Add BP support sparsity analysis: threshold sweep + gradient histograms

A1 Synthetic: all methods have >93% support at τ=1e-6 (gradients rarely zero)
A2 CIFAR: massive gap — BP 98.4% vs DFA 0.4% vs SB 21% vs CB 3%
  DFA-trained CIFAR networks have near-zero BP gradients for 99.6% of samples
  This explains why Gamma is unreliable for CIFAR non-BP methods

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

5 files changed, 80246 insertions, 0 deletions

diff --git a/experiments/bp_support_sparsity.py b/experiments/bp_support_sparsity.py
new file mode 100644
index 0000000..0ee08d1
--- /dev/null
+++ b/experiments/bp_support_sparsity.py
@@ -0,0 +1,276 @@
+"""
+BP Support Sparsity Analysis.
+A1: threshold sweep, log-gradient stats, active-subset Gamma, energy-weighted Gamma
+A2: same for CIFAR
+All from checkpoints — no retraining.
+"""
+import os, sys, csv, json, argparse, numpy as np, torch, torch.nn.functional as F
+from torch.utils.data import DataLoader, TensorDataset
+sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
+from models.residual_mlp import ResidualMLP
+
+class StudentBlock(torch.nn.Module):
+    def __init__(self, d, alpha=1.0):
+        super().__init__()
+        self.ln=torch.nn.LayerNorm(d);self.w=torch.nn.Linear(d,d,bias=False)
+        torch.nn.init.normal_(self.w.weight,std=0.01);self.alpha=alpha
+    def forward(self, h):
+        return self.w(((1-self.alpha)*self.ln(h)+self.alpha*torch.tanh(self.ln(h))))
+
+class StudentNet(torch.nn.Module):
+    def __init__(self, d, C, L, alpha=1.0):
+        super().__init__()
+        self.blocks=torch.nn.ModuleList([StudentBlock(d,alpha) for _ in range(L)])
+        self.out_head=torch.nn.Linear(d,C);self.num_blocks=L;self.d_hidden=d
+    def forward(self, x, return_hidden=False):
+        h=x;hi=[h] if return_hidden else None
+        for b in self.blocks:
+            h=h+b(h)
+            if return_hidden:hi.append(h)
+        lo=self.out_head(h)
+        return (lo,hi) if return_hidden else lo
+
+class TeacherNet(torch.nn.Module):
+    def __init__(self, d, C, L, alpha=1.0, seed=0):
+        super().__init__()
+        self.alpha=alpha;rng=torch.Generator().manual_seed(seed)
+        self.Ws=torch.nn.ParameterList()
+        for _ in range(L):
+            W=torch.randn(d,d,generator=rng)*0.3/(d**0.5)
+            U,S,Vh=torch.linalg.svd(W,full_matrices=False)
+            self.Ws.append(torch.nn.Parameter(U@torch.diag(S.clamp(max=0.3))@Vh,requires_grad=False))
+        self.U=torch.nn.Parameter(torch.randn(C,d,generator=rng)/(d**0.5),requires_grad=False)
+    def forward(self, x):
+        h=x
+        for W in self.Ws:h=h+((1-self.alpha)*h+self.alpha*torch.tanh(h))@W.T
+        return h@self.U.T
+
+
+def get_bp_grads(model, x, y, device, is_cifar=False):
+    """Get per-layer BP gradients via manual forward."""
+    model.eval()
+    L = model.num_blocks
+    if is_cifar:
+        h0 = model.embed(x.detach())
+    else:
+        h0 = x.detach()
+    h_list = [h0.clone().requires_grad_(True)]
+    for b in model.blocks:
+        h_list.append(h_list[-1] + b(h_list[-1]))
+    if is_cifar:
+        lo = model.out_head(model.out_ln(h_list[-1]))
+    else:
+        lo = model.out_head(h_list[-1])
+    loss = F.cross_entropy(lo, y)
+    grads = torch.autograd.grad(loss, h_list)
+    return {l: grads[l].detach() for l in range(L)}
+
+
+def analyze_model(model, x, y, device, is_cifar=False):
+    """Full sparsity analysis for one model."""
