Initial implementation: all models, methods, toy and CIFAR experiments

Debug phase. Toy LQ experiments (3 seeds) complete with terminal gradient matching.
Credit bridge matches state bridge on linear system (~0.94 cosine).
CIFAR experiments in progress.

1 files changed, 395 insertions, 0 deletions

diff --git a/experiments/toy_lq.py b/experiments/toy_lq.py
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+"""
+Phase A: Linear-Quadratic Residual Sanity Check.
+
+Fixed forward dynamics (no forward net training).
+Only train feedback/bridge models.
+Compare DFA, State Bridge, Credit Bridge against exact costate.
+
+System:
+  h_{l+1} = M_l h_l + sigma * xi_l,  xi_l ~ N(0, I)
+  Phi(h_L, y) = 0.5 * ||C h_L - y||^2
+  Exact costate: a_L = C^T (C h_L - y), a_l = M_l^T a_{l+1}
+"""
+import os
+import sys
+import json
+import argparse
+import numpy as np
+import torch
+import torch.nn as nn
+import torch.optim as optim
+from datetime import datetime
+
+sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
+
+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, bridge_residual
+)
+
+
+def generate_stable_dynamics(d, L, spectral_max=0.05, seed=42):
+    """Generate stable linear maps M_l = I + A_l with ||A_l||_2 <= spectral_max."""
+    rng = np.random.RandomState(seed)
+    Ms = []
+    for _ in range(L):
+        A = rng.randn(d, d).astype(np.float32)
+        # Scale to desired spectral norm
+        u, s, v = np.linalg.svd(A, full_matrices=False)
+        A = A * (spectral_max / s[0])
+        M = np.eye(d, dtype=np.float32) + A
+        Ms.append(torch.from_numpy(M))
+    return Ms  # list of (d, d)
+
+
+def rollout_forward(h0, Ms, sigma, L, device):
+    """Roll out forward dynamics: h_{l+1} = M_l h_l + sigma * xi_l."""
+    batch = h0.shape[0]
+    d = h0.shape[1]
+    hiddens = [h0]
+    h = h0
+    for l in range(L):
+        M = Ms[l].to(device)
+        noise = sigma * torch.randn(batch, d, device=device)
+        h = h @ M.T + noise
+        hiddens.append(h)
+    return hiddens  # [h_0, ..., h_L]
+
+
+def terminal_loss(hL, C, y):
+    """Phi(hL, y) = 0.5 * ||C hL - y||^2, returns per-sample loss."""
+    diff = hL @ C.T - y  # (batch, m)
+    return 0.5 * (diff ** 2).sum(dim=-1)  # (batch,)
+
+
+def exact_costate(hiddens, Ms, C, y, device):
+    """Compute exact costate a_l for all layers."""
+    L = len(hiddens) - 1
+    hL = hiddens[L]
+    # Terminal: a_L = C^T (C h_L - y)
+    diff = hL @ C.T - y  # (batch, m)
+    a_L = diff @ C  # (batch, d)
+
+    costates = [None] * (L + 1)
+    costates[L] = a_L
+    for l in range(L - 1, -1, -1):
+        M = Ms[l].to(device)
+        costates[l] = costates[l + 1] @ M  # a_l = M_l^T a_{l+1} -> a_{l+1} @ M
+    return costates
+
+
+def make_forward_fn_from_layer(hiddens, Ms, C, y, sigma, start_layer, device):
+    """Create a function that rolls forward from layer start_layer and returns per-sample loss."""
