5m_proto_1024_v3_geometrically_cv_aligned.py

"""
SVAE — Structural Binding Constant
=====================================
Matrix (V, 24): V rows in D=24 space.
At D=24, CV ≈ 0.29154 BY CONSTRUCTION — no loss needed.

The sweep proved it:
  V=200,  D=24 → CV=0.2914
  V=1024, D=24 → CV=0.2916
  V=1992, D=24 → CV=0.2911
  V is irrelevant. D determines CV.

The encoder produces a (V, 24) matrix.
The rows ARE an embedding: V tokens in D=24 space.
Their CV is ~0.29 by the dimensional law.
The SVD decomposes this embedding into its spectral structure.
The decoder reconstructs from the decomposition.

No CV loss. Monitor only. The geometry is inherent.

pip install "git+https://github.com/AbstractEyes/geolip-core.git"
"""

import torch
import torch.nn as nn
import torch.nn.functional as F
import torchvision
import torchvision.transforms as T
import math

try:
    from geolip_core.linalg import svd as geolip_svd
    HAS_GEOLIP = True
    print("Using geolip-core SVD (Gram + eigh)")
except ImportError:
    HAS_GEOLIP = False
    print("geolip-core not found, fallback to torch.svd_lowrank")


# ── CM for monitoring (not loss) ──

def cayley_menger_vol2(points):
    B, N, D = points.shape
    gram = torch.bmm(points, points.transpose(1, 2))
    norms = torch.diagonal(gram, dim1=1, dim2=2)
    d2 = F.relu(norms.unsqueeze(2) + norms.unsqueeze(1) - 2 * gram)
    cm = torch.zeros(B, N + 1, N + 1, device=points.device, dtype=points.dtype)
    cm[:, 0, 1:] = 1.0
    cm[:, 1:, 0] = 1.0
    cm[:, 1:, 1:] = d2
    k = N - 1
    sign = (-1.0) ** (k + 1)
    fact = math.factorial(k)
    return sign * torch.linalg.det(cm.float()).to(points.dtype) / ((2 ** k) * (fact ** 2))


def cv_of(emb, n_samples=200):
    if emb.dim() != 2 or emb.shape[0] < 5:
        return 0.0
    N, D = emb.shape
    pool = min(N, 512)
    indices = torch.stack([torch.randperm(pool, device=emb.device)[:5] for _ in range(n_samples)])
    vol2 = cayley_menger_vol2(emb[:pool][indices])
    valid = vol2 > 1e-20
    if valid.sum() < 10:
        return 0.0
    vols = vol2[valid].sqrt()
    return (vols.std() / (vols.mean() + 1e-8)).item()


BINDING_CONSTANT = 0.29154


# ── Data ──

def get_cifar10(batch_size=256):
    transform = T.Compose([
        T.ToTensor(),
        T.Normalize((0.4914, 0.4822, 0.4465), (0.2470, 0.2435, 0.2616)),
    ])
    train_ds = torchvision.datasets.CIFAR10(root='./data', train=True, download=True, transform=transform)
    test_ds = torchvision.datasets.CIFAR10(root='./data', train=False, download=True, transform=transform)
    train_loader = torch.utils.data.DataLoader(train_ds, batch_size=batch_size, shuffle=True, num_workers=2)
    test_loader = torch.utils.data.DataLoader(test_ds, batch_size=batch_size, shuffle=False, num_workers=2)
    return train_loader, test_loader


# ── SVAE ──

class SVAE(nn.Module):
    def __init__(self, matrix_v=48, D=24):
        """
        matrix_v: number of rows (vocabulary size of the implicit embedding)
        D: embedding dimension = number of singular values = 24 for binding constant
        """
        super().__init__()
        self.matrix_v = matrix_v  # V — number of embedding rows
        self.D = D                # D — embedding dimension
        self.img_dim = 3 * 32 * 32
        self.mat_dim = matrix_v * D

        self.encoder = nn.Sequential(
            nn.Linear(self.img_dim, 512),
            nn.GELU(),
            nn.Linear(512, 512),
            nn.GELU(),
            nn.Linear(512, self.mat_dim),
        )
        self.decoder = nn.Sequential(
            nn.Linear(self.mat_dim, 512),
            nn.GELU(),
            nn.Linear(512, 512),
            nn.GELU(),
            nn.Linear(512, self.img_dim),
        )

    def encode(self, images):
        B = images.shape[0]
        M = self.encoder(images.reshape(B, -1)).reshape(B, self.matrix_v, self.D)

        if HAS_GEOLIP:
            U, S, Vh = geolip_svd(M)
        else:
            U, S, V = torch.svd_lowrank(M, q=self.D)
            Vh = V.transpose(1, 2)

        return {
            'U': U, 'S': S, 'Vt': Vh,
            'M': M,  # the embedding matrix — rows are V points in D=24
        }

    def decode_from_svd(self, U, S, Vt):
        B = U.shape[0]
        M_hat = torch.bmm(U * S.unsqueeze(1), Vt)
        return self.decoder(M_hat.reshape(B, -1)).reshape(B, 3, 32, 32)

    def forward(self, images):
        svd = self.encode(images)
        recon = self.decode_from_svd(svd['U'], svd['S'], svd['Vt'])
        return {'recon': recon, 'svd': svd}

