# Run cell 1 and cell 2, shape factory and model then run this to continue. # ablation showed random chance without the full geometric architecture. # ============================================================================= # CELL 5: Architecture Ablation — MLP Baseline with Same Loss # Requires: Cell 1 + Cell 2 already executed (constants, generator, deform_grid) # Question: Is the loss creating the behavior, or the architecture? # # Same composite loss, same data, same hyperparams. # Plain MLP replaces: tracer attention, capacity cascade, # differentiation gate, curvature head, rectified flow arbiter. # ============================================================================= import math, time, numpy as np import torch import torch.nn as nn import torch.nn.functional as F from pathlib import Path device = torch.device("cuda" if torch.cuda.is_available() else "cpu") if device.type == "cuda": torch.backends.cuda.matmul.allow_tf32 = True torch.backends.cudnn.allow_tf32 = True torch.backends.cudnn.benchmark = True use_amp = device.type == "cuda" amp_dtype = (torch.bfloat16 if (device.type == "cuda" and torch.cuda.is_bf16_supported()) else torch.float16) # ============================================================================= # MLP Baseline — same output contract as GeometricShapeClassifier # ============================================================================= class MLPBaseline(nn.Module): """Plain MLP producing the same output dict as GeometricShapeClassifier. No geometric inductive bias. Same loss surface.""" def __init__(self, grid_size=GS, n_classes=NUM_CLASSES, n_curvatures=NUM_CURVATURES, trunk_dim=256): super().__init__() inp = grid_size ** 3 # 125 self.trunk = nn.Sequential( nn.Linear(inp, 512), nn.GELU(), nn.Linear(512, 512), nn.GELU(), nn.Linear(512, trunk_dim), nn.GELU(), nn.Linear(trunk_dim, trunk_dim), nn.GELU(), ) # Primary classifier self.classifier = nn.Sequential( nn.Linear(trunk_dim, 128), nn.GELU(), nn.Dropout(0.1), nn.Linear(128, n_classes)) # Capacity analog: fill ratios (4 dims, sigmoid) self.fill_head = nn.Sequential( nn.Linear(trunk_dim, 64), nn.GELU(), nn.Linear(64, 4), nn.Sigmoid()) # Learned capacities for diversity loss self.cap_head = nn.Sequential( nn.Linear(trunk_dim, 32), nn.GELU(), nn.Linear(32, 4), nn.Softplus()) # Peak dimension (4-class) self.peak_head = nn.Sequential( nn.Linear(trunk_dim, 32), nn.GELU(), nn.Linear(32, 4)) # Overflow (4 dims, sigmoid) self.overflow_head = nn.Sequential( nn.Linear(trunk_dim, 32), nn.GELU(), nn.Linear(32, 4), nn.Sigmoid()) # Volume regression self.volume_head = nn.Sequential( nn.Linear(trunk_dim, 64), nn.GELU(), nn.Linear(64, 1)) # Cayley-Menger determinant sign self.cm_head = nn.Sequential( nn.Linear(trunk_dim, 64), nn.GELU(), nn.Linear(64, 1), nn.Tanh()) # Curvature binary self.curved_head = nn.Sequential( nn.Linear(trunk_dim, 32), nn.GELU(), nn.Linear(32, 1), nn.Sigmoid()) # Curvature type (8-class) self.curv_type_head = nn.Sequential( nn.Linear(trunk_dim, 64), nn.GELU(), nn.Linear(64, n_curvatures)) # Second classifier (arbiter analog) self.refiner = nn.Sequential( nn.Linear(trunk_dim, 128), nn.GELU(), nn.Dropout(0.1), nn.Linear(128, n_classes)) # Confidence and blend self.confidence_head = nn.Sequential( nn.Linear(trunk_dim, 32), nn.GELU(), nn.Linear(32, 1), nn.Sigmoid()) self.blend_head = nn.Sequential( nn.Linear(trunk_dim, 32), nn.GELU(), nn.Linear(32, 1), nn.Sigmoid()) def forward(self, grid, labels=None): B = grid.shape[0] x = grid.reshape(B, -1).float() feat = self.trunk(x) initial_logits = self.classifier(feat) refined_logits = self.refiner(feat) blend = self.blend_head(feat).squeeze(-1) class_logits = (blend.unsqueeze(-1) * initial_logits + (1 - blend.unsqueeze(-1)) * refined_logits) conf = self.confidence_head(feat).squeeze(-1) return { "class_logits": class_logits, "initial_logits": initial_logits, "refined_logits": refined_logits, "fill_ratios": self.fill_head(feat), "peak_logits": self.peak_head(feat), "overflows": self.overflow_head(feat), "capacities": self.cap_head(feat), "volume_pred": self.volume_head(feat).squeeze(-1), "cm_pred": self.cm_head(feat).squeeze(-1), "is_curved_pred": self.curved_head(feat), "curv_type_logits": self.curv_type_head(feat), "trajectory_logits": [refined_logits], "flow_loss": torch.tensor(0.0, device=grid.device), "refined_confidence": self.confidence_head(feat), "blend_weight": blend, "confidence": conf, "alternation": torch.zeros(B, device=grid.device), "features": feat, } # ============================================================================= # Loss Functions (identical to Cell 3) # ============================================================================= def _safe_bce(inp, tgt): with torch.amp.autocast('cuda', enabled=False): return F.binary_cross_entropy(inp.float(), tgt.float()) def capacity_fill_loss(fr, dt): return _safe_bce(fr, dt) def overflow_reg(on, dt): pk = dt.sum(dim=-1).long() - 1 loss = sum(on[b, pk[b].item():].sum() for b in range(on.shape[0])) return loss / (on.shape[0] + 1e-8) def cap_diversity(c): return -c.var() def peak_loss(l, t): return F.cross_entropy(l, t) def cm_loss(p, t): return F.mse_loss(p, torch.sign(t)) def curved_bce(p, t): return _safe_bce(p.squeeze(-1), t) def ctype_loss(l, t): return F.cross_entropy(l, t) # ============================================================================= # Data — load cached or generate + cache # ============================================================================= DATASET_PATH = Path("./cached_dataset.pt") N_SAMPLES = 500000 SEED = 42 if DATASET_PATH.exists(): print(f"Loading cached dataset from {DATASET_PATH}...") t0 = time.time() _cached = torch.load(DATASET_PATH, weights_only=True) if _cached["n_samples"] == N_SAMPLES and _cached["seed"] == SEED: train_ds = ShapeDataset.__new__(ShapeDataset) val_ds = ShapeDataset.__new__(ShapeDataset) for k in ["grids", "labels", "dim_conf", "peak_dim", "volume", "cm_det", "is_curved", "curvature"]: setattr(train_ds, k, _cached["train"][k]) setattr(val_ds, k, _cached["val"][k]) print(f"Loaded {len(train_ds)} train + {len(val_ds)} val in {time.time()-t0:.1f}s") else: print(f"Cache mismatch — regenerating") DATASET_PATH.unlink() if not DATASET_PATH.exists(): print("Generating dataset...") all_samples = generate_parallel(N_SAMPLES, seed=SEED, n_workers=8) n_train = int(len(all_samples) * 0.8) train_ds = ShapeDataset(all_samples[:n_train]) val_ds = ShapeDataset(all_samples[n_train:]) print(f"Caching to {DATASET_PATH}...") cache_data = { "n_samples": N_SAMPLES, "seed": SEED, "train": {k: getattr(train_ds, k) for k in ["grids", "labels", "dim_conf", "peak_dim", "volume", "cm_det", "is_curved", "curvature"]}, "val": {k: getattr(val_ds, k) for k in ["grids", "labels", "dim_conf", "peak_dim", "volume", "cm_det", "is_curved", "curvature"]}, } torch.save(cache_data, DATASET_PATH) size_mb = DATASET_PATH.stat().st_size / 1e6 print(f"Cached: {size_mb:.0f}MB | {len(train_ds)} train + {len(val_ds)} val") train_loader = torch.utils.data.DataLoader( train_ds, batch_size=4096, shuffle=True, num_workers=4, pin_memory=True, persistent_workers=True) val_loader = torch.utils.data.DataLoader( val_ds, batch_size=4096, shuffle=False, num_workers=4, pin_memory=True, persistent_workers=True) # ============================================================================= # Train # ============================================================================= model = MLPBaseline().to(device) n_params = sum(p.numel() for p in model.parameters()) print(f"MLPBaseline: {n_params:,} params") print(f"(GeometricShapeClassifier was 1,852,870 params)") if