+    L = len(Ms)
+
+    def forward_fn(h):
+        current = h
+        for l in range(start_layer, L):
+            M = Ms[l].to(device)
+            # No noise for perturbation test (deterministic rollout)
+            current = current @ M.T
+        return terminal_loss(current, C, y)
+
+    return forward_fn
+
+
+def run_experiment(args):
+    device = torch.device(f'cuda:{args.gpu}' if torch.cuda.is_available() else 'cpu')
+    torch.manual_seed(args.seed)
+    np.random.seed(args.seed)
+
+    # Hyperparams
+    d = args.d_hidden       # 64
+    m = args.output_dim     # 10
+    L = args.num_layers     # 12
+    sigma = args.sigma      # 0.03
+    batch_size = args.batch_size  # 256
+    num_steps = args.num_steps    # 5000
+    lr_fb = args.lr_fb            # 1e-3
+    lam = args.lam                # 0.1
+    K = args.K                    # 8
+    ema_momentum = args.ema_momentum  # 0.995
+    sigma_bridge = args.sigma_bridge  # 0.03
+
+    print(f"=== Toy LQ Experiment ===")
+    print(f"d={d}, m={m}, L={L}, sigma={sigma}, seed={args.seed}")
+    print(f"device={device}")
+
+    # Generate fixed dynamics
+    Ms = generate_stable_dynamics(d, L, spectral_max=0.05, seed=args.seed)
+    C = torch.randn(m, d, device=device) / np.sqrt(d)
+
+    # DFA random feedback matrices
+    Bs_dfa = []
+    for l in range(L + 1):
+        B = torch.randn(d, m, device=device) / np.sqrt(m)
+        Bs_dfa.append(B)
+
+    # State Bridge model
+    state_bridge = StateBridgeNet(d_hidden=d, s_dim=m, time_embed_dim=16,
+                                   hidden_dim=128, num_layers=2).to(device)
+    opt_state = optim.Adam(state_bridge.parameters(), lr=lr_fb)
+
+    # Credit Bridge value net
+    value_net = ValueNet(d_hidden=d, s_dim=m, time_embed_dim=16,
+                          hidden_dim=128, num_layers=2).to(device)
+    value_net_ema = create_ema_model(value_net)
+    opt_value = optim.Adam(value_net.parameters(), lr=lr_fb)
+
+    # Training logs
+    log = {
+        'steps': [],
+        'state_bridge_loss': [],
+        'credit_bridge_loss': [],
+        'dfa_costate_cos': [],
+        'state_costate_cos': [],
+        'credit_costate_cos': [],
+        'dfa_rho': [],
+        'state_rho': [],
+        'credit_rho': [],
+        'dfa_nudge': [],
+        'state_nudge': [],
+        'credit_nudge': [],
+        'bridge_residual': [],
+    }
+
+    for step in range(1, num_steps + 1):
+        # Generate data
+        h0 = torch.randn(batch_size, d, device=device)
+        y = torch.randn(batch_size, m, device=device)
+
+        # Forward rollout
+        hiddens = rollout_forward(h0, Ms, sigma, L, device)
+        hL = hiddens[L]
+
+        # Terminal error
+        e_T = (hL @ C.T - y)  # (batch, m) - gradient of Phi w.r.t. prediction
+
+        # Terminal modulation code s = e_T (P=I)
+        s = e_T.detach()
+
+        # ---- Train State Bridge ----
+        state_loss = 0.0
+        hL_detached = hL.detach()
+        for l in range(L):
+            h_l_det = hiddens[l].detach()
+            t_l = torch.full((batch_size,), l / L, device=device)
+            pred_hL = state_bridge(h_l_det, t_l, s)
+            state_loss = state_loss + ((pred_hL - hL_detached) ** 2).sum(dim=-1).mean()
+        state_loss = state_loss / L
+
+        opt_state.zero_grad()
+        state_loss.backward()
+        opt_state.step()
+
+        # ---- Train Credit Bridge (value net) ----
+        # Terminal boundary: V(h_L, 1, s) should equal Phi(h_L, y)
+        hL_det = hL.detach().requires_grad_(False)
+        t_L = torch.ones(batch_size, device=device)
+        true_loss = terminal_loss(hL_det, C, y).detach()
+
+        V_terminal = value_net(hL_det, t_L, s)
+        loss_term = ((V_terminal - true_loss) ** 2).mean()
+
+        # Bridge consistency
+        loss_bridge = 0.0
+        for l in range(L):
+            h_l_det = hiddens[l].detach()
+            t_l = torch.full((batch_size,), l / L, device=device)
+            t_l_next = torch.full((batch_size,), (l + 1) / L, device=device)
+
+            V_l = value_net(h_l_det, t_l, s)
+
+            # Generate noisy next states
+            with torch.no_grad():
+                M = Ms[l].to(device)
+                h_next_det = hiddens[l + 1].detach()
+
+                log_terms = []
+                for k in range(K):
+                    noise = sigma_bridge * torch.randn(batch_size, d, device=device)
+                    h_next_noisy = h_next_det + noise
