int, default=10000)
+    parser.add_argument('--n_test', type=int, default=2000)
+    parser.add_argument('--batch_size', type=int, default=256)
+    parser.add_argument('--epochs', type=int, default=60)
+    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('--lam', type=float, default=0.1)
+    parser.add_argument('--K', type=int, default=4)
+    parser.add_argument('--sigma_bridge', type=float, default=0.05)
+    parser.add_argument('--ema_momentum', type=float, default=0.995)
+    parser.add_argument('--term_grad_weight', type=float, default=1.0)
+    parser.add_argument('--gpu', type=int, default=1)
+    parser.add_argument('--output_dir', type=str, default='results/synth_ladder')
+    args = parser.parse_args()
+
+    device = torch.device(f'cuda:{args.gpu}' if torch.cuda.is_available() else 'cpu')
+    print(f"Device: {device}")
+    print(f"Alphas: {args.alphas}")
+    print(f"Depths: {args.depths}")
+    print(f"Seeds: {args.seeds}")
+
+    os.makedirs(args.output_dir, exist_ok=True)
+
+    all_results = {}
+
+    for alpha in args.alphas:
+        for L in args.depths:
+            for seed in args.seeds:
+                key = f"a{alpha}_L{L}_s{seed}"
+                result = run_single(alpha, L, seed, args, device)
+                all_results[key] = result
+
+                # Save incrementally
+                out_path = os.path.join(args.output_dir, f'synth_{key}.json')
+                with open(out_path, 'w') as f:
+                    json.dump(serialize(result), f, indent=2)
+
+    # Save combined summary
+    summary = {}
+    for key, result in all_results.items():
+        s = {}
+        for method in ['bp', 'dfa', 'state_bridge', 'credit_bridge']:
+            r = result[method]
+            diag = r['diagnostics']
+            s[method] = {
+                'test_acc': r['log']['test_acc'][-1],
+                'mean_bp_cosine': float(np.mean(diag['bp_cosine'])),
+                'mean_rho': float(np.mean(diag['perturbation_rho'])),
+                'mean_nudge_001': float(np.mean(diag['nudging']['0.001'])),
+                'mean_nudge_003': float(np.mean(diag['nudging']['0.003'])),
+                'mean_nudge_01': float(np.mean(diag['nudging']['0.01'])),
+                'bp_cosine_per_layer': [float(x) for x in diag['bp_cosine']],
+                'rho_per_layer': [float(x) for x in diag['perturbation_rho']],
+                'nudge_per_layer': [float(x) for x in diag['nudging']['0.01']],
+            }
+            if method == 'state_bridge' and 'state_pred_error_per_layer' in diag:
+                s[method]['state_pred_error_per_layer'] = [float(x) for x in diag['state_pred_error_per_layer']]
+                s[method]['mean_state_pred_error'] = float(np.mean(diag['state_pred_error_per_layer']))
+            if method == 'credit_bridge':
+                s[method]['final_value_loss'] = r['log']['value_loss'][-1]
+                s[method]['final_term_loss'] = r['log']['term_loss'][-1]
+                s[method]['final_bridge_loss'] = r['log']['bridge_loss'][-1]
+                s[method]['final_tgrad_loss'] = r['log']['tgrad_loss'][-1]
+        summary[key] = s
+
+    summary_path = os.path.join(args.output_dir, 'summary.json')
+    with open(summary_path, 'w') as f:
+        json.dump(summary, f, indent=2)
+    print(f"\nSummary saved to {summary_path}")
+
+    # Save config
+    config = serialize(vars(args))
+    config_path = os.path.join(args.output_dir, 'config.json')
+    with open(config_path, 'w') as f:
+        json.dump(config, f, indent=2)
+
+    # Print final summary table
+    print("\n" + "=" * 100)
+    print("SYNTHETIC NONLINEARITY LADDER - SUMMARY")
+    print("=" * 100)
+    print(f"{'Config':<20} {'Method':<20} {'Acc':>8} {'Gamma':>8} {'rho':>8} {'nudge':>10}")
+    print("-" * 100)
+    for key in sorted(summary.keys()):
+        for method in ['bp', 'dfa', 'state_bridge', 'credit_bridge']:
+            s = summary[key][method]
+            print(f"{key:<20} {method:<20} {s['test_acc']:>8.4f} {s['mean_bp_cosine']:>8.4f} "
+                  f"{s['mean_rho']:>8.4f} {s['mean_nudge_01']:>10.6f}")
+        print("-" * 100)
+
+
+if __name__ == '__main__':
+    main()