device.type == "cuda" and hasattr(torch, 'compile'): try: model = torch.compile(model, mode="default") print("torch.compile: enabled") except Exception as e: print(f"torch.compile: skipped ({e})") epochs = 80 lr = 3e-3 optimizer = torch.optim.AdamW(model.parameters(), lr=lr, weight_decay=1e-4) warmup_epochs = 5 def lr_lambda(ep): if ep < warmup_epochs: return (ep + 1) / warmup_epochs return 0.5 * (1 + math.cos(math.pi * (ep - warmup_epochs) / (epochs - warmup_epochs))) scheduler = torch.optim.lr_scheduler.LambdaLR(optimizer, lr_lambda) w = {"cls": 1.0, "fill": 0.3, "peak": 0.3, "ovf": 0.05, "div": 0.02, "vol": 0.1, "cm": 0.1, "curved": 0.2, "ctype": 0.2, "arb_cls": 0.8, "arb_traj": 0.2, "arb_conf": 0.1, "flow": 0.5} use_scaler = use_amp and amp_dtype == torch.float16 scaler = torch.amp.GradScaler('cuda', enabled=use_scaler) print(f"\nAblation: MLPBaseline vs GeometricShapeClassifier") print(f"Same loss ({len(w)} terms), same data, same schedule") print(f"{'='*70}") best_val_acc = 0 t_start = time.time() for epoch in range(epochs): t0 = time.time() model.train() correct, total = 0, 0 correct_init, correct_ref = 0, 0 for grid, label, dc, pd, vol, cm, ic, ct in train_loader: grid = grid.to(device, non_blocking=True) label = label.to(device, non_blocking=True) dc = dc.to(device, non_blocking=True) pd = pd.to(device, non_blocking=True) vol = vol.to(device, non_blocking=True) cm = cm.to(device, non_blocking=True) ic = ic.to(device, non_blocking=True) ct = ct.to(device, non_blocking=True) grid = deform_grid(grid, p_dropout=0.05, p_add=0.05, p_shift=0.08) optimizer.zero_grad(set_to_none=True) with torch.amp.autocast('cuda', enabled=use_amp, dtype=amp_dtype): out = model(grid, labels=label) loss_first = (w["cls"] * F.cross_entropy(out["initial_logits"], label) + w["fill"] * capacity_fill_loss(out["fill_ratios"], dc) + w["peak"] * peak_loss(out["peak_logits"], pd) + w["ovf"] * overflow_reg(out["overflows"], dc) + w["div"] * cap_diversity(out["capacities"]) + w["vol"] * F.mse_loss(out["volume_pred"], torch.log1p(vol)) + w["cm"] * cm_loss(out["cm_pred"], cm) + w["curved"] * curved_bce(out["is_curved_pred"], ic) + w["ctype"] * ctype_loss(out["curv_type_logits"], ct)) loss_arb = w["arb_cls"] * F.cross_entropy(out["refined_logits"], label) traj_loss = 0 for step_i, step_logits in enumerate(out["trajectory_logits"]): step_weight = (step_i + 1) / len(out["trajectory_logits"]) traj_loss += step_weight * F.cross_entropy(step_logits, label) traj_loss /= len(out["trajectory_logits"]) loss_arb += w["arb_traj"] * traj_loss loss_arb += w["flow"] * out["flow_loss"] with torch.no_grad(): is_correct = (out["refined_logits"].argmax(1) == label).float() loss_arb += w["arb_conf"] * _safe_bce( out["refined_confidence"].squeeze(-1), is_correct) with torch.no_grad(): init_correct = (out["initial_logits"].argmax(1) == label).float() ref_correct = (out["refined_logits"].argmax(1) == label).float() blend_target = torch.where(init_correct >= ref_correct, torch.ones_like(init_correct) * 0.8, torch.ones_like(init_correct) * 0.2) loss_arb += 0.1 * _safe_bce(out["blend_weight"], blend_target) loss_blend = w["cls"] * F.cross_entropy(out["class_logits"], label) loss = loss_first + loss_arb + loss_blend scaler.scale(loss).backward() scaler.unscale_(optimizer) torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0) scaler.step(optimizer) scaler.update() correct += (out["class_logits"].argmax(1) == label).sum().item() correct_init += (out["initial_logits"].argmax(1) == label).sum().item() correct_ref += (out["refined_logits"].argmax(1) == label).sum().item() total += grid.size(0) scheduler.step() if epoch == 0 and device.type == "cuda": peak = torch.cuda.max_memory_allocated() / 1e9 print(f"VRAM peak: {peak:.2f}GB | throughput: {total/(time.time()-t0):.0f} samples/s") # Validate