    @staticmethod
    def effective_rank(S):
        p = S / (S.sum(-1, keepdim=True) + 1e-8)
        p = p.clamp(min=1e-8)
        return (-(p * p.log()).sum(-1)).exp()


# ── Training ──

def train(epochs=50, lr=1e-3, device='cuda'):
    device = torch.device(device if torch.cuda.is_available() else 'cpu')
    train_loader, test_loader = get_cifar10(batch_size=256)

    D = 24
    V = 48
    model = SVAE(matrix_v=V, D=D).to(device)
    opt = torch.optim.Adam(model.parameters(), lr=lr)
    sched = torch.optim.lr_scheduler.CosineAnnealingLR(opt, T_max=epochs)

    total_params = sum(p.numel() for p in model.parameters())
    print(f"SVAE — Structural Binding Constant")
    print(f"  Matrix: ({V}, {D}) — {V} rows in D={D} space")
    print(f"  Expected row CV ≈ {BINDING_CONSTANT} (no loss, by construction)")
    print(f"  SVD: {'geolip-core' if HAS_GEOLIP else 'torch.svd_lowrank'}")
    print(f"  Compression: {model.img_dim} → {D} ({model.img_dim // D}:1)")
    print(f"  Params: {total_params:,}")
    print("=" * 85)
    print(f"{'ep':>3} | {'loss':>7} {'recon':>7} | "
          f"{'t_recon':>7} | "
          f"{'S0':>6} {'SD':>6} {'ratio':>6} {'erank':>6} | "
          f"{'row_cv':>7} {'Δbc':>7}")
    print("-" * 85)

    for epoch in range(1, epochs + 1):
        model.train()
        total_loss, n = 0, 0

        for images, labels in train_loader:
            images = images.to(device)
            opt.zero_grad()
            out = model(images)

            loss = F.mse_loss(out['recon'], images)
            loss.backward()
            opt.step()

            total_loss += loss.item() * len(images)
            n += len(images)

        sched.step()

        if epoch % 2 == 0 or epoch <= 3:
            model.eval()
            test_recon, test_n = 0, 0
            test_S = None
            test_erank = 0
            row_cvs = []
            nb = 0

            with torch.no_grad():
                for images, labels in test_loader:
                    images = images.to(device)
                    out = model(images)
                    test_recon += F.mse_loss(out['recon'], images).item() * len(images)
                    test_n += len(images)
                    test_erank += model.effective_rank(out['svd']['S']).mean().item()

                    # CV of matrix rows: each M[i] is (V, D) — V points in D=24
                    # Sample a few to keep it fast
                    if nb < 5:
                        for b in range(min(4, len(images))):
                            row_cvs.append(cv_of(out['svd']['M'][b]))

                    if test_S is None:
                        test_S = out['svd']['S'].mean(0).cpu()
                    else:
                        test_S += out['svd']['S'].mean(0).cpu()
                    nb += 1

            test_erank /= nb
            test_S /= nb
            ratio = (test_S[0] / (test_S[-1] + 1e-8)).item()
            mean_row_cv = sum(row_cvs) / len(row_cvs) if row_cvs else 0
            delta_bc = abs(mean_row_cv - BINDING_CONSTANT)

            print(f"{epoch:3d} | {total_loss/n:7.4f} {total_loss/n:7.4f} | "
                  f"{test_recon/test_n:7.4f} | "
                  f"{test_S[0]:6.3f} {test_S[-1]:6.3f} {ratio:6.2f} "
                  f"{test_erank:6.2f} | "
                  f"{mean_row_cv:7.4f} {delta_bc:7.4f}")

    # ── Final Analysis ──
    print()
    print("=" * 85)
    print("FINAL ANALYSIS")
    print("=" * 85)

    model.eval()
    all_S, all_recon_err, all_labels = [], [], []
    all_row_cvs = []

    with torch.no_grad():
        for images, labels in test_loader:
            images = images.to(device)
            out = model(images)
            all_S.append(out['svd']['S'].cpu())
            all_recon_err.append(
                F.mse_loss(out['recon'], images, reduction='none')
                .mean(dim=(1, 2, 3)).cpu())
            all_labels.append(labels.cpu())

            # Row CV for a sample of images
            for b in range(min(8, len(images))):
                all_row_cvs.append(cv_of(out['svd']['M'][b]))

    all_S = torch.cat(all_S)
    all_recon_err = torch.cat(all_recon_err)
    all_labels = torch.cat(all_labels)

    erank = model.effective_rank(all_S)
    mean_row_cv = sum(all_row_cvs) / len(all_row_cvs)

    print(f"\n  Architecture: ({V}, {D}) — {V} rows × D={D}")
    print(f"  Recon MSE: {all_recon_err.mean():.6f} ± {all_recon_err.std():.6f}")
    print(f"  Effective rank: {erank.mean():.2f} ± {erank.std():.2f}")
    print(f"\n  Row CV (matrix rows as D={D} embedding):")
    print(f"    Measured: {mean_row_cv:.4f}")
    print(f"    Target:   {BINDING_CONSTANT}")
    print(f"    Delta:    {abs(mean_row_cv - BINDING_CONSTANT):.4f}")
    print(f"    {'✓ AT BINDING CONSTANT' if abs(mean_row_cv - BINDING_CONSTANT) < 0.01 else '✗ Not at binding constant'}")