+                    V_next = value_net_ema(h_next_noisy, t_l_next, s)
+                    log_terms.append(-V_next / lam)
+
+                log_terms_stack = torch.stack(log_terms, dim=-1)  # (batch, K)
+                V_target = -lam * (torch.logsumexp(log_terms_stack, dim=-1) - np.log(K))
+
+            loss_bridge = loss_bridge + ((V_l - V_target.detach()) ** 2).mean()
+
+        loss_bridge = loss_bridge / L
+        loss_value = loss_term + loss_bridge
+
+        opt_value.zero_grad()
+        loss_value.backward()
+        opt_value.step()
+        update_ema(value_net, value_net_ema, ema_momentum)
+
+        # ---- Evaluation ----
+        if step % args.eval_every == 0 or step == 1:
+            with torch.no_grad():
+                eval_batch = min(batch_size, 128)
+                h0_eval = torch.randn(eval_batch, d, device=device)
+                y_eval = torch.randn(eval_batch, m, device=device)
+                hiddens_eval = rollout_forward(h0_eval, Ms, sigma, L, device)
+                hL_eval = hiddens_eval[L]
+                e_T_eval = hL_eval @ C.T - y_eval
+                s_eval = e_T_eval.detach()
+
+                # Exact costate
+                costates_exact = exact_costate(hiddens_eval, Ms, C, y_eval, device)
+
+            # Compute credits for each method at each layer
+            dfa_cos_layers = []
+            state_cos_layers = []
+            credit_cos_layers = []
+            dfa_rho_layers = []
+            state_rho_layers = []
+            credit_rho_layers = []
+            dfa_nudge_layers = []
+            state_nudge_layers = []
+            credit_nudge_layers = []
+            bridge_res_layers = []
+
+            for l in range(L + 1):
+                h_l = hiddens_eval[l].detach()
+                a_exact = costates_exact[l].detach()
+                t_l = torch.full((eval_batch,), l / L, device=device)
+
+                # DFA credit
+                a_dfa = e_T_eval @ Bs_dfa[l].T  # (batch, d)
+
+                # State bridge credit
+                h_l_req = h_l.clone().requires_grad_(True)
+                pred_hL = state_bridge(h_l_req, t_l, s_eval)
+                # Loss through state bridge prediction
+                pred_out = pred_hL @ C.T  # Use C as output projection for consistency
+                pred_loss = 0.5 * ((pred_out - y_eval) ** 2).sum(dim=-1)
+                a_state = torch.autograd.grad(pred_loss.sum(), h_l_req, create_graph=False)[0]
+
+                # Credit bridge credit
+                h_l_req2 = h_l.clone().requires_grad_(True)
+                V_l = value_net(h_l_req2, t_l, s_eval)
+                a_credit = torch.autograd.grad(V_l.sum(), h_l_req2, create_graph=False)[0]
+
+                # Costate cosine
+                dfa_cos_layers.append(cosine_similarity_batch(a_dfa, a_exact))
+                state_cos_layers.append(cosine_similarity_batch(a_state, a_exact))
+                credit_cos_layers.append(cosine_similarity_batch(a_credit, a_exact))
+
+                # Perturbation correlation and nudging (skip terminal layer for forward_fn)
+                if l < L:
+                    fwd_fn = make_forward_fn_from_layer(hiddens_eval, Ms, C, y_eval, sigma, l, device)
+
+                    dfa_rho = perturbation_correlation(h_l, a_dfa, fwd_fn, epsilon=1e-3, M=16)
+                    state_rho = perturbation_correlation(h_l, a_state.detach(), fwd_fn, epsilon=1e-3, M=16)
+                    credit_rho = perturbation_correlation(h_l, a_credit.detach(), fwd_fn, epsilon=1e-3, M=16)
+                    dfa_rho_layers.append(dfa_rho)
+                    state_rho_layers.append(state_rho)
+                    credit_rho_layers.append(credit_rho)
+
+                    dfa_nud = nudging_test(h_l, a_dfa, fwd_fn, eta=0.01)
+                    state_nud = nudging_test(h_l, a_state.detach(), fwd_fn, eta=0.01)
+                    credit_nud = nudging_test(h_l, a_credit.detach(), fwd_fn, eta=0.01)
+                    dfa_nudge_layers.append(dfa_nud)
+                    state_nudge_layers.append(state_nud)
+                    credit_nudge_layers.append(credit_nud)
+
+                    # Bridge residual for credit bridge
+                    if l < L:
+                        t_l_next = torch.full((eval_batch,), (l + 1) / L, device=device)
+                        h_next = hiddens_eval[l + 1].detach()
+                        noisy_list = [h_next + sigma_bridge * torch.randn_like(h_next) for _ in range(K)]