model.eval() vc, vt, vcc, vct = 0, 0, 0, 0 vc_init, vc_ref = 0, 0 with torch.no_grad(), torch.amp.autocast('cuda', enabled=use_amp, dtype=amp_dtype): for grid, label, dc, pd, vol, cm, ic, ct in val_loader: grid = grid.to(device, non_blocking=True) label = label.to(device, non_blocking=True) ic = ic.to(device, non_blocking=True) out = model(grid) vc += (out["class_logits"].argmax(1) == label).sum().item() vc_init += (out["initial_logits"].argmax(1) == label).sum().item() vc_ref += (out["refined_logits"].argmax(1) == label).sum().item() vt += grid.size(0) vcc += ((out["is_curved_pred"].squeeze(-1) > 0.5).float() == ic).sum().item() vct += grid.size(0) val_acc = vc / vt val_init = vc_init / vt val_ref = vc_ref / vt curved_acc = vcc / vct marker = " *" if val_acc > best_val_acc else "" if val_acc > best_val_acc: best_val_acc = val_acc dt = time.time() - t0 if (epoch + 1) % 10 == 0 or epoch == 0 or marker: print(f"Ep {epoch+1:3d}/{epochs} [{dt:.1f}s] | " f"blend {val_acc:.3f} init {val_init:.3f} arb {val_ref:.3f} | " f"curved {curved_acc:.3f}{marker}") total_time = time.time() - t_start print(f"\nDone in {total_time:.0f}s ({total_time/60:.1f}min)") # ============================================================================= # Per-Class Breakdown # ============================================================================= print(f"\n{'='*70}") print(f"Per-Class Results — MLPBaseline") print(f"{'='*70}") model.eval() cc_b = {n: 0 for n in CLASS_NAMES} cc_i = {n: 0 for n in CLASS_NAMES} cc_r = {n: 0 for n in CLASS_NAMES} ct_c = {n: 0 for n in CLASS_NAMES} with torch.no_grad(), torch.amp.autocast('cuda', enabled=use_amp, dtype=amp_dtype): for grid, label, *_ in val_loader: grid = grid.to(device, non_blocking=True) label = label.to(device, non_blocking=True) out = model(grid) pb = out["class_logits"].argmax(1) pi = out["initial_logits"].argmax(1) pr = out["refined_logits"].argmax(1) for k in range(len(label)): name = CLASS_NAMES[label[k].item()] cc_b[name] += (pb[k] == label[k]).item() cc_i[name] += (pi[k] == label[k]).item() cc_r[name] += (pr[k] == label[k]).item() ct_c[name] += 1 print(f"\n{'Class':22s} | {'Blend':>5s} {'Init':>5s} {'Arb':>5s} | " f"{'Corr':>4s}/{'Tot':>4s} | {'Type':8s} Curvature") print("-" * 85) for name in CLASS_NAMES: if ct_c[name] == 0: continue ab = cc_b[name]/ct_c[name] ai = cc_i[name]/ct_c[name] ar = cc_r[name]/ct_c[name] info = SHAPE_CATALOG[name] print(f" {name:20s} | {ab:.3f} {ai:.3f} {ar:.3f} | " f"{cc_b[name]:4d}/{ct_c[name]:4d} | " f"{'CURVED' if info['curved'] else 'rigid':8s} {info['curvature']}") # ============================================================================= # Summary Comparison # ============================================================================= print(f"\n{'='*70}") print(f"ABLATION SUMMARY") print(f"{'='*70}") print(f" MLPBaseline: {n_params:>10,} params | best val acc: {best_val_acc:.4f}") print(f" GeometricShapeClassifier: 1,852,870 params | best val acc: 0.9022") print(f" Delta: {n_params - 1852870:>+10,} params | " f"delta acc: {best_val_acc - 0.9022:+.4f}") print() if best_val_acc >= 0.89: print(" -> Loss is doing most of the work.") print(" The composite multi-task signal is sufficient to discover") print(" geometric structure without architectural inductive bias.") elif best_val_acc >= 0.80: print(" -> Architecture contributes meaningfully.") print(" The loss provides signal but the geometric inductive bias") print(" (capacity cascade, tracers, flow arbiter) adds real value.") else: print(" -> Architecture is critical.") print(" The MLP cannot recover the same behavior from loss alone.") print(" Geometric inductive bias is doing the heavy lifting.") print(f"\n Curved detection: {curved_acc:.3f}") print(f" Training time: {total_time:.0f}s ({total_time/60:.1f}min)")