    # Spectrum profile
    S_mean = all_S.mean(0)
    total_energy = (S_mean ** 2).sum()
    print(f"\n  Singular value profile:")
    cumulative = 0
    for i in range(len(S_mean)):
        e = (S_mean[i] ** 2).item()
        cumulative += e
        pct = cumulative / total_energy * 100
        bar = "█" * int(S_mean[i].item() * 30 / (S_mean[0].item() + 1e-8))
        print(f"    S[{i:2d}]: {S_mean[i]:8.3f}  cum={pct:5.1f}%  {bar}")

    # Per-class
    cifar_names = ['plane', 'car', 'bird', 'cat', 'deer',
                   'dog', 'frog', 'horse', 'ship', 'truck']
    print(f"\n  Per-class:")
    print(f"    {'class':>6}  {'recon':>8}  {'erank':>6}  {'S0':>7}  {'SD':>7}  {'ratio':>6}")
    for c in range(10):
        mask = all_labels == c
        rc = all_recon_err[mask].mean().item()
        er = erank[mask].mean().item()
        s0 = all_S[mask, 0].mean().item()
        sd = all_S[mask, -1].mean().item()
        ratio = s0 / (sd + 1e-8)
        print(f"    {cifar_names[c]:>6}  {rc:8.6f}  {er:6.2f}  {s0:7.3f}  {sd:7.3f}  {ratio:6.2f}")

    # Cross-class spectral variance
    class_S_means = torch.stack([all_S[all_labels == c].mean(0) for c in range(10)])
    s_var = class_S_means.std(0)
    print(f"\n  Cross-class S variance (top 5 most discriminative):")
    _, top_idx = s_var.topk(5)
    for idx in top_idx:
        i = idx.item()
        print(f"    S[{i:2d}]: var={s_var[i]:.4f}")

    # ── Reconstruction grid ──
    print(f"\n  Saving reconstruction grid...")
    import matplotlib
    matplotlib.use('Agg')
    import matplotlib.pyplot as plt

    mean_t = torch.tensor([0.4914, 0.4822, 0.4465]).reshape(1, 3, 1, 1).to(device)
    std_t = torch.tensor([0.2470, 0.2435, 0.2616]).reshape(1, 3, 1, 1).to(device)

    model.eval()
    with torch.no_grad():
        images, labels = next(iter(test_loader))
        images = images.to(device)
        out = model(images)

        selected_idx = []
        for c in range(10):
            class_idx = (labels == c).nonzero(as_tuple=True)[0]
            selected_idx.extend(class_idx[:2].tolist())

        orig = images[selected_idx]
        U = out['svd']['U'][selected_idx]
        S = out['svd']['S'][selected_idx]
        Vt = out['svd']['Vt'][selected_idx]

        mode_counts = [1, 4, 8, 16, D]
        mode_counts = list(dict.fromkeys([m for m in mode_counts if m <= D]))
        prog_recons = []
        for n_modes in mode_counts:
            r = model.decode_from_svd(U[:, :, :n_modes], S[:, :n_modes], Vt[:, :n_modes, :])
            prog_recons.append(r)

    def denorm(t):
        return (t * std_t + mean_t).clamp(0, 1).cpu()

    n_samples = len(selected_idx)
    n_cols = 2 + len(mode_counts)
    fig, axes = plt.subplots(n_samples, n_cols, figsize=(n_cols * 1.5, n_samples * 1.5))
    col_titles = ['Original'] + [f'{m} mode{"s" if m > 1 else ""}' for m in mode_counts] + ['|Error|×5']

    for i in range(n_samples):
        axes[i, 0].imshow(denorm(orig[i:i+1])[0].permute(1, 2, 0).numpy())
        for j, r in enumerate(prog_recons):
            axes[i, j+1].imshow(denorm(r[i:i+1])[0].permute(1, 2, 0).numpy())
        err_col = 1 + len(prog_recons)
        diff = (denorm(orig[i:i+1]) - denorm(prog_recons[-1][i:i+1])).abs() * 5
        axes[i, err_col].imshow(diff.clamp(0, 1)[0].permute(1, 2, 0).numpy())
        c = labels[selected_idx[i]].item()
        axes[i, 0].set_ylabel(cifar_names[c], fontsize=8, rotation=0, labelpad=35)

    for j, title in enumerate(col_titles):
        axes[0, j].set_title(title, fontsize=8)
    for ax in axes.flat:
        ax.axis('off')

    plt.tight_layout()
    plt.savefig('/content/svae_recon_grid.png', dpi=200, bbox_inches='tight')
    print(f"  Saved to /content/svae_recon_grid.png")
    try:
        plt.show()
    except:
        pass
    plt.close()


if __name__ == "__main__":
    train()