+    L = model.num_blocks
+    bp = get_bp_grads(model, x, y, device, is_cifar)
+
+    thresholds = [1e-8, 1e-7, 1e-6, 1e-5, 1e-4]
+    batch = x.size(0)
+
+    results = {'thresholds': {}, 'log_grad_norms': [], 'per_layer': []}
+
+    # Per-layer analysis
+    all_norms = []
+    for l in range(L):
+        g = bp[l]
+        norms = g.norm(dim=-1)  # (batch,)
+        all_norms.append(norms)
+        log_norms = torch.log10(norms.clamp(min=1e-20)).cpu().numpy()
+        results['log_grad_norms'].append(log_norms.tolist())
+
+        layer_res = {'layer': l}
+        for tau in thresholds:
+            s = (norms > tau).float().mean().item()
+            layer_res[f's_tau_{tau}'] = s
+        results['per_layer'].append(layer_res)
+
+    # Threshold sweep (averaged over layers)
+    for tau in thresholds:
+        mean_s = np.mean([res[f's_tau_{tau}'] for res in results['per_layer']])
+        results['thresholds'][str(tau)] = mean_s
+
+    # Active-subset Gamma and energy-weighted Gamma for each threshold
+    # (self-cosine for now — comparing BP with BP; real cross-method needs credit source)
+    # We store raw norms for post-processing
+    results['mean_grad_norm'] = np.mean([n.mean().item() for n in all_norms])
+    results['median_grad_norm'] = np.mean([n.median().item() for n in all_norms])
+    results['grad_norm_percentiles'] = {}
+    stacked = torch.cat(all_norms)
+    for p in [10, 25, 50, 75, 90, 95, 99]:
+        results['grad_norm_percentiles'][str(p)] = np.percentile(stacked.cpu().numpy(), p)
+
+    return results
+
+
+def run_analysis(args):
+    device = torch.device(f'cuda:{args.gpu}')
+    os.makedirs(args.output_dir, exist_ok=True)
+    seeds = [42, 123, 456, 789, 1024, 2048, 3000, 4000, 5000, 6000]
+    thresholds = [1e-8, 1e-7, 1e-6, 1e-5, 1e-4]
+
+    # ===== A1 Synthetic =====
+    print("=== A1 Synthetic ===", flush=True)
+    alphas = [0.0, 0.5, 1.0]; depths = [4, 8]; d = 128; C = 10
+    methods = ['bp', 'dfa', 'state_bridge', 'credit_bridge']
+
+    a1_threshold_rows = []
+    a1_histogram_data = {}
+
+    for alpha in alphas:
+        for L in depths:
+            # Use seed=42 for histogram (representative)
+            teacher = TeacherNet(d, C, L, alpha, seed=0).to(device)
+            torch.manual_seed(42 + 10000)
+            X_test = torch.randn(512, d, device=device)
+            with torch.no_grad():
+                Y_test = teacher(X_test).argmax(-1)
+
+            for method in methods:
+                # Aggregate over seeds for threshold table
+                seed_results = []
+                for seed in seeds:
+                    ckpt = f'results/confirmatory/checkpoints_A1/a{alpha}_L{L}_{method}_s{seed}.pt'
+                    if not os.path.exists(ckpt):
+                        continue
+                    torch.manual_seed(seed)
+                    model = StudentNet(d, C, L, alpha).to(device)
+                    model.load_state_dict(torch.load(ckpt, map_location=device))
+                    res = analyze_model(model, X_test, Y_test, device, is_cifar=False)
+                    seed_results.append(res)
+
+                    # Threshold rows
+                    for tau in thresholds:
+                        a1_threshold_rows.append({
+                            'alpha': alpha, 'depth': L, 'method': method, 'seed': seed,
+                            'threshold': tau, 'support_fraction': res['thresholds'][str(tau)]
+                        })
+
+                # Histogram data for seed=42 only
+                if seed_results:
+                    key = f"a{alpha}_L{L}_{method}"
+                    a1_histogram_data[key] = {
+                        'log_grad_norms': seed_results[0]['log_grad_norms'],
+                        'percentiles': seed_results[0]['grad_norm_percentiles'],
+                        'mean_norm': seed_results[0]['mean_grad_norm'],
+                        'median_norm': seed_results[0]['median_grad_norm'],
+                    }
+
+                if seed_results:
+                    mean_s = np.mean([r['thresholds']['1e-06'] for r in seed_results])
+                    print(f"  a={alpha} L={L} {method}: s(1e-6)={mean_s:.4f}, "
+                          f"mean_norm={np.mean([r['mean_grad_norm'] for r in seed_results]):.2e}", flush=True)
+
+    # Save A1 threshold CSV
+    out1 = os.path.join(args.output_dir, 'A1_threshold_sweep.csv')
+    with open(out1, 'w', newline='') as f:
+        w = csv.DictWriter(f, fieldnames=['alpha','depth','method','seed','threshold','support_fraction'])
+        w.writeheader(); w.writerows(a1_threshold_rows)
+    print(f"A1 threshold: {len(a1_threshold_rows)} rows -> {out1}", flush=True)
+
+    # Save A1 histogram JSON
+    out1h = os.path.join(args.output_dir, 'A1_histogram_data.json')
+    def to_serializable(obj):
+        if isinstance(obj, (np.floating, np.integer)): return float(obj)
+        if isinstance(obj, np.ndarray): return obj.tolist()
+        return obj
+    with open(out1h, 'w') as f:
+        json.dump(a1_histogram_data, f, indent=2, default=to_serializable)
+    print(f"A1 histogram data -> {out1h}", flush=True)
+
+    # ===== A2 CIFAR =====
+    print("\n=== A2 CIFAR ===", flush=True)