+                        br = bridge_residual(value_net, value_net_ema, h_l, t_l, s_eval,
+                                              noisy_list, t_l_next, lam)
+                        bridge_res_layers.append(br)
+
+            # Average across layers
+            avg_dfa_cos = np.mean(dfa_cos_layers)
+            avg_state_cos = np.mean(state_cos_layers)
+            avg_credit_cos = np.mean(credit_cos_layers)
+            avg_dfa_rho = np.mean(dfa_rho_layers)
+            avg_state_rho = np.mean(state_rho_layers)
+            avg_credit_rho = np.mean(credit_rho_layers)
+            avg_dfa_nudge = np.mean(dfa_nudge_layers)
+            avg_state_nudge = np.mean(state_nudge_layers)
+            avg_credit_nudge = np.mean(credit_nudge_layers)
+            avg_bridge_res = np.mean(bridge_res_layers) if bridge_res_layers else 0.0
+
+            log['steps'].append(step)
+            log['dfa_costate_cos'].append(avg_dfa_cos)
+            log['state_costate_cos'].append(avg_state_cos)
+            log['credit_costate_cos'].append(avg_credit_cos)
+            log['dfa_rho'].append(avg_dfa_rho)
+            log['state_rho'].append(avg_state_rho)
+            log['credit_rho'].append(avg_credit_rho)
+            log['dfa_nudge'].append(avg_dfa_nudge)
+            log['state_nudge'].append(avg_state_nudge)
+            log['credit_nudge'].append(avg_credit_nudge)
+            log['bridge_residual'].append(avg_bridge_res)
+            log['state_bridge_loss'].append(state_loss.item())
+            log['credit_bridge_loss'].append(loss_value.item())
+
+            print(f"Step {step}/{num_steps}")
+            print(f"  Costate cos  - DFA: {avg_dfa_cos:.4f}, State: {avg_state_cos:.4f}, Credit: {avg_credit_cos:.4f}")
+            print(f"  Perturb rho  - DFA: {avg_dfa_rho:.4f}, State: {avg_state_rho:.4f}, Credit: {avg_credit_rho:.4f}")
+            print(f"  Nudging      - DFA: {avg_dfa_nudge:.4f}, State: {avg_state_nudge:.4f}, Credit: {avg_credit_nudge:.4f}")
+            print(f"  Bridge res   - {avg_bridge_res:.4f}")
+            print(f"  Losses       - State: {state_loss.item():.4f}, Credit: {loss_value.item():.4f}")
+            print(f"  Per-layer costate cos (credit): {['%.3f' % x for x in credit_cos_layers]}")
+
+    # Save results
+    os.makedirs(args.output_dir, exist_ok=True)
+    results = {
+        'config': vars(args),
+        'log': log,
+        'final_per_layer': {
+            'dfa_costate_cos': dfa_cos_layers,
+            'state_costate_cos': state_cos_layers,
+            'credit_costate_cos': credit_cos_layers,
+            'dfa_rho': dfa_rho_layers,
+            'state_rho': state_rho_layers,
+            'credit_rho': credit_rho_layers,
+            'dfa_nudge': dfa_nudge_layers,
+            'state_nudge': state_nudge_layers,
+            'credit_nudge': credit_nudge_layers,
+            'bridge_residual': bridge_res_layers,
+        }
+    }
+
+    out_path = os.path.join(args.output_dir, f'toy_lq_seed{args.seed}.json')
+    with open(out_path, 'w') as f:
+        json.dump(results, f, indent=2)
+    print(f"\nResults saved to {out_path}")
+
+    # Also save models
+    torch.save(value_net.state_dict(), os.path.join(args.output_dir, f'value_net_seed{args.seed}.pt'))
+    torch.save(state_bridge.state_dict(), os.path.join(args.output_dir, f'state_bridge_seed{args.seed}.pt'))
+
+    return results
+
+
+def main():
+    parser = argparse.ArgumentParser(description='Toy LQ Sanity Check')
+    parser.add_argument('--d_hidden', type=int, default=64)
+    parser.add_argument('--output_dim', type=int, default=10)
+    parser.add_argument('--num_layers', type=int, default=12)
+    parser.add_argument('--sigma', type=float, default=0.03)
+    parser.add_argument('--batch_size', type=int, default=256)
+    parser.add_argument('--num_steps', type=int, default=5000)
+    parser.add_argument('--lr_fb', type=float, default=1e-3)
+    parser.add_argument('--lam', type=float, default=0.1)
+    parser.add_argument('--K', type=int, default=8)
+    parser.add_argument('--ema_momentum', type=float, default=0.995)
+    parser.add_argument('--sigma_bridge', type=float, default=0.03)
+    parser.add_argument('--eval_every', type=int, default=200)
+    parser.add_argument('--seed', type=int, default=42)
+    parser.add_argument('--gpu', type=int, default=1)
+    parser.add_argument('--output_dir', type=str, default='results/toy_lq')
+    args = parser.parse_args()
+    run_experiment(args)
+
+
+if __name__ == '__main__':
+    main()