+    import torchvision, torchvision.transforms as transforms
+    tv = transforms.Compose([transforms.ToTensor(),
+                              transforms.Normalize((0.4914,0.4822,0.4465),(0.2470,0.2435,0.2616))])
+    tel = DataLoader(torchvision.datasets.CIFAR10('./data', False, download=True, transform=tv),
+                     256, False, num_workers=4)
+    for x, y in tel:
+        x = x.view(x.size(0), -1).to(device); y = y.to(device); break
+
+    L_c, d_c = 4, 256
+    a2_threshold_rows = []
+    a2_histogram_data = {}
+
+    for method in methods:
+        seed_results = []
+        for seed in seeds:
+            ckpt = f'results/confirmatory/checkpoints_A2/{method}_s{seed}.pt'
+            if not os.path.exists(ckpt):
+                continue
+            torch.manual_seed(seed)
+            model = ResidualMLP(3072, d_c, 10, L_c).to(device)
+            model.load_state_dict(torch.load(ckpt, map_location=device))
+            res = analyze_model(model, x, y, device, is_cifar=True)
+            seed_results.append(res)
+
+            for tau in thresholds:
+                a2_threshold_rows.append({
+                    'method': method, 'seed': seed,
+                    'threshold': tau, 'support_fraction': res['thresholds'][str(tau)]
+                })
+
+        if seed_results:
+            key = method
+            a2_histogram_data[key] = {
+                'log_grad_norms': seed_results[0]['log_grad_norms'],
+                'percentiles': seed_results[0]['grad_norm_percentiles'],
+                'mean_norm': seed_results[0]['mean_grad_norm'],
+                'median_norm': seed_results[0]['median_grad_norm'],
+            }
+            mean_s = np.mean([r['thresholds']['1e-06'] for r in seed_results])
+            print(f"  {method}: s(1e-6)={mean_s:.4f}, "
+                  f"mean_norm={np.mean([r['mean_grad_norm'] for r in seed_results]):.2e}, "
+                  f"median_norm={np.mean([r['median_grad_norm'] for r in seed_results]):.2e}", flush=True)
+
+    out2 = os.path.join(args.output_dir, 'A2_threshold_sweep.csv')
+    with open(out2, 'w', newline='') as f:
+        w = csv.DictWriter(f, fieldnames=['method','seed','threshold','support_fraction'])
+        w.writeheader(); w.writerows(a2_threshold_rows)
+    print(f"A2 threshold: {len(a2_threshold_rows)} rows -> {out2}", flush=True)
+
+    out2h = os.path.join(args.output_dir, 'A2_histogram_data.json')
+    with open(out2h, 'w') as f:
+        json.dump(a2_histogram_data, f, indent=2, default=to_serializable)
+    print(f"A2 histogram data -> {out2h}", flush=True)
+
+    # ===== Summary =====
+    print(f"\n{'='*70}", flush=True)
+    print("SUMMARY: Support fraction s(τ) at τ=1e-6 (mean over 10 seeds)", flush=True)
+    print(f"{'='*70}", flush=True)
+
+    print("\nA1 Synthetic:")
+    for alpha in alphas:
+        for L in depths:
+            print(f"  alpha={alpha}, L={L}:")
+            for method in methods:
+                vals = [r['support_fraction'] for r in a1_threshold_rows
+                        if r['alpha']==alpha and r['depth']==L and r['method']==method and r['threshold']==1e-6]
+                if vals:
+                    print(f"    {method}: s(1e-6) = {np.mean(vals):.4f} ± {np.std(vals):.4f}")
+
+    print("\nA2 CIFAR:")
+    for method in methods:
+        vals = [r['support_fraction'] for r in a2_threshold_rows
+                if r['method']==method and r['threshold']==1e-6]
+        if vals:
+            print(f"  {method}: s(1e-6) = {np.mean(vals):.4f} ± {np.std(vals):.4f}")
+
+    print("\nDONE", flush=True)
+
+
+def main():
+    p = argparse.ArgumentParser()
+    p.add_argument('--gpu', type=int, default=0)
+    p.add_argument('--output_dir', type=str, default='results/confirmatory')
+    args = p.parse_args()
+    run_analysis(args)
+
+if __name__ == '__main__':
+    main()
diff --git a/results/confirmatory/A1_histogram_data.json b/results/confirmatory/A1_histogram_data.json
new file mode 100644
index 0000000..67c8add
--- /dev/null
+++ b/results/confirmatory/A1_histogram_data.json
@@ -0,0 +1,74378 @@
+{
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+      ]
+    ],
+    "percentiles": {
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+      "25": 0.0013972371816635132,
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+    },
+    "mean_norm": 0.001606332793016918,
+    "median_norm": 0.0015977540606399998
+  }
+}
\ No newline at end of file
diff --git a/results/confirmatory/A1_threshold_sweep.csv b/results/confirmatory/A1_threshold_sweep.csv
new file mode 100644
index 0000000..d208249
--- /dev/null
+++ b/results/confirmatory/A1_threshold_sweep.csv
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diff --git a/results/confirmatory/A2_histogram_data.json b/results/confirmatory/A2_histogram_data.json
new file mode 100644
index 0000000..acd73ee
--- /dev/null
+++ b/results/confirmatory/A2_histogram_data.json
@@ -0,0 +1,4190 @@
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+}
\ No newline at end of file
diff --git a/results/confirmatory/A2_threshold_sweep.csv b/results/confirmatory/A2_threshold_sweep.csv
new file mode 100644
index 0000000..1cf8142
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